MATHEMATICS AND STATISTICS AT THE UNIVERSITY OF

MATHEMATICS AND STATISTICS

AT THE UNIVERSITY OF

VERMONT: 1800–2000

Two Centuries of Achievement

April 2018

Overleaf: Lord House at 16 Colchester Avenue, main oﬃce of the Department of

Mathematics and Statistics since the 1980s.

Copyright

c

 UVM Department of Mathematics and Statistics, 2018

Contents

Preface iii

Sources iii

The Administrative Support Staﬀ iv

The Context of UVM Mathematics iv

A Digression: Who Reads an American Book? v

Chapter 1. The Early Years, 1800–1825 1

1. The Curriculum 2

2. James Dean, 1807–1814 and 1822–1825 4

3. Mathematical Instruction 21

4. Students 23

Chapter 2. The Benedictine Era, 1825–1854 25

1. George Wyllys Benedict 25

2. George Russell Huntington 27

3. Farrand Northrup Benedict 27

4. Curriculum 28

5. Students 29

6. The Library 30

7. The Williams Professorship 32

Chapter 3. A Generation of Struggle, 1854–1885 35

1. The Second Williams Professor 35

2. Curriculum 37

3. The University Environment 37

4. UVM Becomes a Land-grant Institution 38

5. Women and People of Color Come to UVM 39

6. UVM Reaches Out to Vermont High Schools 41

7. Religion at UVM 42

Chapter 4. The Beginnings of Growth, 1885–1914 45

1. Personnel 45

2. Curriculum 49

3. New Personnel 50

Chapter 5. Another Generation of Struggle, 1915–1954 53

1. New Personnel 53

2. Curriculum 57

3. The Financial Situation 58

4. The Mathematical Environment 58

5. The Kenney Award 60

i

ii CONTENTS

Chapter 6. Into the Mainstream: 1955–1975 61

1. Personnel 61

2. Research. Graduate Degrees 64

Chapter 7. Statistics Comes to UVM 69

Chapter 8. UVM in the Worldwide Community: 1975–2000 71

1. Reorganization: Lecturers 71

2. Reorganization: Research Groups, 1975–1988 72

3. The Ph. D. Program: the Rocky Road to Renewal 73

4. The Year 2000 and Beyond 76

UVM Mathematics and Statistics Faculty, 1800–2000 79

Bibliography 83

Subject Index 85

Name Index 97

Preface

As the bicentennial of the founding of UVM approached in 1990, a committee

was formed to organize a proper celebration of the occasion. This committee so-

licited proposals from the faculty for projects suitable to the celebration. At the

suggestion of my colleague Jeﬀ Dinitz, I proposed to write the history of mathe-

matics at UVM. The essays that follow constitute a revised and updated version

of the article that resulted from that proposal. Many of the people named in the

original essay have died in the quarter-century that has elapsed since the writing.

That sad fact, and the wish to correct what I now see as the wrong slant on certain

events, has prompted the present revision. The reader is warned, however, that I

have certain cantankerous political and historical opinions that I do not attempt

to disguise. (It goes without saying that no one is obliged to agree with them.)

The general organizing principle for what follows is that of a matrix whose rows are

indexed by historical periods and whose columns are indexed by the areas of rele-

vance to the mathematical history: personalities, teaching, research, students, and

the mathematical environment. Not every position in this matrix will be occupied,

but these are the general categories that will be discussed.

The reader will notice early on that I appear to wander away from the subject

matter of mathematics and statistics. That deviation from the straight and narrow

path is deliberate. I believe that the greatest interest in this story lies in the people

who were involved. The promotion of teaching and research is a human enterprise,

and I have chosen to follow a number of story lines that are tangential to the

subject whenever they involve human activities that give a ﬂavor of what it was

like to be at UVM at a given time. In any case, I think a strict, orderly recital

of what was taught and what was discovered would be deadly dull. To that end,

it will be noticeable that I give the exact date of birth for all the people referred

to, the only exceptions being personalities from ancient Greece and Rome, famous

authors, Presidents of the United States, Supreme Court justices, and United States

senators and representatives, whom I consider well-enough known from general

history books.

Sources

The following material was gleaned from a wide variety of sources. The most

important source of documentary material was the University Archives. I am partic-

ularly indebted to David Blow, the University Archivist at the time of the original

writing, for his constant and eﬃcient help and suggestions in locating the docu-

ments I needed. These documents include the personnel ﬁles on the characters

involved, the minutes of the meetings of the Board of Trustees (known originally

as the Corporation), and the University Catalogs. The Wilbur Collection at the

iii

iv Preface

Bailey–Howe Library has also been a valuable source of material. Finally, I am in-

debted to various retired colleagues for their personal reminiscences: Heath Riggs,

Ivan Hershner, N. James Schoonmaker, Joseph Izzo, and most especially George

Nicholson, whose mathematical career spanned more than one-third of the history

of mathematics at UVM up to the time when this project was begun.

Note added 24 March 2018: I am especially grateful to my fellow emeritus professor

John Lawlor for reading the semi-ﬁnal version of this document and sending me

many suggestions that have greatly improved it. For that, and for many other

things, especially hundreds of cryptic puzzles from Cox–Rathvon, and Maltby, I

am much indebted to you, Jack.

The Administrative Support Staﬀ

Because of the way records are kept, it is a nearly impossible task to report on

the activities of the essential support staﬀ, without which no oﬃce can function.

These administrators are the unsung warriors in the battle against ignorance. They

generally do not get recognized, and are forgotten by history. They were the ones

who booked travel, handled textbook requisitions, sent notices around to the faculty,

and facilitated the ceremonial and social occasions—the student awards, the fall

picnic, the end-of-semester potlucks, and much else—that helped to knit us all

together. I can only note with gratitude the invaluable help I received during my

years on the UVM faculty and mention the names of the three that I remember

best during the years from 1970 to the present. To Jackie Marlow, Janet Ferguson,

and Karen Wright, thank you! for all that you did to keep the Department of

Mathematics and Statistics running smoothly.

Having mentioned the social and ceremonial occasions, I ﬁnd this an appropri-

ate place to express the joy I have had in belonging to this wonderful organization,

as a faculty member for 35 years, and now 15 years in retirement. I remember with

particular fondness the quarter-century of playing softball with the “Eulers.” To

all my colleagues among the faculty and staﬀ, and to the students who made the

whole enterprise worthwhile, thank you!

Roger Cooke

25 March 2018

And now, to work.

The Context of UVM Mathematics

For the general history of UVM there are various secondary sources, for example

Lindsay ([3]). For that reason, the details of many issues that have come before

the trustees of the University since its founding will be neglected. Only the issues

that have led to fundamental changes in the way the University operates will be

discussed. Before we begin expounding the details of the mathematical development

of UVM, it may be well to expend a few words on the perspective within which

this mathematics is to be judged, whether local, national, or global. We might

consider UVM in the context of its educational mission in Vermont and northern

New England, or as an example of an early American university, or in the context

of world mathematics. Each of these perspectives provides a special kind of insight

into the mathematical activity that has taken place at UVM.

A DIGRESSION: WHO READS AN AMERICAN BOOK? v

Taking the local point of view, we ﬁnd some rather well-educated mathemati-

cians at UVM, even in the early nineteenth century, when large parts of Vermont

were a howling wilderness and Burlington was two long days’ journey in a horse-

drawn carriage distant from better established institutions such as Dartmouth and

Williams College. These professors were teaching mathematics in some depth to

ordinary citizens aspiring to careers as lawyers, physicians, clergy, or farmers. Some

of them even conducted original research and published it.

The national perspective reminds us that, although UVM is the twentieth oldest

university in America, there many New England colleges already in existence at the

time of its founding in 1791. These institutions provided the early UVM faculty.

Harvard, which was founded before Newton was born, had already celebrated its

sesquicentennial before UVM was even conceived. The national point of view also

brings an awareness of the expansion and democratization of education after the

Civil War, in which UVM faculty participated.

A Digression: Who Reads an American Book?

The perspective of worldwide mathematics invites comparison with European

universities founded about the same time as UVM but on the periphery of the

scholarly world whose primary centers were in Paris, G¨ottingen, Berlin, and Lon-

don, universities such as Christiania (Oslo) in Norway (founded in 1811 as Royal

Frederick University) and Kazan in Russia (founded 1804). From this perspec-

tive one can see clearly the retarding inﬂuence exerted by an ocean 3,000 miles

wide that separated American scholars from the great centers of European learn-

ing. The University of Oslo, for example, was hardly founded when it produced

one of the giants of nineteenth-century mathematics, Niels Henrik Abel (5 August

1802–6 April 1829), who died at the age of 26, but not before producing some

of the most profound work ever done on elliptic functions, theory of equations,

and analysis. Oslo went on to produce a steady stream of such ﬁgures throughout

the nineteenth century. At its formation, Kazan already had the young Nikolai

Ivanovich Lobachevskii (1 December 1792–24 February 1856), one of the creators

of hyperbolic geometry, as an upper-level student, even though conditions in Russia

were less conducive to mathematical achievement in the more remote areas such as

Kazan, and no other prominent mathematicians worked there until the twentieth

century. (Another famous graduate of Kazan University was the writer Leo Tol-

stoy (9 September 1828–20 November 1910), who attended while Lobachevskii was

rector there. Lenin (22 April 1870–21 January 1924) also spent a brief time there

before being expelled for radical activity.) Abel and Lobachevskii were geniuses,

but had they been in Vermont it is unlikely that any European now alive would

have heard of them. Abel traveled to the major centers of mathematical activity,

and the University of Kazan imported such scholars as Johann Christian Martin

Bartels (17 April 1769–20 December 1836), former teacher of the mathematical gi-

ant Carl Friedrich Gauss (30 April 1777–23 February 1855), to inspire Lobachevskii

and his classmates.

UVM, in contrast, was signiﬁcantly smaller than these European universities

and dedicated primarily to teaching. Although UVM was founded in close cooper-

ation with the government of the State of Vermont and the village of Burlington,

these governments were not seeking to win international prestige by the excellence

of their scholars. The aim was education for the professions. The early faculty,

vi Preface

graduates of such places as Harvard, Dartmouth, and Williams, tended to frame

the curriculum in accordance with their own background. Very few Americans,

and none at all from Vermont, studied at the feet of the great German and French

masters until late in the nineteenth century, and until the last few decades of the

period of this narrative no mathematicians from Europe came to UVM to impart

their knowledge. The situation in America was described with breathtaking arro-

gance and condescension in 1820 by an egregious ass known as the Rev. Sydney

Smith (3 June 1771–22 February 1845), who wrote what is surely the cheapest shot

ever to appear in the Edinburgh Review:

In the four quarters of the globe, who reads an American book?

Or goes to an American play? Or looks at an American picture or

statue? What does the world yet owe to American physicians or

surgeons? What new substances have their chemists discovered?

Or what old ones have they advanced? What new constellations

have been discovered by the telescopes of Americans? Who drinks

out of American glasses? Or eats from American plates? Or wears

American coats or gowns? Or sleeps in American blankets? Fi-

nally, under which of the old tyrannical governments of Europe is

every sixth man a slave, whom his fellow-creatures may buy and

sell and torture?

The Reverend conveniently forgot to mention that some of the support for the

American Revolution a half-century earlier had come from Americans who were

attempting to establish the very manufacturing industries whose absence he de-

plored, and that they were being forbidden to do so by his government, which was

protecting the interests of the wealthy classes that controlled Parliament. Even

more conveniently, he forgot that the abomination that was slavery had been es-

tablished in America by his own government, and that its continuation had been

one of the “tyrannical acts of the British King” listed by Thomas Jeﬀerson in the

original draft of the Declaration of Independence.

1

All that is proof that Smith was an incompetent social commentator. That he

was, in addition, an upper-class twit, is shown by his sneering at the condition of arts

and sciences in the United States. British culture, and European culture in general,

was built on a continuous tradition of art and scholarship dating back centuries to

Medieval times and before. To reproach people living in frontier conditions for not

producing works of comparable quality is simply stupid. Nationalist polemics aside,

the community of American scholars in the early nineteenth century, though small,

contained some people of international stature, whom the Reverend Smith might

have known about, had he been less myopic and better informed about science.

Among them were the following ﬁve:

• Joseph Henry (17 December 1797–13 May 1878), a physicist and professor

at Princeton after 1832, who discovered the phenomenon now known as

electromagnetic induction in 1831, almost simultaneously with the great

British scientist Michael Faraday (22 September 1791–25 August 1867).

Faraday, of course, had the advantage of communicating what he had dis-

covered to the transcendent genius James Clerk Maxwell (13 June 1831–5

November 1879), and as a result, Faraday’s law that a changing magnetic

1

Mark Twain pointed out that in 1820, England still possessed more slaves in its overseas

colonies than were in the United States.

A DIGRESSION: WHO READS AN AMERICAN BOOK? vii

ﬁeld creates an electric ﬁeld became one of the four famous Maxwell laws.

In honor of Henry’s work, the unit of electrical inductance is named the

henry.

• Benjamin Silliman (8 August 1779–24 November 1864), an American

chemist and geologist, who taught at Yale and founded the ﬁrst American

scientiﬁc journal, The American Journal of Science, in 1818. (It was com-

monly called Silliman’s Journal in the nineteenth century.) After getting

the A. B. and A. M. at Yale in 1796 and 1799 respectively, he became a

tutor at Yale and studied for the law. He then traveled to the University

of Pennsylvania in 1802 to study chemistry. When he returned to Yale in

1804, he gave the ﬁrst course of lectures in chemistry there. He traveled

to Edinburgh, Scotland in 1805 for further study and returned that year

with a new interest in geology.

• Nathaniel Bowditch (26 March 1773–16 March 1838), perhaps the greatest

audodidact America has ever produced. Although very poor and working

as an apprentice, he began to teach himself algebra in 1786 at the age of

13. Within six years, he had taught himself calculus, Latin, and French as

well, and was able to read Newton’s Principia and Laplace’s M´ecanique

c´eleste. In 1802, he produced the ﬁrst edition of Bowditch’s Practical Nav-

igator, a work that became a standard reference on all American ships.

He became a member of the American Academy of Arts and Sciences

in 1799 and was elected to the American Philosophical Society in 1809.

Over a decade or more, he labored on a translation of the ﬁrst volume

of Laplace’s masterpiece of astronomy, expanding the latter’s terse argu-

ments and producing an inﬂuential work of American scholarship. The

value of these works was recognized abroad, and Bowditch was elected to

the Edinburgh Royal Society and Royal Irish Academy. Besides astron-

omy and navigation, he was also interested in statistics and actuarial work

and refused several oﬀers of professorships at prestigious universities, since

he was making more money running his own companies.

• James Dean (26 November 1776–20 January 1849), UVM’s ﬁrst professor

of mathematics and natural philosophy. Not quite on a level with the pre-

vious three, he nevertheless wrote a number of scientiﬁc and mathematical

papers, some of which merited inclusion in the Royal Society Catalogue

of Scientiﬁc Papers for the period 1800–1863. He had some professional

contact with the three mentioned above, and can nearly hold his own as a

scholar in their company. He published papers in Silliman’s Journal and

corresponded with Joseph Henry, to whom he bequeathed his scientiﬁc

instruments.

• Robert Adrain (born in Carrickfergus, Ireland on 30 September 1775, died

in New Brunswick, NJ on 10 August 1843). Adrain became a member of

the group known as United Irishmen (a mixed Catholic–Protestant so-

ciety), which led an unsuccessful rebellion against British rule in 1798.

He then emigrated to the United States, where he became, along with

Bowditch, one of the two most eminent mathematicians in the country.

In 1808, he published an investigation of the normal (“Gaussian”) distri-

bution, one year before Gauss himself did so. (Neither of them was the

viii Preface

ﬁrst to do so, both having been anticipated by Pierre-Simon Laplace (23

March 1749–5 March 1827).)

The Math/Stat Eulers, 1989. Kneeling, left to right: Andrew

Cooke, Dan Archdeacon, Jeﬀ Dinitz, Jim Burgmeier. Stand-

ing, left to right: Larry Kost, Roger Cooke, Lloyd Simon, Jim

Fenwick, Dave Dummit, Jack Lawlor, Jonathan Sands, Dave

Morency, Sandy Karstens, Taka Ashikaga.

CHAPTER 1

The Early Years, 1800–1825

The University of Vermont was chartered in 1791 by act of the Vermont legis-

lature and given the right to collect rent from a large amount of land in Vermont.

There were apparently many diﬃculties to be overcome, and no progress was made

in acquiring a physical plant or a faculty until the citizens of Middlebury procured

a rival charter in 1800 and petitioned for the transfer of the University’s lands

to their institution. Perhaps by coincidence, that was the exact year when UVM

ﬁnally appointed a president.

1

UVM’s ﬁrst president was a Congregational minis-

ter, the Reverend Daniel Clarke Sanders, born at Sturbridge, MA on 3 May 1768,

who had graduated from Harvard in 1788. From 1794 to 1800, he was pastor of

the Congregational Church in Vergennes. He remained at UVM as president until

1814, when the University, short of funds and students, closed down and leased its

buildings to the government for use in the war against the British. During his time

as president of the University, he published a small book entitled History of the

Indian Wars with the First Settlers of the United States (Montpelier, 1812), which

contains, among other information, some material on the then-recent campaigns of

Andrew Jackson against the Creek tribe. After leaving UVM, Sanders returned to

Massachusetts (Medﬁeld), where he took the same path as the Boston Transcen-

dentalists, out of Congregationalism and into Unitarianism. He was pastor of the

Medﬁeld Unitarian Church from 1815 to 1829. During this time, he continued to

be active in promoting education and served as a delegate to the Massachusetts

Constitutional Convention of 1820. He died in Medﬁeld on 18 October 1850.

Perhaps spurred into action by the rivalry with Middlebury, Rev. Sanders began

tutoring four students in 1800, although they were not yet formally matriculated

as we would describe students today. Formal instruction began, with Sanders as

the only faculty member, in 1801. For all but one semester from 1800 to 1806,

he personally supervised the studies of all UVM students, a task that kept him

occupied eight hours a day. The minutes of the Board of Trustees’ meeting of

13 January 1801 (Vol. 1, p. 51) record that, “The president appointed to procure

a tutor reported that no suﬃciently qualiﬁed and respectable character was to be

obtained in this State at present.” Perhaps because of the year of tutoring, Sanders

ruled that these students were ready to receive their degrees in 1804.

2

1

Biographical sketches of ten of the ﬁrst eleven presidents of UVM can be found on pp. 39–

42 of the second volume of the The National Cyclopedia of American Biography (J. T. White,

Clifton, NJ, 1893), which is the source of much of the information about them contained in the

present work.

2

Union College in Schenectady, NY, which obtained an oﬃcial charter as a university from

the State of New York, in 1795, had been functioning as “the Academy” before its founding.

Despite being chartered four years later than UVM, it was able to hold its ﬁrst commencement in

1797, seven years before UVM.

1

2 1. THE EARLY YEARS, 1800–1825

1. The Curriculum

Lindsay ([3], pp. 85–88) gives the admission requirements and the curriculum

for the four-year course of study as described in the laws of the University from

that time. The admission requirements were all classical: the ability to translate

the ﬁrst six books of the Aeneid, the four orations of Cicero against Cataline,

and the four Gospels in Greek.

3

Admission to the University at this time, and

until late in the nineteenth century, was by examination. The prospective student

would appear at the University at a speciﬁed time—usually the week before UVM’s

commencement—and present himself for examination by the faculty. In keeping

with the admission requirements, the curriculum also placed a heavy emphasis on

a literary and classical education, but mathematics was not neglected. In fact, one

may well ask who today has an intimate knowledge of all the mathematics courses

in the following list, some of which have passed out of the standard curriculum or

been absorbed into more comprehensive courses:

Second year. 1st: Vulgar Arithmetick. 2d: Logarithms and Al-

gebra 3d: Geometry and Euclid’s Elements. Plane Trigonometry.

Mensuration of superﬁces and solids. Gauging. Mensuration of

heights and distances

Third year. 1st: Surveying and Levelling. Navigation. Conick

Sections. Dialling. Spherical Geometry. Projections of the Sphere.

Spherical Trigonometry and Spherical Astronomy

(“Dialling” is the theory of sundials.)

The emphasis on spherical geometry, trigonometry, and astronomy is explained

by the needs of navigation. These subjects, along with geography (another im-

portant obligatory part of the curriculum) were considered essential parts of one’s

knowledge of the world. Without them one’s appreciation of even English literature

is impoverished.

4

Lindsay ([3], p. 69) expresses some puzzlement that the calcula-

tion of eclipses was universal in all colleges of the time and considers its presence in

the curriculum “probably a hangover from the medieval curriculum.” In fact, the

calculation of eclipses has some potential application in commerce: observation of

a predicted eclipse can be used to determine terrestrial longitude approximately.

Latitude is easy to determine, at least in the northern hemisphere. One has

only to go outdoors at night and observe the elevation of the pole star. That

elevation is the latitude of the point of observation. This statement is a slight

oversimpliﬁcation, since the pole star isn’t exactly true north, but the point is that

latitude is easily determined. Any known star can be observed at its culmination

(transit of the local meridian), and the local latitude can then be worked out from

spherical trigonometry. Even if one lives at the bottom of a mine shaft, one can

work out latitude; for example, it is the arcsine of the fraction of a revolution that

a Foucault pendulum precesses in one sidereal day, and the direction of precession

distinguishes northern latitude from southern.

3

A student who could meet these requirements nowadays would be considered to have com-

pleted a good portion of a classics major!

4

Many people have found that the chief diﬃculty in coming to an appreciation of works

like Milton’s Paradise Lost is occasioned by the numerous allusions to rivers, mountains, and

mythological ﬁgures that were familiar to educated people in earlier centuries but mean nothing

to most people nowadays.

1. THE CURRICULUM 3

Longitude, on the other hand, is more diﬃcult to calculate. All observers at

a given latitude observe the same stars following the same path each day, and the

only diﬀerence between two points on the same parallel is in the time at which a

given star is at a given right ascension. The problem is to determine how many

degrees one’s own location is west or east of the intersection of its circle of latitude

with the Greenwich meridian. Direct measurement is precluded by the topography

of the earth. If one knew what time it was in Greenwich when it is noon locally,

of course, the longitude would be determined exactly. Each hour of time diﬀerence

between local mean solar time and Greenwich mean time represents a diﬀerence

of 15 degrees of longitude. For that reason, the British government had oﬀered a

prize for a clock that would keep accurate time on board a ship. Setting such a

clock to Greenwich time, one would then always be able to calculate longitude by

comparing local solar time with the clock time. Such clocks were not easy to develop

and were far from cheap and reliable. The cheap way of calculating longitude, once

astronomy was suﬃciently sophisticated to predict planetary motion with accuracy,

was to use a big clock in the sky.

For instance, the moon undergoes changes of phase. If one could chart these

phases accurately enough, it would only be necessary to look at the moon to know

what time it is in Greenwich. Unfortunately, the moon’s phases change too slowly

to permit measuring those changes over the period of a few hours. When Galileo

discovered the moons of Jupiter, he realized that their conﬁgurations, once worked

out, could be a much better “universal clock” than moon-related phenomena such

as phases or tides. They were actually used for this purpose in some surveying

work. The most easily observable clock of this type, however, is a lunar eclipse (a

solar eclipse is not visible simultaneously at widely separated places). This use of

eclipses in calculating longitude was known from very early times. A lunar eclipse

on 20 September 330 B. C. E. was observed at both Arbela (44

◦

E, the city of Erbil

in the territory of modern Iraq) and Carthage (10

◦

E, on the northern coast of

Africa), and these observations were used by Ptolemy to calculate the diﬀerence

in longitude between the two places ([4], p. 668). The accurate mapping of the

world was still a matter of pressing practical importance in the early nineteenth

century, and editors of scientiﬁc journals were eager to have accurate observations

of eclipses to compare with the predicted times. For that reason, one must disagree

with Lindsay’s assessment of this part of the curriculum.

As for the rest of the curriculum, it was not the latest in research mathematics.

The calculus, already 150 years old, was not part of the curriculum; nor were the

researches in mathematical physics due to the great eighteenth-century mathemati-

cians Leonhard Euler (15 April 1707–18 September 1783), Pierre-Simon Laplace,

Joseph-Louis (Giuseppe Lodovico) Lagrange (25 January 1736–10 April 1811), and

others, much less the torrent of creativity emanating from the French

´

Ecole Poly-

technique in the ﬁrst half of the nineteenth century. This work had hardly reached

the United States in 1804, and in particular had not reached Vermont. Laplace’s

M´ecanique c´eleste had, however, reached Boston and, as mentioned above, soon in-

spired a translation by Nathaniel Bowditch that far excelled the original in clarity

of expression.

1.1. Physical apparatus. Teaching at UVM was by lecture, since there was

very little opportunity for laboratory work. What we now call laboratory equip-

ment used for instruction was known in those days as “philosophical apparatus”

4 1. THE EARLY YEARS, 1800–1825

and described by UVM’s sixth president, John Wheeler (11 March 1798–12 April

1862), who served in that capacity from 1833 to 1849, in an address at UVM’s

semicentennial celebration in 1852 ([9], p. 2):

Of astronomical and philosophical apparatus, there was a tele-

scope, planetarium, quadrants, two sets of 24-inch Globes, and

other necessary articles of value, besides seven hundred dollars’

worth of instruments purchased of the Rev. Dr. Prince of Salem,

Mass., by individuals, and deposited for the use of the University,

in the Philosophical Chamber. The apparatus was more complete,

than in any of the Colleges in New England, except Harvard and

Yale.

Lindsay ([3], p. 106) mentions a catalog from The Rev. Dr. Prince

5

listing

objects for sale, including glass plates ground so as to make an airtight joint, a

ﬂask beam for weighing air, a pipe of mephitic air (carbon dioxide), a long glass

tube with plate and collar of leather for the Torricellian experiment [showing the

decrease of atmospheric pressure with altitude], a model water pump of brass and

glass to show the action of valves, an electric generator turned by winch, an electrical

cannon for ﬁring hydrogen gas, a battery consisting of nine jars, a microscope, and

many other objects. Lindsay reports that only one of these objects remained in the

early 1950s, a compound magnet encased in brass.

1.2. Textbooks. There does not seem to be any record of textbooks, if any,

used for the instruction at the earliest period. The library was not a rich source of

reading material. The minutes of the Board of Trustees’ meeting in January 1811

(Vol. 1, p. 154), lists the entire University library of the time. It consisted of thirty

volumes, with a heavy emphasis on literature and divinity studies. The few science

books available were all devoted to the applied parts of science, such as (Erasmus)

Darwin’s

6

Zoonomia, Priestley’s

7

Corruption, Priestley’s On Air (5 volumes), and

“Paine’s Geography.”

8

There were altogether six professors/tutors of mathematics up to 1855, and we

shall devote almost all our attention to the three most prominent of them, the ﬁrst

and the last two, saying rather little (since less is known) about the other three.

2. James Dean, 1807–1814 and 1822–1825

In 1807 Mr. James Dean was deemed “suitably qualiﬁed and respectable” to be

a tutor of mathematics and astronomy, and in 1809 he became the ﬁrst professor

5

John Prince, 22 July 1751–7 June 1836.

6

12 December 1731–18 April 1802, an English physician, grandfather of the famous Charles

Darwin.

7

Joseph Priestley, 24 March 1733–6 February 1804, a Separatist theologian and chemist, the

discoverer of oxygen.

8

Actually, John Payne (dates unknown). The British Dictionary of National Biography, Vol.

XLIV (1895), p. 111, says he went into business with a man named Joseph Johnson (15 November

1738–20 December 1809) in the publishing ﬁrm of Johnson and Payne in Paternoster Row, London.

This ﬁrm burned down in 1770, after which he began writing a large number of books. His book

A New and Complete System of Universal Geography was published by John Low, New York,

during the years 1798–1800. A copy of this book was sold at auction by Christie’s, New York, on

24 June 2009. It went for $375, even though Christie’s had evaluated it in the range of $800–$1200.

This may be the book referred to in the minutes. Or that book may be his two-volume Universal

Geography, published by Johnson in 1791.

2. JAMES DEAN, 1807–1814 AND 1822–1825 5

of mathematics and natural philosophy at UVM. No portraits of James Dean seem

to have survived, but his physical appearance and character were described in

President Wheeler’s semicentennial address ([9], p. 24):

He possessed a mathematical mind, distinguished for its clearness

and accuracy, rather than its depth and scientiﬁc insight. He de-

voted himself to the life of a student, and acquired much, and

various knowledge, rather than comprehension and profound prin-

ciples. He was rigid in his discipline, the sharp lines of which were

perhaps increased, by an occasional irritability of temper, which

seemed to spring from his very peculiar physical constitution. He

was inordinately ﬂeshy, and in such way as to give the appearance

rather of disease than of health. His inﬂuence in the University was

marked by adherence to law and order, in the simple and earnest

pursuit of its objects.

In other words, according to Wheeler, Dean was a dabbler and dilettante, one

who preferred breadth to depth. These are precisely the qualities needed in a pro-

fessor at an institution devoted solely to teaching, although Wheeler’s tone suggests

that he thought otherwise. Despite Wheeler’s patronizing characterization of him,

Dean became a scholar of some note, and his biography appears in the National

Cyclopedia of American Biography. This biographical sketch, however, is very brief,

and for the rest of what is known about Dean, including many interesting activities

unrelated to scholarship, we must turn to other sources, the most immediate one of

which is a biographical article ([2]) by George Frederick Houghton (born in Guil-

ford, VT on 31 May 1820, died in St. Albans, VT on 22 February 1870), a lawyer

who graduated from UVM in 1839 and served in the Vermont legislature during

the 1840s. He was one of the founders of the Vermont Historical Society and wrote

many articles for its journal.

2.1. Early years. James Dean was born at Windsor, VT on 26 November

1776, to Willard and Parnell Dean. His older brother Noah had been born on 30

August 1772, and his sister Abigail was born on 8 March 1785. He had at least

one other sister, Eleanor, who died in 1809, and two younger brothers, John and

Nathaniel, both of whom were born in the late 1780s and died in the early 1790s.

He received the A. B. degree from Dartmouth in 1800. He then became the ﬁrst

principal of the Montpelier Academy, which was founded on 7 November of that

year. Little is known of this institution, as Montpelier was sparsely settled at the

time, having only 839 inhabitants. In 1813, by act of the Vermont legislature, the

Academy was superseded by the Washington County Grammar School, which has

a more detailed written history. Dean received an honorary A. M. degree from the

University of Vermont in 1806. After serving for two years as a tutor in mathemat-

ics, he was appointed the University’s ﬁrst Professor of Mathematics and Natural

Philosophy in 1809.

UVM’s ﬁrst professor of mathematics was, by American standards of the time,

intellectually respectable as a researcher, as will be seen below. Was he a good

teacher? There is some evidence that he was an interesting and inspiring lecturer.

When he became professor in 1809 (actually on 24 April 1810), he delivered an

inaugural address in the manner of the German Antrittsrede, entitled An Oration

on Curiosity. This 19-page summary history of natural philosophy is based on

6 1. THE EARLY YEARS, 1800–1825

what was then popularly believed about ancient Greek philosophy, especially about

Pythagoras, and is very inaccurate in the light of later scholarship. But it served

a useful purpose in its time and was printed and published by the Samuel Mills

Press in Burlington in May 1810 at the request of the students. We may infer,

then, that they found him to be an interesting lecturer. We mention in passing

that, during this time, he lived in the Lucy Ann Abbot House, now known as

Nicholson House, at 41 South Prospect Street, which was later inhabited by two

other UVM professors of mathematics, then became the home of the Department

of Mathematics for several decades, and was eventually named after a long-serving

mathematician.

The Lucy Ann Abbot House at 41 South Prospect Street. Built

in the ﬁrst decade of the nineteenth century, it acquired its name

from the person who owned it from 1871 to 1875. It was brieﬂy

the residence of James Dean during the second decade of the

nineteenth century. In the ﬁnal decade of that century it was

for a time the residence of mathematics professor Arthur Dexter

Butterﬁeld and in the 1930s the residence of mathematics profes-

sor Myron Ellis Witham. In the twentieth century, the Depart-

ment of Mathematics and Statistics was located in it for several

decades, during which time it was renamed Nicholson House in

honor of George Hubert Nicholson, who taught at UVM from

1923 through 1973.

James Dean left UVM in 1814 along with President Sanders, when the Uni-

versity closed and rented its buildings to the American government for use in the

war against the British. In his years at UVM up to that point his salary, nomi-

nally $400 per year when he was appointed in 1809, had not been regularly paid.

The University accounts in January 1811 show that he was owed $847.15. This

was surely not a sum one could easily aﬀord to spare at the time. The University,

however, was not going to settle easily. In the discussion leading up to the closing

of the University (Minutes of the meetings of the Board of Trustees, Vol. II, p. 55,

meeting of 24 March 1814) we read:

Resolved, That the Treasurer in paying the debts due from the

Corporation to the late President and Professors, pay to them in

2. JAMES DEAN, 1807–1814 AND 1822–1825 7

proportion to their existing debts, provided Professor Dean with-

draws his suit without Cost, at the same time having respect to

what greater proportion anyone has already received. And if said

Dean does not so withdraw his suit, pay said President and Pro-

fessor Chamberlain ﬁrst. . .

Jason Chamberlain (6 May 1783–31 July 1820) had been appointed Professor

of the Learned Languages in 1811, and gave his inaugural oration—a discourse in

praise of grammar—on 1 August that year, just as James Dean had done the year

before. Like Dean’s oration, it was published by Samuel Mills Press. Before coming

to UVM, he had been pastor of the Congregational Church in Guilford, VT. On

4 February 1814, Chamberlain wrote to ex-President Thomas Jeﬀerson, sending

him a sample of the Iroquois language and noting that many Iroquois were literate.

Jeﬀerson wrote back to him in July of that year. He in turn wrote back to Jeﬀerson

on 30 November, saying

Inter arma, Musæ silent. [In wartime, the Muses do not speak.]

Our College Ediﬁce is leased to the Government, for the ac-

commodation of the Army; and our Collegiate exercises are sus-

pended. Meanwhile, I have resorted to the practice of the Law, in

order to obtain a reputable support. There are other situations,

here, which would be more congenial to my feelings, but would

not aﬀord a good living. I receive a handsome income from my

practice, and cheerfully submit to my destiny. Though anxious

to obtain general information, and to visit other countries, I shall

probably spend my days in this place.

Thus it appears that he had found a comfortable third profession and was

prepared to practice it in Burlington for the rest of his life. He probably already

knew that he was about to become a father. His daughter Eliza (8 May 1815–13

January 1895) was due to arrive in the spring of 1815. Before her arrival, however,

an event occurred on the other side of the world that was to alter those plans two

years later. In April 1815, Mount Tambora in Indonesia erupted, scattering ash

worldwide and shutting out the sunlight. There was no summer in 1816, either in

North America or in Europe. The eﬀects on Vermont were devastating, as one can

see from the population ﬁgures. Between 1790 and 1800, the population of Vermont

increased by 70,000; between 1800 and 1810, by 60,000; between 1810 and 1820, by

only 18,000; then, between 1820 and 1830, by 45,000 again. That drastic dip in the

rate of growth over the decade from 1810 to 1820 in comparison with those that

preceded and followed is a measure of what must have been major disruptions in

the lives of Vermonters. Many of them headed west, hoping, no doubt, for a better

life. (There were positive lures as well. This was the time when the Midwest was

settled, and large amounts of very fertile land became available.) Among those who

did so was the Rev. Prof. Chamberlain.

9

After leaving UVM, he moved far west,

to Jackson, MO,

10

where he practiced law, with success, but not for long. On 12

August 1820, the Arkansas Weekly Gazette reported the following:

9

See the article by Marius B. P´eladeau, ([6], footnote on p. 29).

10

Missouri and Arkansas were still territories at this time, not yet states. Missouri became

a state in 1820, Arkansas in 1836.

8 1. THE EARLY YEARS, 1800–1825

Drowned about the 31st in attempting to ford Eleven Point in

Lawrence County in this Territory, Jason Chamberlain Esq., a

very respectable attorney at law of Jackson, Missouri. Mr. C

was a native of Vermont but has resided in Missouri for the last

few years.

2.2. Interregnum (1815–1821). Dean stayed away from UVM for seven

years, during which time the duties of the presidency of UVM were carried out

by the Rev. Samuel Austin, a strict Calvinist, in contrast to his predecessor, who,

as noted, inclined to theological liberalism. Austin was born in New Haven, CT

on 7 October 1760, graduated from Yale in 1783, and served as pastor of the First

Congregational Church in Worcester, MA from 1790 until his appointment at UVM

in 1815. (The National Cyclopedia of American Biography asserts that he studied

with “Dr. Jonathan Edwards” at Yale. It is not clear who that might be. It could

not be the famous Boston-based, ﬁre-and-brimstone preacher of that name, who

died in 1758, two years before Austin was born, although he also was a graduate

of Yale, in 1720.) He was in conﬂict with the trustees at some points, and the

University’s ﬁnancial position was quite precarious at this time. He left UVM on

21 March 1821 and served afterward as pastor of a church in Glastonbury, CT,

where he died on 4 December 1830.

During the ﬁrst part of this seven-year period, instruction in mathematics and

astronomy was carried on by Ebenezer Burgess. The Historical Catalogue of Brown

University, published in 1914, lists Burgess as a tutor at that institution in the

period 1811–1813. Born in Wareham, Massachusetts on 1 April 1790, he was a

preceptor at the University Grammar School in Providence during the years 1809–

1811. He graduated from Andover Theological Seminary in 1815 and received a

D. D. from Middlebury College in 1835. He taught at UVM from 1815 to 1817.

After leaving UVM, he was an agent of the American Colonization Society for

Africa in 1817–1818. In 1821, he was ordained a Congregationalist minister and

was pastor of the First Church of Dedham, MA for ﬁfty years, from 1820 until his

death in 1870.

Burgess’s successor was the Rev. Gamaliel Smith Olds. Born in Granville, MA

on 11 February 1777, he graduated from Williams College in 1801 and was tutor

there until 1805, when he became its ﬁrst professor of mathematics and natural

philosophy. After serving at UVM in 1819 and 1820, he taught at Amherst College

for a year and then for several years at the University of Georgia before moving

to Circleville, OH, where he died on 13 June 1848. He wrote a pamphlet, now in

the Wilbur Collection of the Bailey–Howe Library, bearing the title, “Statement

of Facts Relative to the Appointment of the Author to the Oﬃce of Professor of

Chemistry in Middlebury College and the Termination of his Connexion with that

College,” published by Denio and Phelps, Greenﬁeld, MA, 1818. As Rev. Olds tells

the story, he was approached by Middlebury College in 1816 and asked to take

the position of professor of chemistry. Not feeling quite qualiﬁed, he asked for a

delay of one year in assuming the position, to which the president of Middlebury

College assented orally. Olds was to be paid while preparing himself by listening

to Benjamin Silliman’s course of lectures at Yale. When he wrote requesting his

salary, however, the president of Middlebury College responded, “that our treasury

is at present entirely empty, and is likely to remain so, I apprehend, for some time.”

2. JAMES DEAN, 1807–1814 AND 1822–1825 9

Before his year of preparatory study was expired, Middlebury changed its mind

and annulled the appointment, apparently claiming some impropriety on the part

of Rev. Olds. It was the charges against him that provoked the pamphlet.

11

The

minutes of the UVM Board of Trustees indicate that he was the fourth person to

whom the position of professor of natural philosophy was oﬀered, the ﬁrst three

chosen having declined the honor.

2.3. Tutor at Dartmouth, 1816–1819. In order to explain this phase of

Dean’s career, we need an extensive digression into the history of Dartmouth Col-

lege. The College has its origins in two schools founded in Lebanon, CT by the

Rev. Eleazar Wheelock (born in Windham, CT on 22 April 1711—that is probably

an old-style date, corresponding to 3 May on the Gregorian calendar, since Britain

did not adopt the Gregorian calendar until 1752—and died in Hanover, NH on 24

April 1779). The ﬁrst of these schools, founded in the 1730s, was termed a “Lat-

tin” school by Rev. Wheelock, and was a traditional liberal-arts institution of its

time. The second school, which was founded two decades later in the 1750s, was a

charity school for children of the aboriginal tribes in the colonies. The plan was to

bring two boys from each tribe (so that they would retain their native language)

and christianize them, turning them into missionaries to their own people. The

colonists very much wanted to convert the native tribes, partly out of religious

zeal, and partly because they hoped that, once the tribes were christianized, the

devastating wars with them would come to an end. The Seven Years’ War (1757–

1763), known in the United States as the French and Indian War, had shown how

important it was to get peace with the aboriginal inhabitants of the region.

To this cause, in 1754, a prosperous farmer in Lebanon, CT named Joshua

Moor(e) (1683–2 October 1756) donated two acres of land and two buildings that

together had a value of approximately £500. For that reason, the school was

named Moor’s Charity School. Wheelock was in contact with the Scottish Society

for Propagating Christian Knowledge, with whose help he was able to procure

ﬁnancial support in Britain, in particular from Lord Dartmouth.

12

By 1769, he had received an oﬃcial charter from George III, which, following

the usual tedious string of paragraphs beginning, “Whereas” and “Whereupon”,

contains the following declaration:

We, considering the premises [the aforementioned string of where-

ases and whereupons] and being willing to encourage the laudable

and charitable design of spreading Christian knowledge among the

savages of our American wilderness, and also that the best means of

education be established in our province of New Hampshire, for the

beneﬁt of said province, do, of our special grace, certain knowledge

and mere motion, by and with the advice of our counsel for said

11

Whatever the merits of the charges laid against Professor Olds, the ﬁnancial diﬃculties at

Middlebury in that year are easy to understand in the light of the natural disaster of the “year

without a summer” (1816, as noted above). The College had an ambitious plan to make education

free of tuition charges and had procured pledges from the local landowners to provide the funds.

But the absence of one summer led to widespread crop failure, and thence to ﬁnancial disaster for

Middlebury.

12

William Legge, 2nd Earl of Dartmouth (20 June 1731–15 July 1801). From 1772 to 1775,

he was Secretary of State for the Colonies, an oﬃce established in 1768 to deal with the unrest in

the American colonies after the passing of the Townsend Acts.

10 1. THE EARLY YEARS, 1800–1825

province, by these presents, will, ordain, grant and constitute that

there be a college erected in our said province of New Hampshire

by the name of Dartmouth College, for the education and instruc-

tion of youth of the Indian tribes in this land in reading, writing,

and all parts of learning which shall appear necessary and expe-

dient for civilizing and christianizing children of pagans, as well

as in all liberal arts and sciences, and also of English youth and

any others. And the trustees of said college may and shall be one

body corporate and politic, in deed, action, and name, and shall

be called, named, and distinguished by the name of the Trustees

of Dartmouth College.

Eleazar Wheelock was the ﬁrst president of Dartmouth College. His son John

Wheelock (28 January 1754–4 April 1817) was in the ﬁrst (1771) graduating class of

Dartmouth College and succeeded to its presidency after his father’s death in 1779.

In the meantime, of course, the American Revolution intervened, leading to eight

years of war (1775–1783). John Wheelock fought on the American side. Although

many Vermonters did also (notably Ethan Allen), Vermont was never an oﬃcially

chartered colony of the crown and thus no Vermonters signed the Declaration of

Independence.

13

Many New Hampshire residents out on the western border of the colony felt

estranged from the government in Portsmouth. Led by John Wheelock, twelve

towns on the Connecticut River declared themselves to have seceded from New

Hampshire and petitioned to be included in the Republic of Vermont. These towns,

in the end, remained part of New Hampshire. The close cooperation between

Vermont and western New Hampshire is attested by the support that the General

Assembly of the Republic of Vermont gave to Dartmouth College. At its June 1785

session the Assembly passed the following resolution:

“An Act granting twenty-three thousand acres of Land to the

Trustees of Dartmouth College, and the President of Moor’s Char-

ity School, to and for the use of the said College and School, for

ever.”

The Legislature, having a high sense of the importance of the

institution of Dartmouth College and Moor’s Charity School, to

mankind at large, and to this commonwealth in particular; its

situation and connexions being most favourable to diﬀuse useful

knowledge through the same. Be it therefore enacted, &c. that

13

In fact, Vermont did not exist yet. At the time, Vermont was known as New Connecticut,

and its territory was the subject of a dispute between New York and New Hampshire. Some

residents of the territory gathered at Westminster on 15 January 1777 and wrote their own Dec-

laration of Independence from the British crown. The name Vermont was adopted about six

months later at Windsor on 8 July 1777, when the constitution of the Republic of Vermont was

adopted. Most Vermonters held title to their land granted by Benning Wentworth, governor of

New Hampshire. The colony of New York, however, claimed what is now Vermont as its territory.

Vermonters with New Hampshire titles hired Ethan Allen and his cronies to defend their land and

run oﬀ settlers from New York. In the end, Parliament ruled in favor of New York, but by then

it was too late. Vermont had declared itself to be a republic. When the Continental Congress

refused to recognize it, the Republic petitioned the British to be made a part of Canada. In

order to settle the dispute, in 1790, New York agreed to the present border so that Vermont could

enter the Union as the fourteenth state. The Vermont General Assembly voted to pay New York

$31,000 in compensation.

2. JAMES DEAN, 1807–1814 AND 1822–1825 11

there be, and hereby is granted to the Trustees of Dartmouth Col-

lege, and the President of Moor’s Charity School, and to their

successors, twenty-three thousand acres of land within this State,

to be ascertained and chartered upon the conditions hereafter pro-

vided in this act; to be to and for the use of said College and

School, for ever.

And be it further enacted, that the surveyor-general for the

time being, be and hereby is directed (as soon as the survey of

the State is compleated, there being a suﬃciency of ungranted

lands remaining) to survey in one tract the twenty-three thousand

acres, if that quantity of ungranted land, proper for cultivation,

can be found in one parcel; or otherwise survey the like quantity

in diﬀerent parcels, under the direction, and to the approbation,

of the President of the said institution.

And be it further enacted, that the Governor and Council of

this State for the time being, be and hereby are requested to issue

a charter of incorporation for the same, when so surveyed, to the

Trustees of Dartmouth College, and the President of Moor’s Char-

ity School, and to their successors, to be to and for the use and

beneﬁt of the said College and School, forever.

The Surveyor General mentioned would have been James Whitelaw, born on 11

February 1748 in Old Monkland, Scotland, died in Ryegate, VT on 29 April 1829.

The oﬃce of Surveyor General was not regularized at the time, although it was

recognized as such. In 1797, it was formalized as an oﬃce to which a candidate was

elected at a joint meeting of the Governor, the Council, and the General Assembly.

We note that 23,040 acres amounts to 36 square miles, exactly the size of a

township, which normally consists of 36 square sections, each one mile on a side.

A section equals 640 acres. Family farms in America have typically consisted of

a quarter-section of land, or 160 acres. On 14 June 1785, the Governor issued a

charter for a tract of land six miles square. That tract became Wheelock Township.

It still exists under that name in the northwest corner of Caledonia County and

had a population of 621 in the 2000 census. It is actually about 10% larger than

the standard 36-square-mile township, occupying, as it does, 39.8 square miles. By

oﬀering homesteads rent-free for a number of years, Dartmouth was able to attract

settlers to Wheelock, and within a decade was getting about $1000 per year in rents

from this land. In the end, though, this agreement was better for Vermont than

for Dartmouth. Under an old contract, any full-time resident of Wheelock who is

accepted at Dartmouth is able to attend tuition-free.

By 1807, however, Vermont had its own university, which had managed to

graduate three classes of students; and meanwhile, it turned out that Dartmouth

was no longer educating native missionaries. As a result, Chapter CXVIII of the

1807 Legislative Acts of Vermont reads as follows:

“An Act, directing a suit, for the purpose of ascertaining the va-

lidity of the charter of Wheelock”

§1. It is hereby enacted by the General Assembly of the State of

Vermont, That Daniel Buck and Titus Hutchinson, Esqrs. be, and

they hereby are authorized and directed, at the expense and on the

behalf of this State, to institute a suit, before the Supreme Court,

12 1. THE EARLY YEARS, 1800–1825

pursuant to the mode pointed out in the act, entitled, “An act

directing the mode of taking forfeitures of grants, and charters”—

for the purpose of inquiring into the validity of that part of the

grant and charter of the township of Wheelock, therein given and

granted to John Wheelock, Esquire, President of Moor’s Charity

School.

§2. And it is hereby further enacted, That the 7th of the act

aforesaid, entitled, “An act directing the mode of taking forfeitures

of grants and charters,” be, and the same is hereby repealed, so

far, and so far only, that the same shall not in any way, aﬀect the

suit by this act directed to be brought.

Passed Nov. 10, 1807

Titus Hutchinson, who was born at Grafton, MA on 29 April 1771 and died in

Woodstock VT on 24 August 1856, was a member of the General Assembly at this

time. He served on the Vermont Supreme Court from 1825 to 1833, as Chief Judge

the last two years. He later became a trustee of the University.

Daniel Buck, who was born at Hebron, CT on 9 November 1753 and died in

Chelsea, VT on 16 August 1816, served as a Federalist representative in Congress

from 1795 to 1797 and, as indicated here, later in the General Assembly.

Although it does not appear that the charter was revoked at that time, Dart-

mouth began to experience “growing pains,” when it acquired an endowed chair of

theology, a bequest from trustee John Phillips, LL. D. (17 December 1719–21 April

1795) in 1789.

14

As the College expanded, rivalries arose over the distribution of

resources and over a philosophy of education. A pamphlet published in 1816 and

bearing the title Sketches of the History of Dartmouth College and Moor’s Char-

ity School, with a Particular Account of Some Late Remarkable Proceedings of the

Board of Trustees from the Year 1771 to the Year 1815 gives details of the evolution

of the dispute. Without going into those details, we shall summarize a few aspects

of the case.

In addition to the ﬁnancial and philosophical disagreements, the case reﬂected

two diﬀerent political currents of the time, with the old Federalists (John Adams’s

party), represented by the majority of the Board of Trustees, contesting control

with the Democratic-Republicans (Thomas Jeﬀerson’s party). The Democratic-

Republican minority wanted the State of New Hampshire to take over the College

on the grounds that the original charter came from George III, of whom the state

government was the legal successor. On 27 June 1816, the legislature (1) renamed

the corporation, which had been the Trustees of Dartmouth College; it was thence-

forth to be the Trustees of Dartmouth University; (2) enlarged the membership in

the Board from 13 to 21; (3) appointed a 25-man Board of Overseers; (4) put the

ultimate power to decide the future of the institution in the hands of the Board of

Overseers.

This was exactly what the minority among the trustees had wanted. The trea-

surer William H. Woodward (born in Virginia 17 September 1774, died in Hanover,

NH, 8 August 1818), whom the majority had believed to be on its side, joined the

14

Phillips had previously made gifts to Dartmouth, and one of the conditions of this gift

was that his previous donations be earmarked for the use of the chair of theology; to his previous

bequests he added 400 acres of land, which had at the time a value of £37, 10d, the pound sterling

being still in use.

2. JAMES DEAN, 1807–1814 AND 1822–1825 13

minority, which thereby became the majority, and was appointed Secretary of the

Board of Trustees of Dartmouth University. The former Federalist majority of the

trustees refused to accept this takeover, and demanded that Woodward turn over

the books, seal, deeds, and other appurtenances of the corporation to them. He

refused. They sued. The state superior court found for Woodward. The trustees

appealed to the Supreme Court, of which the illustrious John Marshall was then

Chief Justice. The case became famous as Trustees of Dartmouth College v. Wood-

ward. The case for the trustees was argued successfully by none other than Daniel

Webster, Dartmouth class of 1801 (and hence a contemporary at Dartmouth with

James Dean).

2.4. Return to UVM, 1822–1824, and a year at Union College, 1825–

1826. Marshall’s decision for the plaintiﬀs became a landmark in corporate law.

Dartmouth remained a private institution. But one of the casualties of the decision

was the position that James Dean had as tutor, since he had been hired by the

Trustees of Dartmouth University, not the Trustees of Dartmouth College. He left

oﬀ teaching for a while and ultimately came back to UVM from 1822 through 1824,

where UVM’s third president, replacing Rev. Austin, was the Rev. Daniel Haskel.

Haskel was born in Preston, CT in July 1784 and graduated from Yale in 1802. His

degree, unlike his predecessor’s, was A. M., not D. D. He was pastor of the First

Calvinist Congregational Society of Burlington before becoming president of UVM.

Haskel was a man of broad humanistic learning, well versed in geography and his-

tory, as he demonstrated in the quarter-century after he left UVM. Unfortunately,

in addition to UVM’s ﬁnancial woes, with which he struggled heroically, there was

a disastrous ﬁre in May 1824, which destroyed the College Ediﬁce, the University’s

only building, causing the loss of the library and laboratories as well, and driving

President Haskel to a nervous breakdown. He spent the rest of his life in quiet

academic pursuits.

Together with the geographer John Calvin Smith (born about 1809, died 11

June 1890), he was the author of a 732-page compendium entitled A Complete

Descriptive and Statistical Gazetteer of the United States of America (Sherman and

Smith, New York, 1848). In that same year (the year of his death, on 9 August), he

published A Chronological History of the World (J. H. Colton, New York). Earlier

(1833), he had published Lessons in Astronomy (publisher and place unknown).

After the ﬁre, the duties of president were brieﬂy assumed by James Dean.

Unfortunately, a disagreement arose between Dean and the trustees that year over

the fate of three students whom Dean believed unworthy of a degree. The trustees

sided with the students, and Dean left to take up a position at Union College in

Schenectady, NY, from which he received an honorary Doctor of Divinity degree in

1847.

15

I have not been able to ascertain what Dean did during his year at Union

College—there is a hiatus in the records at just that year—but it is certain that he

returned to Burlington at the end of it.

At this point, we pause in the story of mathematics at UVM, leaving it without

a president or a professor of mathematics, to ﬁnish our biography of the interesting

character James Dean, after which we will resume our account of the two decades

from 1805 to 1825.

15

UVM awarded him the degree of Doctor of Law that same year.

14 1. THE EARLY YEARS, 1800–1825

2.5. Entrepreneurial activity: The Champlain Glass Company. What

Dean was doing between 1826 and his death in 1849 was long buried in obscure

documents. Only recently has one scholar unearthed his activity for the ten-year

period from 1827 to 1837. I am indebted to L. Diana Carlisle, the author of an

article ([1]) that ﬁlls in the details of Dean’s participation in this enterprise. Re-

turning to Burlington in 1827, Dean formed a partnership with two men named

John Peck (1 May 1785–24 July 1864) and John S. Foster (22 July 1773–6 Janu-

ary 1834) and founded The Champlain Glass Company, incorporated by act of the

General Assembly of Vermont on 27 October 1827. Under three diﬀerent names

this company produced high-quality window panes and other glassware in Burling-

ton from 1828 until 1840. Dean must have become prosperous from this enterprise,

although the company overextended itself in 1831 by buying shares in the Redwood

Glass Company near Plattsburgh, New York. It was induced to do so by a member

of its Board, one Charles W. Corning,

16

who proposed that the company borrow

$2400 from each of James Dean and John Peck for this venture. Obviously, if they

were in a position to lend so much money, the two must have made a considerable

fortune from the company. This hypothesis is conﬁrmed in the case of Peck by the

large house he inhabited and the fact that he owned the land along South Willard

Street starting at Maple Street. (It was ﬁeld and forest at the time, however.) John

Foster left the enterprise at that time and moved across Lake Champlain to join

another glass-manufacturing ﬁrm, from which he was dismissed in 1833. He tried

to start yet another such ﬁrm, but died suddenly the following year.

Dean and Peck eventually had to sue to recover their money, and the company

(or rather, its successor) was declared forfeit, so that they owned the company free

and clear of all debt. Not until 1839 did Dean manage to liquidate his share of it.

By that time, he was well past 60 and apparently able to retire with an independent

income.

2.6. A missed opportunity: The American exploring expedition. An

adventure that came near to Dean but passed him by is nevertheless worthy of our

attention for the light it shows on American society then and now. This glimpse

into Dean’s life in the year 1828 and again in 1836 is provided by the 1975 book

([8]) by William Ragan Stanton. The portion of the story that leads up to Dean’s

near-connection with this expedition begins and ends in a way that is typically

American. It begins with a theory that only the most radical UFOlogists could

believe after the two poles had been reached by expeditions: That the earth is

hollow, there being an empty core drilled out of it, so to speak, from one pole to

the other. (The aforementioned fringe UFOlogists believed that “ﬂying saucers”

are built by creatures living inside and emerge through these holes.) This bizarre

theory, which had nothing scientiﬁc to recommend it, even in the beginning, was the

brainchild of one John Cleves Symmes, Jr. (5 November 1780–19 June 1829), who

believed it mostly on theological grounds. Symmes even built models of his hollow

earth. Despite the unpromising nature of this hypothesis, it could not be deﬁnitively

refuted without sending an expedition to one of the poles, and that fact led Jeremiah

N. Reynolds (1799–25 August 1858), a newspaper editor in Wilmington, OH in

1824, to attempt to organize such an expedition.

16

It is coincidental that he had the name of another famous glass company. That company

is named for the city of Corning, NY, with which this Corning has no known connection. Indeed,

I have not been able to unearth any further information on him.

2. JAMES DEAN, 1807–1814 AND 1822–1825 15

The idea was attractive even to intellectuals who rejected the hypothesis, since

it oﬀered a chance to go exploring, always an exciting prospect to those with a

scientiﬁc curiosity. The expedition was getting well organized in 1828, with support

from the Secretary of the Navy, and nearly succeeded. For a scientiﬁc expedition,

real scientists would have to be taken aboard ships of the United States Navy,

and they would do the essential work to complete the mission. In particular, an

astronomer was needed, and apparently James Dean, professor and entrepreneur

at the time, aged 52, was eager to join up. The project fell through, however, also

in a typically American way. The year 1828 was an election year, in which the

incumbent President John Quincy Adams was to be turned out of oﬃce by the

western hero Andrew Jackson.

For reasons that I cannot fathom,

17

historians have admired the latter, calling

him a “masterful” President who helped to bring democracy down to the common

people. In my view this Jacksonian democracy, more thoroughgoing than the Jef-

fersonian version, of which I am an adherent, has had pernicious eﬀects throughout

American history. It has led to the belief that ignorant people can decide scien-

tiﬁc issues just as well as scientists. The result is the present backwardness of

Americans, led by politicians and media commentators with no understanding of

the relevant science who blithely declare themselves the equal of the Academy of

Sciences in deciding, for example, the question of anthropogenic climate change.

The consequences, not only to America, but to the entire world, are liable to be

catastrophic.

In the context of James Dean’s career, this arrogance of the “common people”

was forcefully expressed by South Carolina Senator Robert Young Hayne, who was

chair of the Committee on Naval Aﬀairs in 1828. Hayne declared that the scientists

who were to be aboard the ships ought to be “mere agents and instruments of the

oﬃcers,” but if the expedition was mounted, those odious scientists would reap “the

glory of the enterprise, if any glory was to be acquired in it” ([8], p. 24). Thus,

he played the role of the champion of the people against the elitist intellectuals for

whom he had no use whatever. The expedition was scuttled.

Under Jackson’s successor, Martin Van Buren, the expedition was reorganized,

and this time it would actually be launched, but without Vermont’s native son

James Dean. According to Stanton ([8], p. 48),

Professor James Dean of the University of Vermont, who had

been eager to join the expedition of eight years earlier, was now

over sixty and felt himself too old to embark on so arduous a

journey.

2.7. Dean’s best-remembered legacy. On 5 April 1832, Daniel Webster,

who was a senator from Massachusetts at the time, read into the Senate record

a “Report on the Subject of Apportionment of Representation, in the House of

17

By all accounts, Jackson was an ignorant, arrogant man whose crimes against humanity

would nowadays rank him with the great moral monsters of all time. I don’t mean merely that

he kept slaves. Many people, trapped in their time, did that. But, to take just one example, he

dispossessed the Cherokee tribe of its lands in Georgia, even though the Supreme Court of the

United States had declared in Worcester v. Georgia that they held sovereignty over these lands.

The resulting Trail of Tears as the Cherokees and four other tribes were relocated west of the

Mississippi River, led to the cruel deaths from starvation and exposure of thousands of innocent

people. I do not believe that any positive verdict can be rendered on this man’s life.

16 1. THE EARLY YEARS, 1800–1825

Representatives of the United States.” In his report, Webster included an appendix

under the title “Extract of a Letter from Professor James Dean”:

I cannot express my rule so densely and perspicuously as I would

wish; but the meaning is, that each State shall have such a number

of Representatives, that the population for each shall be the nearest

possible, whether over or under, to [ ]. The number for each state

may be ascertained thus: Divide the representative number by the

number assumed to ﬁll the blank, disregarding the remainder; the

quotient, or the next greater number, will be the number of Rep-

resentatives. In order to determine which is the proper one, divide

the representative number of the State by the two numbers sepa-

rately, then subtract the least quotient from the assumed number,

and the assumed number from the other quotient; and that from

which results the least remainder is the number of Representatives

for the State.

This letter is not among those published in the multi-volume edition of Web-

ster’s correspondence. That could mean two things: (1) Webster did not keep the

letter after inserting its contents into the Senate record, or that the letter was sub-

sequently lost; (2) the letter was actually sent to someone else, who showed it to

Webster. In either case, the assertion sometimes made that Dean wrote to Webster

on this issue cannot be conﬁrmed, although it is plausible that he did so.

Dean truly did not express his rule as “perspicuously” as he might have. When

he says, “Divide the representative number” he should have said “Divide the pop-

ulation of the state by the number chosen to go between the brackets.” The latter

number is to be the number of constituents (including children) that each repre-

sentative is to represent. In his day, this number was ﬂexible, since the size of

the House was not ﬁxed. It had begun as the number 30,000, which in our day

would require a House consisting of more than 10,000 representatives. It was early

on realized that the House could rapidly become unwieldy this way, and after each

census, it became a contentious political problem to decide on the size of the House.

The problem became particularly acute after the censuses of 1870 and 1880,

where a seeming paradox appeared: A state might have fewer representatives in

a larger house than it would get in a smaller one. The particular case that is

best remembered is that of Alabama. After the 1880 census, it was determined

that in a House of 299 representatives, Alabama would have 8, but if the number

was increased to 300, then Alabama would get only 7, given the procedures then

in eﬀect. In our day, when the size of the House is permanently ﬁxed at 435,

the number that goes into the brackets in Dean’s proposal would be (as of 2015)

308745538/435, that is, approximately 709,760 constituents (including children)

per representative. (The numerator in this fraction is the oﬃcial population of

the country according to the census of 2010.) For California, for example, whose

population was given in the 2010 census as 37,253,956, Dean’s instruction leads to

a quotient of 37253956 × 435/308745538, which is 52.4881. Thus, the number of

representatives due California should be either 52 or 53.

Dean’s instruction is to divide the population of California by these two num-

bers, getting quotients of 716,422 and 702,904. Then, since 716422 – 709760 =

6662 and 709760 – 702904 = 6856, the quotient upon division by 52 is closer, and

California would get 52 representatives. (In the system actually used, it got 53.)

2. JAMES DEAN, 1807–1814 AND 1822–1825 17

2.8. Political activity. Nothing is known about Dean’s political leanings up

to the age of 60, which he attained in 1836. From that time on until a few months

before his death in 1849, he is regularly mentioned in Vermont newspapers as

a political activist. Andrew Jackson’s autocratic style and policies soon led to

dissension in his party, and the result was the formation of a new political party in

America, which adopted the name of the British liberal party and called itself the

Whig Party. It leaned toward the liberal side, but advocated written constitutions,

strictly adhered to, and protection of minorities against the tyranny of the majority.

The party arose in the middle of Jackson’s second term in oﬃce, around 1834, under

the leadership of Senator Henry Clay of Kentucky, who together with Senators

Daniel Webster of Massachusetts and John Caldwell Calhoun of South Carolina

managed to reconcile the conﬂicting interests of their very diﬀerent regions of the

country through diplomatic compromises that held the Union together until 1860.

The Whigs took a ﬁrm stand against Jackson’s Indian Removal policies, and

generally opposed the extension of slavery into new territories. Their main quarrel

with the Jacksonians was over protective tariﬀs, which the Whigs wanted and the

Democrats didn’t, and over the existence of a national bank, which the Whigs

favored, and which Jackson was determined to destroy. (He succeeded, and a severe

depression ensued after he left oﬃce.) They managed to get two of their number

elected President, namely William Henry Harrison in 1840 and Zachary Taylor in

1848, both of whom were war heroes and both of whom died in oﬃce, Harrison

having served only one month and Taylor ﬁfteen months. Their successors John

Tyler and Millard Fillmore bring the number of Whig Presidents to four. There

might have been ﬁve, but for a split in the Whig Party that caused Henry Clay to

lose the 1844 election to James K. Polk by a very narrow margin.

The Burlington Free Press

18

was a Whig newspaper from the outset, and

in 1836 it helped to organize public opinion in Vermont against Jackson’s heir-

apparent, the Democratic Party candidate Martin Van Buren. It proudly pro-

claimed itself the supporter of William Henry Harrison for the presidency. Dean

was a Whig and attended the organizing convention that year. In preparation for

it, a few local organizers met in Burlington on 24 February 1836. The following

resolution calling for organization of this party was printed in the Burlington Free

Press on 4 March 1836:

Resolved, that all freemen of this state present or who may be

present at the convention who disapprove of the oﬃce holder’s

nomination at Baltimore for the Presidency, and of the nominee,

pledged to follow in the footsteps of the present incumbent, be

invited to take part in this convention and to participate in its

deliberations.

The Free Press goes on to say that a committee had been appointed to prepare

the business of the statewide Whig convention, which was to be held in June of

that year, and that James Dean was a member of this committee. On 24 June, the

Free Press noted that “Mr. Dean” had been elected to draft the party’s platform,

and that

18

Properly, the Burlington Weekly Free Press, but for simplicity we shall always use this

name, which is the name of its modern successor.

18 1. THE EARLY YEARS, 1800–1825

On motion of Mr. James Dean: Resolved, that the [Chittenden]

county committee be requested to correspond with the commit-

tees of Franklin, Grand Isle, and Orleans Counties and make ar-

rangements for holding a District Convention for the purpose of

nominating a suitable candidate to represent this District in Con-

gress.

At that time, Vermont had four congressional districts, of which the four above-

named counties formed District Three. Dean himself stood for election in this

district in 1844, albeit as a member of the Liberty Party (see below) rather than

as a Whig. As is well-known, Van Buren won the election of 1836, but rapidly lost

popularity due to the depression, which was blamed on Jackson’s attack on the

national bank. In 1840, Harrison was again the Whig candidate, and was elected.

The editors of the Free Press were jubilant, proclaiming on 6 November that OK

19

stood for Orful Konﬂagration.

As already mentioned, however, Harrison died only one month into his term and

was succeeded by John Tyler. As often happens with reform parties, success leads

to the need to govern, and that in turn leads to compromises with the opposition

that displease the party faithful. By 1844, two groups had split oﬀ from the Whig

Party. The ﬁrst was the Liberty Party, which was more radical on the subject of

slavery than the Whig Party. The other was the Locofocos, named after a cigar

that, like a railroad ﬂare, could be used to light itself. (The Italian word for ﬁre

is fuoco.) The latter was a working-class party, which took its name from the use

of the abovementioned self-lighting cigars to light its meeting hall in New York

after the Democratic Tammany machine politicians had turned oﬀ the gas lighting.

As already mentioned, Dean was the Liberty Party candidate for Congress from

Vermont’s Third District that year; he was not elected, nor were any other Liberty

Party candidates. Still, the party’s role as a spoiler, which third parties often are,

has some credibility. The party won about 16,000 votes in New York. Had Clay

won 11,000 of them, he would have become President.

By 1848, the Liberty Party and the Locofocos had combined with disgruntled

Whigs to form the Free Soil Party. Martin Van Buren moved far enough left to

gain that party’s nomination, but not nearly far enough to satisfy the abolitionists

among them and those who had opposed the annexation of Texas and the Mexican

War under President Polk. Knowing that an abolitionist candidate was a guar-

anteed loser, Van Buren had pledged that he would do nothing to end slavery in

Washington, DC.

The Free Press had remained loyally Whig and wrote about the Free Soil Party

with lofty condescension on 25 August 1848:

THE FREE SOIL CONVENTION TODAY

A formidable array of Locofocos and Liberty men with a slight

sprinkling of dismayed Whigs, made up the Free Soil Convention,

which assembled in Burlington Wednesday morning. It was our

19

The now-universal expression OK seems to have originated in America. The Democrats

made use of it in 1836 by forming Democratic OK Clubs to support Van Buren, who, being a

native of Kinderhook, New York, was aﬀectionately called Old Kinderhook. On some theories,

that is in fact the origin of the phrase OK, but it is possible that the Democrats chose that name

because the expression was already current.

2. JAMES DEAN, 1807–1814 AND 1822–1825 19

happiness to attend the morning session and to witness an amus-

ing example of “much ado about nothing”’ A man from Hinesburg,

who was a Locofoco, proposed that a committee of nine, to consist

of three Liberty men, three Locofocos, and three Whigs, nominate

delegates to the convention. . . Prof. Dean of Burlington (Liberty)

was not satisﬁed with this summary method of disposing of an

important motion. He said he had carefully read the Buﬀalo plat-

form, and was not at all satisﬁed with it. That platform (in tender

consideration of the views of Martin Van Buren, doubtless) com-

prehended opposition to the extension of Slavery, but did not come

up to the mark of hostility to its continuance. Prof. Dean was op-

posed not only to the extension, but to the existence of Slavery

in this boasted Republic. The Buﬀalo platform might be broad

enough for some, but did not come up to his standard! (This was

the wettest and coldest blanket that had been thrown upon the rye-

and-indian Convention, and Prof. Dean’s character and reputation

contributed not a little to the damp and the cold!)

The Free Press cited Dean again a week after this meeting, on 1 September:

The Buﬀalo Platform, as intimated by Professor Dean to the late

Van Buren Convention in this village, is just big enough for New

York Barnburners and no bigger! It says not a word about Slav-

ery in the District of Columbia and declares for a “Revenue Tar-

iﬀ”. . . The Locofocos who drew it up and who passed it are the

very men who voted for Polk and Dallas and the Mexican War,

and thereby involved the country in the enormous “national debt”

spoken of. . .

The “Dallas” referred to here is George Miﬄin Dallas (10 July 1792–31 Decem-

ber 1864), former mayor of Philadelphia and vice-president in the Polk administra-

tion from 1845 to 1849. It is possible, though not certain, that the city of Dallas,

TX was named after him.

The United States national debt was retired exactly once in its history, in 1835,

during the presidency of Andrew Jackson. As the Free Press says, the Mexican War

unbalanced the budget again. The Whigs managed to get their candidate, Zachary

Taylor, into the White House in 1848, but the country was becoming ungovernable,

wracked by the dispute over slavery. The Free Soil Party was soon to become the

Republican Party, which got its candidate, Abraham Lincoln, into oﬃce in 1860.

What followed is well-known history.

2.9. Death and legacy. On that inspiring note, Dean’s recorded career comes

to an end. His life came to an end less than ﬁve months later, in Burlington. He

died on 20 January 1849, and is buried in the Elmwood Cemetery in Burlington.

The inscription on his tombstone has been eﬀaced by time, and we are indebted to

George Frederick Houghton ([2]) for preserving it:

JAMES DEAN, LL. D., A. A. S.

Born at Windsor, Vt. November 26, 1776

Died at Burlington, Vt. January 20, 1849

A Friend of Peace,

20 1. THE EARLY YEARS, 1800–1825

Temperance, Knowledge and Freedom

“Nihil humani alienum”

The Latin phrase means “Nothing having to do with man is alien.” It is a

shortening of the phrase due to the Stoic playwright Terence (Terentius), who lived

in the second century B. C. E.: Homo sum, nihil humani a me alienum puto. (I am

a man, and there is no aspect of humanity that I regard as alien to myself.)

In his will (Case 1394, Box 13 in the ﬁles of the Chittenden County Courthouse),

Dean left his sister Abigail as ﬁrst legatee her choice of $100 worth of books from his

personal library. Abigail died on 5 August 1858. His second legatee was his friend

and 1800 classmate at Dartmouth, Caleb Butler of Groton, MA (13 September

1776–7 October 1854, he was the principal instructor at Groton Academy for many

years), who was to have his choice of $100 in books after Abigail chose the ones she

wanted. His third legatee was the physicist Joseph Henry of Princeton, with whom

he had corresponded about the aurora borealis; Prof. Henry received a piezometer,

a forcing pump, and a compressing vessel. Dean also left bequests of $100 in cash

to each of the American Academy of Arts and Sciences and the Massachusetts

Historical Society. The remainder of his estate was to be divided as follows: one-

half to Abigail, one-sixth to his brother Noah (who died on 2 April 1856), and

one-third to be divided among Noah’s children.

2.10. Scholarly works. The modest scholarly reputation that Dean attained

was based on six articles by him listed in the Royal Society Catalogue of Scientiﬁc

Papers (Vol. 2, p. 185). Four of these were published in 1815 in the Memoirs of

the American Academy of Arts and Letters, Vol. 3, Pt. 2. One of the latter is a

detailed report of an observation of the solar eclipse of 17 September 1811. Dean

gives precise statements of the local solar time for the beginning and end of the

eclipse as observed by himself and his companion. (See the remarks above on the

signiﬁcance of eclipses for geography.) The other three articles published in 1815

are connected with geometric astronomy. One is a description of a “cometarium.”

Another is “A method of displaying at one view all the annual cycles of the equation

of time in a complete revolution of the Sun’s apogee.” The misnamed “equation

of time” is the amount by which mean solar time—on which clocks are based—

diﬀers from true solar time. The word equation refers to the process of equalizing

(reconciling) true solar time with mean solar time. It is a periodic function of time,

and Dean’s article provided a small elliptical piece of paper riveted to a chart. By

turning the ellipse, one could determine the amount by which true solar time is

ahead of or behind mean solar time at any given moment.

The most important of the four articles was a tour de force of spherical trigonom-

etry, “An investigation of the apparent motion of the earth viewed from the Moon

arising from the Moon’s librations.” The last word here is the key to this paper.

It is a commonplace that the moon always turns the same face to the earth, but

this commonplace is not strictly true. The moon rotates on its axis at a uniform

rate, but its orbit about the earth is slightly elliptical. As a result, terrestrial as-

tronomers get an occasional peek around the edge of the moon into its hidden side.

This is one kind of libration. The other kind occurs because the moon’s axis of

rotation is not perpendicular to the plane of its orbit around the earth, so that

its northern and southern poles come alternately into view for an observer on the

earth. Looking at these two kinds of libration from the perspective of the moon,

3. MATHEMATICAL INSTRUCTION 21

one ﬁnds that the earth does not remain in a ﬁxed location in the sky, as would

be the case if the commonly held view were accurate. Instead the earth describes

a small but complicated closed curve in the sky over a long period of time. Dean

gave a careful analysis of this curve and showed that it is the curve described by

a pendulum bob at the bottom of a Y-shaped string, in which the vertical stroke

of the Y is 40 times the distance from the fork in the Y to the line through its

two tips. This article so intrigued the astronomer Bowditch that he was inspired to

perform a detailed mathematical analysis of such a pendulum. Bowditch’s article

was published in the same issue of the Memoirs of the American Academy in which

Dean’s four articles appeared.

20

Besides the papers just discussed, Dean also published an observation of several

meteors in Silliman’s American Journal of Science in 1823, and an article “On the

diameter of screws,” in the Boston Journal of Philosophy in 1826, which he rewrote

and expanded in the Journal of the Franklin Institute in 1845, when he was nearing

70 years of age. This paper is an analysis of the properties of a helix, combined with

some frictional considerations, and therefore applies more properly to bolts than

to screws. The problem is to ﬁnd the diameter that enables the ratio of power (he

seems to mean torque) to weight to be minimized. Besides these research papers,

he was the author of a gazetteer of Vermont published in Montpelier in 1808, a

copy of which can be found in the Wilbur Collection of the Bailey–Howe Library.

Among the papers in his ﬁle in the University archives is the letter mentioned

above (written 27 November 1833) to the physicist Joseph Henry, reporting some

meteor observations, and speculating on ways by which it could be proved that

the aurora borealis is electrical in nature. At the time, Henry had only recently

discovered the phenomenon we now call electromagnetic induction—naturally, his

understanding of this phenomenon was very incomplete—and had just been named

a professor at Princeton on the basis of his brilliant work.

Dean’s most enduring contribution to American civilization, however, has been

immortalized as “Dean’s Method” of apportioning the House of Representatives,

which was discussed above. Dean’s Method is explained in detail in the book Fair

Representation by M. L. Balinski and Y. Peyton Young (Yale University Press,

1982).

3. Mathematical Instruction

At the time of James Dean’s return to the University we ﬁnd the ﬁrst university

catalog, dated October 1823, from which we can form a picture of the course of study

followed by the students and taught by the faculty. There were only two professors

in the Classical College, ﬁve in the Medical College. Prof. Dean’s companion in the

Classical College was Lucas Hubbell,

21

A. M., Professor of the Learned Languages.

These two, and perhaps the president (Haskel) taught all 53 of the classical stu-

dents. At the time, UVM adhered to a three-term school year, the autumnal term

extending from September until December, the spring term from March through

mid-May, and the summer term from mid-May through mid-August. The fact that

there was no winter term and the University was closed down during the months

20

The late professor of physics at UVM Albert D. Crowell (12 February 1925–21 September

1985) once gave a detailed discussion of this paper of Dean’s (see The Burlington Free Press, 11

March 1971).

21

Born 30 October 1787 in Lanesboro, MA, died 4 November 1847 in Phelps, NY.

22 1. THE EARLY YEARS, 1800–1825

of January and February needs no explanation, given the harshness of the Vermont

winter.

The mathematical portion of the curriculum was based on a famous series of

textbooks by the British mathematician Charles Hutton (14 August 1737–27 Jan-

uary 1823), a professor at the Royal Military Academy at Woolwich. Hutton’s

Arithmetick occupied the second semester of the Freshman year, Hutton’s Algebra

the ﬁrst term of the sophomore year, and Hutton’s Geometry, Hutton’s Trigonom-

etry, and Hutton’s Conick Sections the third term of the sophomore year. That,

except for a little astronomy in the last term of the junior year, was the extent of

mathematics in the curriculum.

Pycior ([7]) points out that the American editions of these European works

were often modiﬁed by their American editors. This is the case with Hutton’s

work, which was edited by Robert Adrain, the Irish immigrant who was mentioned

in the Preface and who taught at Queen’s College (Rutgers) and Columbia College.

Adrain’s Hutton is bound in two volumes of about six hundred pages each. The

material listed above is all in the ﬁrst of these two volumes. The second volume

covers spherical trigonometry and the “doctrine of ﬂuxions,” that is, the calculus.

Apparently, the second volume was not used in instruction at UVM at this time.

(The volumes now in the stacks of the Bailey-Howe Library belonged to Professor

G. W. Benedict, who arrived at UVM after Dean left for the second time and will

be discussed in the next chapter.) Although a thorough discussion of the contents

of Hutton’s textbooks would require more time and space than the current project

allows, certain points are of suﬃcient interest to be mentioned.

Hutton’s arithmetic goes beyond mere computation to consider many topics

that we now regard as algebra, such as compound interest problems, permutations

and combinations, raising to power (called involution), extraction of roots (called

evolution), logarithms, and mixture problems (called alligation problems and clas-

siﬁed as alligation medial and alligation alternate).

Hutton’s algebra, written at a time when elementary algebra was not yet thor-

oughly elucidated through the use of complex numbers, betrays a lack of insight on

the part of its author and a consequent lack of motivation for most of its methods.

Algebra is deﬁned as “the science of computing by symbols.” Some of the purported

applications of algebra are curious, as they are bound to be, since algebra by itself

(apart from its use in calculus and diﬀerential equations) has very little application

to ordinary human life.

For example, under the heading Application of Arithmetical Progres-

sion to Military Affairs, we ﬁnd problems of the following sort:

A detachment having 12 successive days to march, with orders to

advance the ﬁrst day only two leagues, the second 3

1

2

, and so on

increasing 1

1

2

league each day’s march: What is the length of the

whole march, and what is the last day’s march?

One wonders if students were any better fooled then by such fraudulent “ap-

plications” than they are today. Even the simplest topic of algebra, the solution of

quadratic equations, gives the impression of rules laboriously and mindlessly mem-

orized, to be passed on to students without any reﬂection whatever. Nowhere is

the student told that solving a quadratic equation amounts to ﬁnding two numbers

when one knows their sum and product. The rules for solving cubic equations are

all approximate rules. As Hutton says:

4. STUDENTS 23

There are many particular and prolix rules usually given for the

solution of some of the above-mentioned powers or equations. But

they may be all readily solved by the following easy rule of Double

Position, sometimes called Trial-and-Error.

A formula for solving cubic equations is given, called “Carden’s formula.” Giro-

lamo Cardano (24 September 1500–21 September 1576) was a sixteenth-century

mathematician who either worked out or plagiarized this rule. Again, it is manifest

that the author himself does not understand what he is doing. He gives the rule,

but no proof of it, and never tells the reader that the irreducible case, in which the

formula leads to complex numbers, occurs precisely when the equation has three

real roots, though this fact was known not long after Cardano’s original work. Fur-

thermore, students might have more conﬁdence in the rule if they knew that it

sometimes expresses a very simple integer as the diﬀerence of the cube roots of two

other very complicated irrational expressions. For example, it gives the solution of

the equation x

3

+ 6x = 20 in the form x =

3

p

√

108 + 10 −

3

p

√

108 − 10, and hardly

anyone would recognize this as the statement that x = 2.

Hutton’s geometry escapes all the diﬃculty of the theory of parallels by simply

deﬁning parallel lines to be lines that lie at the same perpendicular distance from

each other at all their points.

22

(Two lines can be equidistant in this sense only in

Euclidean geometry. Thus the deﬁnition of parallelism excludes what is now known

as hyperbolic geometry.) By cutting the Gordian knot thus eﬃciently, he is able to

prove a great deal in very little space, but of course the reader is deprived of any

knowledge of one of the fundamental problems in geometry at the time, the role of

Euclid’s parallel postulate, which is not even stated.

Such was the mathematical education available in Vermont in 1823 for the price

of $20.00 per year tuition, plus board at $1.25 per week (rooms in the University

commons were free). Whether or not inﬂation is taken into account, the cost per

theorem has probably never been so low at any time since.

4. Students

According to the General Catalogue of the University of Vermont, 1791–1890

(Free Press Association, 1890), by 1820 UVM had about 100 living alumni, of whom

51 were lawyers, 20 were (Protestant) clergymen, 5 were physicians, 5 were farmers,

3 were in the armed forces, 3 were merchants, 5 were teachers, 2 were professors,

and 1 was a sea captain (no occupations were given for about four of them).

The most noteworthy alumnus of the early period, from the point of view

of mathematics, was one who studied under James Dean, namely George Palmer

Williams (13 April 1802–4 September 1881) of the class of 1825, who obtained

an LL. D. from Kentucky College in 1849, became an Episcopal priest, and was

professor of mathematics and physics at the University of Michigan from 1841 to

22

Another mathematician of even more naive views, J. J. Callahan (11 January 1878–11 Oc-

tober 1969), president of Duquesne University in the 1930s until he was sacked by popular demand,

announced that he had proved the parallel postulate. His “proof,” published in a book bearing

the title Euclid or Einstein?, cuts through the diﬃculty in exactly the same way. Apparently,

Callahan never realized that Hutton had anticipated him. He also believed that he had proved

that his deﬁnition of parallel lines was equivalent to Euclid’s. (It isn’t.) At another point in his

notable career, he announced a ruler-and-compass angle trisection. One of his fellow priests said

of him, “Father Callahan was the one man I knew who never had a doubt.” His book, by the way,

contains a scurrilous personal attack on Einstein.

24 1. THE EARLY YEARS, 1800–1825

1863. He was president of the faculty at Michigan in 1845–1846 and again in 1848–

1849.

CHAPTER 2

The Benedictine Era, 1825–1854

The University was fortunate in its recovery from the loss of its building and its

senior professor. Over the next 30 years, it attracted two competent scholars, the

ﬁrst of whom also showed good business sense and helped to put the university’s

ﬁnances and physical plant back on a stable foundation.

1. George Wyllys Benedict

A successor to Prof. Dean was soon found in the person of George Wyllys

Benedict. G. W. Benedict was a vigorous and resourceful man, just the person to

put things back together again. It is his copy of Hutton’s course of mathematics

that is now in the stacks of the Bailey–Howe Library. Born in North Stamford, CT

on 11 January 1796, he graduated from Williams College in 1818, then served as

principal of the Academy in Westﬁeld, MA, tutor at Williams College, and principal

of an academy in Newburgh, NY, before accepting the position at UVM. At the

50th anniversary (1854) of the ﬁrst graduating class, Prof. Benedict spoke of his

appointment:

When I came here, I was an entire stranger to the Institution and

to every person connected with it, to the region round about, and

to all its inhabitants. Why I came, I can hardly tell. Certainly, the

inducements held out to me were slight enough. The member of the

Corporation, Hon. Titus Hutchinson, who called upon me, then a

resident in another state, to ask if I would consent to be a candidate

for the professorship of mathematics and natural philosophy, told

me that the college building was burned down, that the Institution

had met with many diﬃculties, and had poverty to contend with.

Through the generosity of individuals, chieﬂy the inhabitants of

Burlington, a partial rebuilding was to be commenced as soon as

mild weather would justify such operations, but a slow growth was

to be looked for, in his judgement. For salary, he could promise

but $600 per annum, and that not very regularly paid. There

was, however, a freedom from discouragement in all that he said,

and a conﬁdence in the continued life and ultimate strength of the

Institution, which won my sympathy, and gained my assent to his

proposal.

This optimism was, in the long run, justiﬁed. Indeed, already on 28 June 1825,

only 13 months after the ﬁre, the cornerstone of the new College Ediﬁce, henceforth

25

26 2. THE BENEDICTINE ERA, 1825–1854

known as the Old Mill, was laid by none other than the Marquis de Lafayette, who

was embarked on a farewell tour of the United States.

1

G. W. Benedict’s energy was sorely needed by the University. It is very largely

thanks to his eﬀorts that a large sum of money was raised to ﬁll the shelves of a

respectable university library. While teaching mathematics at UVM, he sent oﬀ

for publication the one scientiﬁc paper listed under his name in the Royal Society

Catalogue (Vol. 1, p. 270), an observation of a meteor seen in Burlington on 14

April 1826, published in Silliman’s Journal, Vol. XI, (1826), p. 120.

On the ﬁftieth anniversary of the founding of the American Republic (which, as

is well known, was also the day on which both John Adams and Thomas Jeﬀerson

died), Benedict gave a beautifully patriotic oration in praise of the country, but

nevertheless deplored the continued existence of slavery.

His ﬁrst innovation was to add calculus to the curriculum, based on a textbook

by

´

Etienne B´ezout (31 March 1730–27 September 1783), who is remembered for his

work on solving equations by determinants and even more for his many textbooks.

Lindsay ([3], pp. 195–200) recounts Benedict’s construction of the ﬁrst chemistry

laboratory in any American university (despite contrary claims by the University

of Michigan, where a chemistry laboratory was built in 1856). Benedict not only

designed and ﬁnanced this laboratory, he gave comprehensive lectures on electricity

to the community. Although he taught mathematics for only four years—he con-

tinued to teach chemistry until 1847—he became treasurer of the University and

one of its most articulate advocates in the academic world.

UVM was in need of such an advocate, since its curriculum was looked upon

unfavorably by more traditional places. The classical language requirement for

admission was applied only to those who planned to study the classics. Those who

wished to study science or modern literature were exempt from it. G. W. Benedict

wrote a pamphlet in defense of UVM’s policy,

2

which was distributed in the name

of the entire faculty. Explaining why students not specializing in classical studies

did not have to exhibit competence in Greek and Latin, he wrote

It is certainly better for one to get a part well than to attempt all

with the certainty of universal failure.

UVM revived rapidly in part due to his labors, which, however, became bur-

densome to him. He resigned in 1847 for health reasons and went to work for a

company bringing a telegraph line from Troy, NY to Burlington. Soon afterward,

he formed his own company to bring a telegraph from Boston to Burlington. In

1853, he and his son bought the Burlington Free Press. Both were outspoken aboli-

tionists and defenders of the civil rights of freed slaves. Appointed historian of the

University, he wrote a comprehensive history of its early days for Vol. XIII of the

American Quarterly Register. He died in Burlington on 24 September 1871, and

is buried in the Benedict family plot in Green Mount Cemetery. He is honored by

one of the west windows in the John Dewey Lounge of Old Mill.

1

This visit to UVM is commemorated in the statue of Lafayette at the north end of the

College Green.

2

An Exposition of the System of Instruction and Discipline Pursued in the University of

Vermont, Chauncey Goodrich, Burlington, 1831.

3. FARRAND NORTHRUP BENEDICT 27

Window in the John Dewey Lounge of Old Mill honoring George

Wyllys Benedict.

2. George Russell Huntington

As mentioned above, G. W. Benedict taught mathematics at UVM only until

1829. In that year, George Russell Huntington, a graduate of the class of 1826,

who had been a tutor for the previous two years, was appointed professor of mathe-

matics and civil engineering, the ﬁrst mention of engineering at UVM as a separate

discipline. (Rensselaer Polytechnic Institute was only ﬁve years old at the time.

“Natural philosophy” has not been a subject of instruction at UVM since that

time.) Prof. Huntington was born on 23 May 1800 in Woodbury, CT. The 1825

UVM catalog lists him as a senior from Onondaga, NY, but he is not listed among

the students in 1823 or 1824. He left UVM in 1832, when Farrand Northrup Bene-

dict was appointed to the position he had been occupying. He moved west and

settled in Buﬀalo, NY, where he died on 7 January 1872.

3. Farrand Northrup Benedict

Huntington taught only until 1832, when the chair of mathematics and civil

engineering was taken over by Farrand Northrup Benedict, an 1823 graduate of

Hamilton College and apparently a cousin of G. W. Benedict. Both mathematically

and personally, F. N. Benedict is as interesting as his (supposed) cousin G. W.

Benedict. He was born in Parsippany, NJ on 11 March 1803. Upon his graduation

from Hamilton College, he entered the law, but abandoned it after two years and

began to practice as a civil engineer. The Royal Society Catalogue lists one paper

under his name: “A method of determining the temperature of the mercury in a

siphon barometer, from the observed upper and lower readings; and of testing the

accuracy of the instrument,” published in Silliman’s Journal, Vol. XL (1841), pp.

250–263. An earlier publication, overlooked by the Royal Society, bore the title,

“On the sections of a plane, with the solids formed by the revolution of the conic

sections, about axes situated in their planes,” also in Silliman’s Journal, Vol. XXXI

(1837), pp. 258–266.

F. N. Benedict retired rather early from UVM, in 1855, and returned to Parsip-

pany, apparently for the sake of his wife’s health. He was an ardent conservationist

with a keen interest in the Adirondack Mountains, where he purchased tracts of

land to ensure their preservation. In 1874, he undertook an arduous survey of the

28 2. THE BENEDICTINE ERA, 1825–1854

Hudson and Raquette Rivers, albeit for purposes of which modern environmental-

ists would not approve—he wanted to see what potential they had for damming. His

environmental interests are discussed in an article by Warder H. Cadbury bearing

the title, “A Foot-Note to John Todd’s Long Lake,” (Back Log Camp Press, Sobail,

NY, 1957, part of a collection about Long Lake published by Howard I. Becker).

F. N. Benedict is also believed to be the author of the article “The Wilds of North-

ern New York,” published in Putnam’s Monthly, Vol. IV, No. XXL, September

1854, and reprinted as a pamphlet by Purple Mountain Press, Fleischmanns, NY,

2001.

F. N. Benedict died on 26 July 1880. Historians are supposed to maintain a

nonjudgmental aloofness from the characters they write about, but I cannot help

revealing that of all the former professors I have encountered in doing the research

for the present work, he is my favorite, the one I would most like to have met. He

was not only a competent, if slightly eccentric, mathematician, he was also a man

of warm human sympathies. In his ﬁle in the UVM archives there is a letter written

a few months before his death, to the daughters of one of his former pupils.

3

F. N.

Benedict’s letter to Catherine and Laura begins as follows:

Although suﬀering from great weakness and loss of sight, I cannot

refrain, without violence to my feelings, from assuring you of my

deep sympathy in the loss of your dear father. . .

4. Curriculum

The curriculum and entrance requirements at UVM changed slightly during the

1830s, as already mentioned in connection with G. W. Benedict. The 1837 catalog

reveals that UVM had gone from a three-term academic year to a two-term system,

with semesters referred to as the “autumnal term” and the “summer term.” Com-

mencement was on the ﬁrst Wednesday in August. The idle period remained the

months of January and February, for the same obvious climatic reasons as earlier.

Students studied algebra during the autumnal term of the ﬁrst year and geometry,

including solid and spherical geometry, during the summer term of that year. In the

second year they took up conic sections, plane and spherical trigonometry (autum-

nal term) and surveying, navigation, projections, diﬀerential and integral calculus,

and civil engineering (summer term). Science in the third year was devoted to

physics and chemistry, especially mechanics, optics, and crystallography. Finally,

in the fourth year the study of algebra and calculus was resumed, and astronomy

was added. This was quite a respectable curriculum.

4.1. Textbooks. The textbooks used were Bonnycastle’s Algebra, Legendre’s

Geometry in a translation by Charles Davies (22 January 1798–17 September 1876,

professor at the United States Military Academy), Herschel’s Astronomy, and the

Cambridge Course, a series of textbooks used at Harvard. All of these texts were

improvements on the earlier ones.

John Bonnycastle (born on 29 December 1751 in Hardwick, Buckinghamshire,

died on 15 May 1821 in Woolich, Kent) became a professor at the Royal Military

3

This student was evidently Charles Carroll Parker, who was born in Underhill, VT on

26 September 1814 and was listed as a ﬁrst-year student in the 1837 UVM catalog. He was a

clergyman and had two daughters (Catherine and Laura) and a son, Charles Parker, Jr. He died

near F. N. Benedict in Parsippany on 15 February 1880.

5. STUDENTS 29

Academy at Woolwich in 1782. In comparison with his predecessor Charles Hutton,

he was a much clearer writer who seemed to have real insight into his subject. As

for the Parisian Adrien-Marie Legendre (18 September 1752–10 January 1833), he

is one of the greatest mathematicians of all time,

4

and his textbook of geometry is

pellucid. In particular he discusses the problem of parallels and states the parallel

postulate. Likewise, Frederick William Herschel, born in Hannover, Germany on

15 November 1738, was a multi-talented musician, scientist, and mathematician.

He moved to England after the Hannoverians were defeated by the French in 1757

and did his most famous work there. He is best known for having discovered the

planet Uranus on 13 March 1781. He died in Slough, England on 25 August 1822.

Further indication of the content of these courses is fortunately available from

two sets of notes that have been preserved. One is a set of notes on the course in

analytic geometry from the autumnal term of 1848 kept by Matthew Henry Buck-

ham (born in Hinckley, Leicestershire, England on 4 July 1832, died in Burlington

9 November 1910), valedictorian of the UVM class of 1851, who served half his life

(1871–1910) as the eleventh president of UVM. (This was the longest presidential

term in UVM’s history.) Buckham’s notes reveal that the bulk of the course was de-

voted to applications of coordinates to the study of conic sections, whose equations

are given in rectangular, oblique, and polar coordinates. The second notebook is

from the 1849 course in central forces. These notes were preserved by McKendree

Petty, who became the successor to F. N. Benedict as professor of mathematics.

They reveal that the course was an elaboration of Newton’s Principia, Book I, §§

II–III and XII (on the orbits of particles and the attraction of spherical solids). No

attempt is made to ﬁnd simpler or clearer proofs of the propositions than Newton

himself gave. Still, getting students to read and understand Newton directly from

his text must have been no small achievement.

5. Students

Among the mathematical students of this period one should mention Joel Tyler

Benedict (18 January 1821–15 January 1892) of the class of 1843, who later became

a professor of civil engineering (1852) and mathematics (1857) at the New York Free

Academy (founded in 1847, renamed the City College of New York in 1866). He

wrote an algebra text in 1857 that, like the books by Charles Hutton used earlier

at UVM, rather tends to obscure the subject.

The most distinguished alumnus was probably Selim Hobart Peabody, who was

born in Rockingham, VT on 20 August 1829, graduated from UVM in 1852 and

became a professor of mathematics and civil engineering at the Agricultural College

of Pennsylvania in 1854. He obtained a Ph. D. in 1877 and an LL. D. in 1881, both

from the University of Iowa. He was appointed professor of mechanical engineering

at Illinois Industrial University in 1878 and president of the University of Illinois

in 1880,

5

where he served until 1891. In 1893, he headed the department of liberal

arts at the World’s Columbian Exposition in Chicago, then in 1899 was statistician

4

A supposed portrait of Legendre, which made him look something like Mr. Pickwick and

adorned hundreds of books for many decades, has recently been shown to be the portrait of another

man, possibly Legendre’s butcher. What he actually looked like is thus not known, except for a

caricature portrait of him that can be found in various locations.

5

These two institutions are one and the same. Illinois Industrial University was founded at

Champaign–Urbana in 1867 and oﬃcially renamed the University of Illinois in 1885.

30 2. THE BENEDICTINE ERA, 1825–1854

and editor for the United States commission at the Paris Exposition. In 1901,

he was once again superintendent of the liberal arts division at the Pan-American

Exposition in Buﬀalo, NY. He died in St. Louis, MO on 26 May 1903.

Less well-known was Otis David Smith (born in New Haven, VT on 27 June

1831, died at Auburn, AL on 7 May 1905) of the class of 1853, who became professor

of English literature and mathematics at the Agricultural and Mechanical College

of Alabama in Auburn.

Passing over a number of UVM graduates who became prominent politically,

we shall conclude this list with two prominent businessmen who were not, as far

as is known, mathematics majors. Frederick H. Billings (born in Royalton, VT

on 27 September 1823, died in Woodstock, VT on 30 September 1890), a member

of the class of 1844, became president of the Northern Paciﬁc Railroad Company.

Henry Oscar Houghton (no apparent relationship to George Frederick Houghton,

who wrote the article on James Dean mentioned above), was born on 30 April

1823, graduated from UVM in 1846, and died on 25 August 1895. He was one of

the founders of Houghton–Miﬄin publishing company.

6. The Library

During this period the University matured into an institution with a well-

deserved reputation of competence, indeed excellence. The 1843 catalog boasts

that the library “. . . contains upwards of seven thousand volumes, chieﬂy selected.

It is open to the Senior and Junior classes every Saturday—to the Sophomore and

Freshman classes every Wednesday—at noon, during term time. . . ” The acquisition

of this library was a notable feat, made possible by the vision of three prominent

ﬁgures of the time. Two of them were UVM’s sixth president, John Wheeler and

Professor/Treasurer George Wyllys Benedict, who together raised $30,000 to pay

oﬀ some of the university’s debts and reserved $12,000 of these funds to improve the

library and laboratories. The third was Professor (Rev.) Joseph Torrey, who was

born in Rowley, MA on 2 February 1797 and died in Burlington on 26 November

1867. He graduated from Dartmouth in 1816 and was appointed professor of Greek

and Latin at UVM in 1827; he served as the ninth president of UVM during most

of the Civil War, from 1862 to 1866. It was Professor Torrey who journeyed to

Europe in 1835, spending the money very carefully and acquiring 7000 excellent

volumes for about $10,000.

A catalog of the library holdings from 1843 (University Press, Burlington,

printed by Chauncey Goodrich) bears out this claim. Of the 7,000 books some

250 are on mathematics and physics, and these contain some impressive works,

such as John Colson’s translation of Donna Maria Agnesi’s Instituzioni analytiche

(Analytical Institutions) (London 1801), George Airy’s Mathematical Tracts on

Physical Astronomy (Cambridge 1826), many works by John and Jacob Bernoulli,

Roger Cotes, Leonhard Euler, Carl Friedrich Gauss, Colin Maclaurin, Isaac New-

ton, Thomas Young, Lazare Carnot, and the works of the many geniuses at the

´

Ecole Polytechnique, among which were Louis-Fran¸cois Arbogast’s Du calcul des

d´erivations (Strasbourg 1800), and works by Jean-Baptiste Biot, Jean-Baptiste

Delambre, Sylvestre Fran¸cois La Croix, and Sim´eon-Denis Poisson.

Here is some information on the mathematicians named above:

• John Colson (1680–20 January 1760) was the fourth Lucasian professor at

Cambridge (the second being Isaac Newton). He contributed greatly to

6. THE LIBRARY 31

a full understanding of cubic equations. Unfortunately, he mistranslated

Agnesi’s name for the semicubical parabola, whose equation is y

3

= ax

2

.

Agnesi called it a versiera (twisted curve), which Colson conﬂated with

avversiera (wife of the devil), and it is now known as the “witch of

Agnesi”—a lamentable slur on the character of a very ﬁne woman and

mathematician.

• Maria Gaetana Agnesi (16 May 1718–9 January 1799) was a talented

mathematician, but her charitable and religious instincts were strong, and

she eventually devoted her time and her inheritance to assisting the poor.

• George Airy (27 July 1801–2 January 1892) was the Lucasian Professor

at Cambridge after 1826. He is most famous for Airy’s equation y

00

= xy,

and its solutions, known as Airy functions.

• John and Jacob Bernoulli (27 July 1667–1 January 1748 and 6 January

1655–16 August 1705, respectively) were two brothers from a distinguished

Swiss family that produced a dozen outstanding scientists over a period

of a century or more. These two were close disciples of Gottfried Wilhelm

Leibniz (1 July 1646–14 November 1716), co-discoverer with Newton of

the calculus.

• Roger Cotes (10 July 1682–5 June 1716) worked on an edition of New-

ton’s Principia from 1709 to 1713 and had some correspondence with

Newton about methods of approximating irrational numbers. The result

is a method of approximation still known as Newton–Cotes.

• Leonhard Euler, who was mentioned above, was the most profound math-

ematician of the eighteenth century, and the most proliﬁc one of all time.

• Carl Friedrich Gauss, also mentioned above, is regarded by most historians

of the subject as the most profound mathematician of the nineteenth

century, ranked alongside Archimedes and Newton, and just above Euler,

as such things go. (He himself admired Euler above almost all others.)

• Colin Maclaurin (February 1698–14 June 1746) was a Scottish disciple of

Newton, one of his defenders in the controversy over inﬁnitesimals. He is

remembered for the power-series expansion that bears his name.

• Isaac Newton (4 January 1643–31 March 1727)—these dates are Grego-

rian dates, even though in his day the British calendar was Julian—is

suﬃciently well known that no description is needed.

• Thomas Young (13 June 1773–10 May 1829) is best known for his inter-

ference experiments supporting a wave theory of light.

• Lazare Carnot (13 May 1753–2 August 1823) was a French engineer, noted

for having written a calculus text.

• Louis Fran¸cois Arbogast (4 October 1759–18 April 1805) was a mathe-

matical physicist and engineer.

• Jean-Baptiste Biot (21 April 1774–3 February 1862) is remembered for the

Biot–Savart inverse-square law of magnetic induction around a current-

bearing wire.

• Jean-Baptist Delambre (19 September 1749–19 August 1822) worked on

measuring the length of a meridian of longitude on the earth. (The meter

was to be deﬁned so that the total length would be 40,000,000 meters.)

• Sylvestre Fran¸cois La Croix (28 April 1765–24 May 1843) occupied the

chair of analysis at the

´

Ecole Polytechnique after 1799.

32 2. THE BENEDICTINE ERA, 1825–1854

• Sim´eon-Denis Poisson (21 June 1781–25 April 1840) is remembered for

the Poisson probability distribution. He was, according to one historian

of mathematics “the greatest French mathematician of the ﬁrst half of the

nineteenth century.”

The chief deﬁciency that a modern researcher would notice is an absence of

mathematical journals: no Comptes rendus, no Liouville’s Journal,

6

no Crelle’s

Journal.

7

These were the lifeblood of researchers in out-of-the-way parts of Europe,

but entirely missing at UVM. To be sure, the library did have many back numbers

of the Transactions of the Royal Society in an abridgement due to Charles Hutton,

but these dried specimens of mathematics were no substitute for the living plant of

current research.

Instruction at this time was by lecture and textbook reading. There were

apparently no quizzes or midterm examinations. According to the 1844 Catalog,

. . . the students are examined at the close of each study by the

Faculty, and also annually by the Faculty and a committee, during

the three weeks immediately preceding Commencement, in all the

studies pursued under the direction of the Faculty. The examina-

tions are intended to be exact and thorough, and the results in the

case of each student are noted and recorded.

The University was apparently forced to retreat on some of its academic in-

novations, and the requirement of Greek for entrance was restored in 1839. The

University also returned to a three-term academic year, with the eight-week vaca-

tion falling in December and January.

7. The Williams Professorship

Part of the University’s prosperity at this time was due to the generosity of

one Azarias (or Azariah) Williams, born in Sheﬃeld, England on 31 July 1765,

who in 1839 gave the University land estimated in value at $25,000 in return for an

annuity during the remainder of his life. Upon his death on 18 February 1849 the

University became the sole possessor of this land. At its meeting of 10 May 1849

the Trustees adopted the following resolutions:

Resolved, by the Corporation of the University of Vermont, that

a suitable monument of durable material and imposing structure

with an inscription commemorating the great liberality of the de-

ceased to this Institution be erected on some conspicuous site at

the expense of this Corporation.

Resolved, that if the consent of all persons authorized to grant it

can be obtained, the mortal remains of the late Azarias Williams

be removed from their present resting place and deposited under

the proposed monument.

These resolutions seem not to have been carried out, as the remains of the

Hon. Mr. Williams are to this day buried at the Pike Cemetery in Concord (Essex

6

Founded in 1836 by Joseph Liouville (24 March 1809–8 September 1882), it is oﬃcially the

Journal de math´ematiques pures et appliqu´ees.

7

Founded in 1826 by August Leopold Crelle (29 April 1771–24 August 1856), it is still called

Crelle’s Journal, although of course it has had many editors and its oﬃcial name has always been

Journal f¨ur die reine und angewandte Mathematik.

7. THE WILLIAMS PROFESSORSHIP 33

County), VT, where they were no doubt interred some months before this resolution

was taken. In 1853, the Trustees substituted a more modest eﬀort:

Resolved, that out of respect to the memory of Azariah Williams,

the largest donor as yet to this University, the Professorship of

Mathematics be styled the Williams Professorship of Mathematics.

And it was done: F. N. Benedict, in his last year of service, became the ﬁrst

Williams Professor of Mathematics. It was a chair having all the appearance of

an endowed chair, but no funds were ever set aside to endow it. Mr. Williams’s

name continued in the catalog from that day on, although the position of Williams

Professor of Mathematics was vacant for a generation, from the 1960s to the end

of the twentieth century. The title was revived in the year 2000 and bestowed on

Roger Cooke (author of the present work), after whose retirement in 2003 it was

conferred on the late Kenneth I. Gross (14 October 1938–10 September 2017), then

in 2008 on Kenneth I. Golden, and in 2013 on Jeﬀrey Dinitz.

CHAPTER 3

A Generation of Struggle, 1854–1885

The second Williams Professor of Mathematics, the Rev. McKendree Petty,

was appointed at a time of gathering danger to America, as the Civil War drew

near. The University Archives contain Rev. Petty’s diary, begun in 1844, when he

was just 17. There are not many entries, however, until 1855. (The diaries are

arranged as the days of a single year, but were used over many years, with the year

being noted at the beginning of each entry.)

1. The Second Williams Professor

McKendree Petty was born in North Dorset, VT on 4 July 1827. A full-length

biography of him ([10]) was written by his great-grandson, the late Dr. Edward

H. Worthen (15 February 1930–28 December 2016), a specialist in Latin-American

studies. From this biography, we learn that there were serious conﬂicts between

McKendree Petty’s body and his ideals. He married in haste during his sophomore

year at UVM (1847), only four months before the birth of his ﬁrst son ([10], p.

53). At UVM, he was a member of Lambda Iota fraternity, the oldest fraternity

in Vermont, founded in 1836 as a literary and smoking club to protest a university

ban on the use of tobacco.

1

Petty’s obsessive, guilt-ridden personality is reﬂected

in an entry in his diary from January of 1853 containing a bitter self-reproach for

having allowed himself to become addicted to cigarettes ([10], p. 82).

Petty graduated from UVM in 1849, then taught in an academy in Castleton,

VT for one year while preparing to study for the law. He journeyed to Louisiana

and obtained his law degree from Louisiana State University in 1852. He became

Williams Professor at UVM in 1854, and was ordained a Methodist minister in 1859.

As one might expect, when reading the Petty diaries, one gets the impression of a

rather melancholy man with an overly developed conscience. Many of the entries

are full of self-reproach for his lack of achievement, for “evil thoughts,” and other

faults. It may be, however, that the diaries were the safety valve for his gloomier

side. Certainly, he was much loved by his students, who rained tributes on him

after his death in 1887 and for years afterward.

The external conditions of the times were conducive to depression. The diary

entries from 29 May 1856 contain powerful emotional outbursts evoked by the

burning of Lawrence, KS, and the vicious attack on Senator Sumner by Preston

Brooks. Petty, who had lived in the South, describes the horror of a slave auction.

He was an abolitionist and a Republican, as was much of the population of Vermont.

Petty’s reﬂections on the state of the world mix with his own personal problems

1

The club received a generous subsidy from Pierre Lorillard III (20 October 1796–23 Decem-

ber 1867), grandson of the founder of the Lorillard Tobacco Company, which manufactured six

diﬀerent brands of cigarettes ([10], p. 82). The Greek letters in the name of the fraternity are

said to stand for Lorillard Institute.

35

36 3. A GENERATION OF STRUGGLE, 1854–1885

in an entry of 30 December 1862 (a very bleak time for the Union and of course

especially dark and bleak in Vermont, as it always is on that date):

The appointment received of the corporation of the University of

Vermont in 1854 is still held. The anticipations then enjoyed have

not been realized, and today the oﬃce is one of beggary rather

than of ease and competence. Thus, the War, which desolates

the South by the ravages of mighty Armies, disturbs the various

relations of business at the North and changes posts of honorable

independence into undesirable places of meager sustenance. . .

Petty had six children at the time.

Only a few diary entries relate to mathematics, and these are rather elementary

parts of planned lectures. Unlike his three predecessors, he did not teach civil

engineering. He sounds rather burned out in this diary entry from 4 June (no year

given):

Engaged all morning in Diﬀerential Calculus. Find it very diﬃcult

to bring students to any desirable interest in the study. Some

succeed, many are willing to fail and do so without any proper

notion of the nature of their neglect. We are hampered by a class

of students that are here they know not for what—idle, restless,

mischief-making bodies—that bring more or less [illegible] into all

College exercises. These dead limbs, in my opinion, as well for

their own good as for our prosperity, should, after due trial, be

“lopped oﬀ” and allowed to fall to their more appropriate spheres.

McKendree Petty was forced to retire in 1885 by a degenerative neural disease.

He lingered on for another 18 months after retirement and died in Burlington on

23 September 1887. Tributes to him were many. The ﬁrst volume (1888) of UVM’s

yearbook, The Ariel, was dedicated to him. In 1910 his portrait was presented by

grateful former students to Lambda Iota fraternity. This portrait now hangs in the

John Dewey Lounge in Old Mill.

McKendree Petty (1827–1887), second Williams Professor of

Mathematics.

3. THE UNIVERSITY ENVIRONMENT 37

2. Curriculum

Amid the poverty and disorganization created by the Civil War, the mathe-

matics curriculum shrank from its previous dimensions. By 1867, mathematics was

conﬁned to the ﬁrst two years of study in the classical course and its highest level

was a two-month long study of calculus. The textbooks used during Petty’s time

were a series by Elias Loomis (7 August 1811–15 August 1889, professor at the

City University of New York). They are competently written, though it is hard to

see in what way they are an improvement over those used previously. The book

by Legendre that had been used earlier, for example, gives the parallel postulate

in the form given by the Scottish mathematician John Playfair (10 March 1748–20

July 1819): Through a point not on a given line, there can be drawn one and only

one line parallel to the given line. Loomis adopts a slightly diﬀerent wording that

is not quite equivalent: Two intersecting lines cannot both be parallel to the same

line. This formulation rules out the possibility that more than one line can be

drawn through a given point and parallel to a given line, but it does not assure

that there actually is one such line. The existence of such a line is guaranteed by

the tacit assumption that a line is totally ordered and separates the plane into two

disjoint half-planes. A person who wants to know only one-variable calculus might

do just as well to study Loomis’s text as anything written since. (Many subjects

now taught, such as vector calculus, were not in Loomis’s books because they had

not yet been invented; and no physicist nowadays should attempt to get by without

multivariable calculus.)

3. The University Environment

President Wheeler was succeeded by the Rev. Worthington Smith. Rev. Smith

was born in Hadley, MA on 11 October 1795—he was the last UVM President

born in the eighteenth century—and graduated from Williams College in 1816.

He became pastor of the St. Albans Congregational Church on 4 June 1823. He

served as president of UVM for six years, from 1849 to 1855, and during this time

he attempted unsuccessfully to revive negotiations for a merger with Middlebury

College. He died in St. Albans on 13 February 1856.

Rev. Smith was succeeded by Calvin Pease, the ﬁrst UVM alumnus to serve

in that role. He was born in Canaan, CT on 12 August 1813, and received the

bachelor’s degree at UVM in 1838 and a master’s degree in 1841. From 1842 on, he

was professor of classics at UVM. As a result of external economic forces beyond

anyone’s control, UVM’s ﬁnances became precarious during the six years (1855–

1861) leading up to the Civil War. The War itself, as Rev. Petty noted in his diary,

made things even more diﬃcult. In 1862, after resigning the presidency of UVM,

Calvin Pease became Rev. Pease, pastor of a Presbyterian church in Rochester, NY.

He spent only one year in Rochester, however, and returned to Vermont, where he

died on 17 September 1863.

Rev. Pease’s successor, the Rev. Joseph Torrey, who guided the University

through the diﬃcult years of the Civil War, was discussed above in connection

with the university library. Rev. Torrey was the the last of the nine Congrega-

tional/Presbyterian pastors to occupy that oﬃce.

The postwar period was presided over by the most distinguished of all the ﬁrst

ten presidents, James B. Angell. He was born in Scituate, RI on 7 January 1829 and

graduated from Brown University in 1849, where he remained (after a year traveling

38 3. A GENERATION OF STRUGGLE, 1854–1885

around Europe) to teach modern languages. When he took oﬃce as president of

UVM in 1866, there were only 30 students all told. He managed to increase this

number to 60 and (more importantly) to ﬁrm up the university’s ﬁnancial position,

so that professors were better paid. He left UVM in 1871 to become president of

the University of Michigan, where he served until 1909 (!!). He died in Ann Arbor,

MI on 1 April 1916. Angell’s successor, Matthew Buckham, has been discussed

above in connection with the lectures of F. N. Benedict. His presidency of UVM

coincided exactly with his predecessor’s presidency of the University of Michigan.

4. UVM Becomes a Land-grant Institution

One important change at UVM during this period was its incorporation as

a land-grant institution in November 1865, when, under the terms of the Morrill

Act, it became the University of Vermont and State Agricultural College, oﬀering

instruction in engineering and agriculture as well as the classical academic subjects.

Norwich and Middlebury Colleges were once again oﬀered the opportunity to unite

with UVM in a single institution at this time, and once again, both turned it down.

To fulﬁll its part of the law, the State of Vermont was to contribute $8,000 per

year to the maintenance of the State Agricultural College. Justin Smith Morrill,

one of Vermont’s representatives in Congress and the author of the act that created

the land-grant colleges, protested that this was a paltry investment, considering

that the State received in return half the proﬁts from various gifts to the Univer-

sity, including $100,000 from John P. Howard,

2

$20,000 from John N. Pomeroy,

3

and $200,000 from Frederick Billings of the class of 1844, whose presidency of the

Northern Paciﬁc Railroad was mentioned above. However, the State was not in-

clined to hear him (Lindsay, [3], p. 223).

One result of this new structure, shown in the 1866–1867 catalog, was the cre-

ation of the State Agricultural College, containing Sections of Engineering, Mining

and Metallurgy, and Analytical and Agricultural Chemistry. The Agricultural Col-

lege listed McKendree Petty among its faculty, along with Samuel Huntington, Jr.,

4

C. E. as Instructor in Civil Engineering. Huntington was succeeded in the 1869–

1870 catalog by Volney Giles Barbour,

5

who left a considerable mark on engineering

at UVM.

The entrance requirements for the new unit do not appear particularly onerous:

Applicants for admission to the Agricultural College must be at

least 15 years of age, and must bring satisfactory testimonials of

good character, and be able to sustain an examination in all the

parts of a common school education, and particularly in English

2

Born 27 July 1769 in Providence, RI, died in Burlington 24 February 1854. He owned a

major hotel in Burlington and a large estate on the east side of Willard Street, at the top of what

is now Howard Street.

3

Born 29 September 1792 in Burlington and died there on 19 July 1881. He graduated from

UVM in 1809 and eventually became a very successful lawyer, a profession from which he retired

upon receiving a legacy from his father.

4

Born in October 1842, he was an 1861 graduate of Union College. He taught at UVM from

1867 to 1869. By 1900, he was living in Maricopa County, in the Arizona Territory. Information

on him appears to be rather sparse.

5

Born on 2 June 1842 in Canton, CT and died in Minneapolis, MN on 4 June 1901, but

buried in Burlington. He was a professor of civil engineering at UVM for 31 years.

5. WOMEN AND PEOPLE OF COLOR COME TO UVM 39

Grammar, Geography, Arithmetic, and Algebra as far as quadratic

equations. . .

The new sections had some inﬂuence on the curriculum, chieﬂy the addition of

courses in mechanical drawing and projections. This adjunction of new academic

units to the basic core of classical studies and medical studies brought with it the

ﬁrst “turf wars,” with traditional humanists fearing the degradation of academic

standards and the public at large fearing that entrance requirements for the practi-

cal studies they cared about would be made too rigorous. These turf wars continue

unabated between champions of STEM and champions of the humanities right

down to the present day, although nowadays the struggle is purely over resources,

not academic standards.

This change to the charter led to legal complications. The University of Ver-

mont had been chartered by the legislature under that name in 1791, but was

not subsidized through taxation. It relied on endowments, gifts, and tuition for

its income. The newly-created State Agricultural College, however, was a state-

subsidized institution. A further administrative complication arose when these two

institutions were both immediately made subsidiary to a third legal entity called

The University of Vermont and State Agricultural College, which was not subsi-

dized by the legislature. This situation was bound to result in perceived inequities,

which were not resolved until 1955.

5. Women and People of Color Come to UVM

In the 1871 catalog, we ﬁnd the following:

By the recent action of the Trustees, the Academic and Scientiﬁc

departments of the University are open to young women on and

after the ﬁrst day of the Spring Term of the present Academic year.

Young women are admitted to all the courses of the department,

subject to the same conditions as young men. They are required

to board and room in private families approved by the Faculty.

The ﬁrst women students turned out to be of very high caliber, and two of them,

Lida A. Mason and Ellen Eliza Hamilton, were admitted—after some controversy—

to Phi Beta Kappa (which had formed a chapter at UVM in 1849) when they

graduated in 1875. They were the ﬁrst women ever admitted to Phi Beta Kappa

anywhere.

Lida Mason was born in Derby, CT on 7 September 1849 and raised in Jersey

City, NJ. Thus, she was already of the normal age at graduation when she was ﬁnally

allowed to enter UVM. Her presentations at the sophomore, junior, and senior

exhibitions held at UVM every year, on “Luther and Loyola,” “The Puritans and

Art,” and “True Excellence: Conformity to Principle” respectively, were reported

and favorably commented on in the Burlington Free Press. After graduating, she

was named assistant principal at the planned Vermont Academy in Saxton’s River,

VT (founded by the Vermont Baptist Convention), which opened on 6 September

1876. The third catalog of Kappa Alpha Theta sorority from 1894 says she was a

teacher there. However, it gives her address as Burlington. In fact, on 10 September

1877 she married the Burlington dentist Steven Dwight Hodge (2 February 1847–

12 September 1934) and thereafter lived in Burlington. (The couple seem to have

done the marriage ceremony again in Jersey City a month later, on 10 October.

Both Vermont and New Jersey have records of it.) The 1880 US census lists her

40 3. A GENERATION OF STRUGGLE, 1854–1885

occupation as “keeping house.” By that time, she had the given birth to twin

daughters (Lydia and Helen). She attended the centennial commencement of UVM

in July of 1904. She died on 4 July 1921 in Burlington, having suﬀered from arterial

sclerosis for 12 years.

Ellen Hamilton was born in Brandon, VT on 14 January 1853. After gradua-

tion, she taught Latin and Greek in the high school in Claremont, NH from 1875 to

1879, then, in 1880–1881 at Ingham University in Leroy, NY, founded as a “female

seminary” in 1835 and chartered as the ﬁrst women’s university in the United States

in 1852. (It was closed in 1892.) She then went traveling and, in Athens, Greece on

11 January 1883, married her UVM classmate, Congregational minister Frank Ed-

ward Woodruﬀ (20 March 1855–19 November 1922). The couple had two sons and

a daughter. Frank Woodruﬀ eventually became a state legislator from Brunswick,

ME, and after his death, Ellen ran unsuccessfully to ﬁll out his term. (Women had

been able to vote for only two years at that time!) She died in Brunswick on 28

November 1933. Her great-granddaughter Mary Woodruﬀ inherited an extensive

collection of letters between Ellen and Frank from 1870 to 1920, which she donated

to Special Collections at the Bailey–Howe Library.

The ﬁrst African-American member of Phi Beta Kappa was George Washing-

ton Henderson of UVM’s class of 1877. He was born into slavery in Clarke County,

VA on 11 November 1850 and was illiterate 14 years later, when he attached him-

self to a Vermont military unit. He came to Vermont, learned to read, and after

graduating ﬁrst in his class in 1877, received a master’s degree from UVM in 1880.

He later received a divinity degree from Yale and served in a number of distin-

guished positions, including a term as Dean of Fisk University in Nashville, TN

(1904–1909). He later served at Wilberforce University in Ohio until his retirement

in 1932. He died on 3 February 1936 and is buried at Xenia, OH.

Obviously, in the 140 years since those three students, there have been many

women members of Phi Beta Kappa at UVM. African-Americans, however, were

not among the student body in any considerable numbers until very recently. Both

groups have certainly suﬀered discrimination, but it is noteworthy that Henderson

was able to have a good career and the women were not. They could not even

vote until they were well past normal retirement age. While George Washington

Henderson’s career was mostly in “historically black” institutions, and he would,

no doubt, have found it diﬃcult to obtain comparable positions in public or pri-

vate universities, it is very plausible that he would have freely chosen exactly the

positions that he did occupy. The stories of these three after graduation provide

an object lesson in the vast gulf between the career opportunities open to women

and those open to men—even men who face intolerable discrimination. It would

be an interesting project in Women’s Studies to see how these two women raised

their daughters.

5.1. The variety of minorities. The number of ways human beings relate

to one another is immense, and there are many groups besides women and African-

Americans who were absent (or apparently absent) from UVM in its early days,

notably Asians, Hispanics, Native Americans,

6

people with disabilities, and mem-

bers of the LGBT community. The reader will no doubt notice the absence of any

6

I use this term reluctantly. It strikes me as patronizing to identify the descendants of the

aboriginal inhabitants of the land with the name of the nation that disrupted their traditional

ways of living. In addition, having been born in the United States, I ﬁnd that this term applies

6. UVM REACHES OUT TO VERMONT HIGH SCHOOLS 41

reference to people from these groups until the late twentieth century. For exam-

ple, there were surely LGBT people at UVM from early days, but due to severe

prejudice against them, they found it prudent to conceal their orientation.

People from all of these groups have had to struggle for acceptance, even though

UVM, which is not a wealthy university, has made many attempts to integrate them

into the University Community, by supporting organizations like ALANA (Asian-

American, Latino, African-American, Native American), the Center for Cultural

Pluralism, the LGBTQA Coalition, and Advocates for Exceptional Children, which

reaches out to the wider community beyond the University to help learning-disabled

children.

The single greatest obstacle to human progress is the fact that members of

the dominant community everywhere have not fully overcome the tribalism that

excludes people marked as “other.” (The “others” are also tribalistic, of course,

but we are discussing this problem in the context of discrimination inﬂicted on

powerless people.) Progress toward greater inclusiveness has always been painfully

slow and interspersed with periods of reaction in which some gains are reversed.

While most of the gains are made at the level of the University as a whole, or on the

state or federal level, individual initiatives do make a diﬀerence. The Department

of Mathematics and Statistics can be very proud of one of its members, Lecturer

Holly Puterbaugh, who, together with her partner, established in court cases during

the 1980s and 1990s that a qualiﬁed lesbian couple must be allowed to adopt a child

and that same-sex married couples must have the same civil rights as heterosexual

married couples. This action was taken at considerable personal risk, expense, and

stress, and has yielded immeasurable beneﬁts to the entire community, not merely

to the LGBT community.

6. UVM Reaches Out to Vermont High Schools

Still another innovation in this period was the ﬁrst High School contest spon-

sored by UVM, not only in mathematics, but also in other areas of science and in

the classical languages. According to the 1873–1874 catalog (p. 23):

By the liberality of Mrs. M. C. Wheeler of Burlington, $100 was

oﬀered last year in prizes to those who should best sustain the

entrance examinations. This was evenly divided between the Clas-

sical and Scientiﬁc Departments, two prizes ($30 and $20) being

oﬀered in each. A competitive examination in writing resulted as

follows: In the Classical Department, the ﬁrst prize was awarded

to Miss Ethel Persis Sherman of Montgomery, a graduate of the

New London (N.H.) Institution; the second to Miss Lettie Es-

tella Durant, of Montpelier, a graduate of the Montpelier High

School. In the Scientiﬁc Department, the ﬁrst prize was taken

by Charles Wayland Drew, of Burlington, a graduate of Burling-

ton High School; the second by William Thompson of Greenwich,

N. Y., who was ﬁtted for College at the High School in that place.

The questions are reproduced here, as serving in some sort to in-

dicate the kind and degree of preparation which is desired in can-

didates for admission.

exactly to myself; but if I applied it to myself, people would think I was claiming a heritage that

is not my own.

42 3. A GENERATION OF STRUGGLE, 1854–1885

Mrs. M. C. Wheeler was Mary Constance Wheeler, n´ee Rignall, widow of Pres-

ident John Wheeler, born in England on 25 May 1818. She married the widower

John Wheeler in West Roxbury, MA on 10 August 1852. She died on 18 March

1904. Three of the four student winners graduated from UVM. Ethel Persis Sher-

man was born 27 June 1851 and died 13 January 1933. She is listed as a teacher

with a master’s degree in the General Catalogue of the University of Vermont,

1791–1890. She studied in Oxford and Berlin between 1890 and 1892. In 1920, she

was living in San Francisco. Lettie Estella Durant unfortunately died young. Born

on 26 June 1854, she attended UVM from 1873 to 1875, but did not graduate. She

became an insurance agent. She married civil engineer Augustus M. Torrey (21

November 1850–20 August 1902) on 18 June 1878 and died only one year later,

on 20 June 1879. Charles Wayland Drew was born 18 January 1858 and died 25

November 1920 in Minneapolis, MN. He became a professor of chemistry at the

University of Minnesota. William Andrew Thompson, born on 6 December 1854 in

Easton, NY, became a civil engineer, having graduated from UVM with the class

of 1878. The 1890 catalogue just mentioned gives his address as Rock Island, IL,

but he also lived for a while in La Crosse, WI, being involved with control of the

upper Mississippi River. He died on 27 March 1930.

The reference to “the desired preparation” reﬂects the fact that students no

longer had to be examined by the UVM faculty in order to be admitted. The

University was willing to accept the certiﬁcation of a high school. Here are a

few sample mathematical questions. We note that mathematical preparation was

demanded of students in both classical and scientiﬁc divisions.

Algebra: Classical Division

5. Divide a

2

+ a

−2

+ 1 by a

−2

+ a

−1

+ 1.

8. Solve the equation a



1 −

1 − x

2a

2



= x



a +

1 − (1 − a)

3a



Arithmetic: Scientific Division

6. Cube root of 30

265

512

?

Algebra: Scientific Division

3. Reduce the expression

1

a

−

1

1 −

a−1

1+a

.

The purpose aimed at by the mathematical curriculum was stated in the cata-

logs, of which the 1878–1879 catalog is typical:

The high importance of thorough mathematical training, both as a

logical gymnastic and as preparation for practical life, is constantly

kept in view. Instruction is given by means of Recitations and Lec-

tures in Pure and Mixed Mathematics during the ﬁrst two years.

More advanced practical courses are pursued in the Department of

Science.

7. Religion at UVM

Although mathematics is not directly aﬀected by the religious character of an

institution, there are some points where oﬃcial religious observances may aﬀect

instruction. Although the First Amendment to the Constitution forbids Congress

7. RELIGION AT UVM 43

to establish an oﬃcial national religion,

7

the states themselves were subject to no

such restriction, and Massachusetts was oﬃcially Congregationalist until 1828. It is

very noticeable that nine of the ﬁrst ten presidents of UVM were Congregationalist

or Presbyterian ministers, and no one thought it unusual that the University should

include Congregationalist worship in its oﬃcial ceremonies. The position of religion

at UVM during the nineteenth century now seems peculiar. Although founded for

the purpose of secular education and granted public lands for its sustenance, the

University was openly sectarian in its administration. The by-laws of the University

from 1885, Chapter III, §2, p. 11, state

There shall be public prayer in the Chapel every week-day morning

at such hour as the Faculty shall direct, preceded by the reading of

a portion of the Scripture, and other devotional exercises at their

discretion, which service it shall be the duty of the Faculty and

students regularly to attend.

§3. Every student shall attend public worship on the Lord’s

day. During that day nothing shall be done which would disturb

the quiet, or interfere with the religious observance of the day. All

days devoted to religious purposes by the Government of the land

shall be observed in such manner as may be prescribed by the

Faculty.

These rules would seem to preclude the enrollment of devout Catholics, for

whom deliberate participation in Protestant worship was oﬃcially a mortal sin until

the late 1960s. This fact may account for the paucity of French surnames among the

students and faculty at UVM, despite the fact that the French formed a signiﬁcant

portion of the population of Vermont. Almost anyone, of any religious persuasion or

none at all, would nowadays regard it as unjust to take public resources belonging

to the entire population and bestow them for the beneﬁt of one particular religious

group.

In the context of the time, however, one would say that the practice at UVM

simply reﬂected the unconscious world-view of the Protestant majority. Acceptance

of Catholics and Jews as an equal part of this national world-view took considerable

time, and it is noteworthy that other religions have still not achieved full acceptance.

The relaxing of these rules came about piecemeal. The Faculty exempted itself

from compulsory Chapel in 1892. Medical students were exempted in 1912. Only

in 1916 was the existence of non-Protestants rather grudgingly recognized, with

a statement that, “Students who, because of their religious aﬃliation, object to

attendance at Chapel, are excused by the President upon request being made to

him.” Compulsory Chapel was ﬁnally abolished in 1920, making UVM at last, fully

secular.

Not only Catholics and Jews, but also racial minorities have had to struggle

for acceptance at UVM. A summary of the experiences of all these groups can be

found in the article by Older ([5]).

7

Some lawyers argue even today that this amendment merely prevents the naming of any one

Christian denomination as the oﬃcial religion, in the sense of the national churches in England

and Scandinavia and the various nations that once proclaimed the Catholic Church as oﬃcial in

their constitutions. These lawyers argue that it is still permissible to declare the United States

an oﬃcially Christian nation.

CHAPTER 4

The Beginnings of Growth, 1885–1914

In the period from the end of the Civil War and up to the beginning of World

War I, many young Americans went to Europe in pursuit of an education. The

German universities, which were considered the ﬁnest in the world, were particu-

larly hospitable to young Americans, and such mathematicians as Felix Klein (25

April 1849–22 June 1825, professor at G¨ottingen) and Carl Neumann (7 May 1832–

27 March 1825, professor at several universities, eventually at Leipzig) had many

American students. The long-term eﬀect of this Germanization of American uni-

versities was a decreased emphasis on the British-style education for public service

and an increased emphasis on original research as a duty of the professor, an eﬀect

that was reinforced a generation later by European scholars who were refugees from

the Nazis.

All that was in the future, however. The ﬁrst generation of European-educated

Americans for the most part did very little research themselves. Instead they ac-

quainted their students with the contemporary trends in the most advanced centers

of mathematical research. New, high-quality American research universities were

being founded all the time, with Johns Hopkins (1876), Clark University (1889),

Bryn Mawr College (1885), and the University of Chicago (founded in 1856 as a

Baptist university and reinstituted by the American Baptist Education Society in

1890 with a large grant from John D. Rockefeller) being among the most promi-

nent. Meanwhile, the faculty at the long-established places like Harvard, Yale, and

Dartmouth were beginning to gain international reputations as well.

1. Personnel

Among the young Americans who obtained part of their education in Europe

during this period was McKendree Petty’s successor as the Williams Professor of

Mathematics, Archibald Lamont Daniels. He was born in Hudson, MI on 19 June

1849 and obtained the A. B. degree at the University of Michigan in 1876. He then

went to G¨ottingen and Berlin, where he took courses from such great mathemati-

cians as Hermann Amandus Schwarz (25 January 1843–30 November 1921) and

Karl Weierstrass (31 October 1815–19 February 1897). He returned to America

in 1881 and worked on a fellowship at Johns Hopkins until 1883. Hopkins at the

time was only slightly inferior to the great European universities. It had the best

of the new generation of American research mathematicians, including Simon New-

comb (born in Nova Scotia on 12 March 1835, worked for the Naval Observatory in

Washington, DC, died on 11 July 1909), William Edward Story (29 April 1850–10

April 1930, he was the chair of the mathematics department at Clark University

from its founding until 1921), Fabian Franklin (born in Hungary 18 January 1853,

died on 9 January 1939), and Thomas Craig (20 December 1855–8 May 1900) and

had enjoyed the services of the great British algebraists James Joseph Sylvester (3

45

46 4. THE BEGINNINGS OF GROWTH, 1885–1914

September 1814–15 March 1897) and Arthur Cayley (16 August 1821–26 January

1895).

In 1883, Daniels became instructor at Princeton University, taking over the

teaching duties of Henry Burchard Fine,

1

who had gone on leave. Daniels received

the D. Sc. degree from Princeton in 1885 and became instructor in mathematics at

UVM that year. The following year, upon the retirement of McKendree Petty, he

became the third Williams Professor of Mathematics.

Daniels’s research record resembles that of many other ﬁrst-generation Amer-

ican scholars. It consists of three expository articles in the American Journal of

Mathematics, Vols. VI and VII (1884–1885) explaining Weierstrass’s theory of ellip-

tic functions for the beneﬁt of Americans. Daniels has the distinction of being the

only UVM faculty member ever listed in Poggendorﬀ’s

2

Biographisch-Literarisches

Handw¨orterbuch zur Geschichte der exacten Wissenschaften, Bd. 4 (1904), p. 295.

Poggendorf—or rather, his successor—credits Daniels with four years of study in

G¨ottingen, two in Berlin, and one at the Johns Hopkins University “[in] Cambridge,

Mass.”

Daniels preserved the notes from Weierstrass’s 1881 course on analytic function

theory, which were not published with Weierstrass’s collected works and are still of

interest to historians of mathematics. These notes were inherited by his grandson,

Robert V. (Bill) Daniels (4 January 1926–28 March 2010), who had a distinguished

career at UVM as a specialist in Soviet history and a period of service as a state

Senator from Chittenden County.

1.1. Expansion of the faculty. Daniels set about revamping the curriculum

to suit his own background, using the textbooks of Simon Newcomb as the base.

(Physics and mathematics were being taught out of the College of Agriculture

at this time.) By the mid-1890s, he was oﬀering courses in ordinary and partial

diﬀerential equations, projective geometry, and “heat, magnetism, and electricity.”

In 1895 and 1896, he oﬀered a course in geometric function theory and elliptic

functions. Sophisticated material indeed, for an American university of the time!

This being a time of expansion for the University, Daniels regularly had the

assistance of an instructor in teaching the courses. The most interesting of these was

Fred Merritt Corse, born in Bakersﬁeld, VT on 7 September 1864, who received

his A. B. at UVM in 1888, then became Curator of Buildings, Secretary of the

Faculty, Registrar, Instructor in Mathematics, and Instructor in Political Economy

over the period 1891–1894 while also obtaining a master’s degree from Columbia

University. In 1894, he went on leave of absence. After leaving UVM he taught at

Brooklyn Institute, then joined the Singer company in 1899, which he left in 1902

to join the New York Life Insurance Company. As manager of the Russian division

of the company in Petersburg, he spent 16 years getting to know the Russians.

He returned to America with his family after the Russian Revolution and, in two

1

Born 14 September 1858, died 22 December 1928. Until 1969, the mathematics department

at Princeton was housed in a magniﬁcently paneled building named Fine Hall. In that year, it

moved into a section of a tall tower near the football stadium, dubbed “Finer Hall” by Professor

Robert C. Gunning.

2

Johann Poggendorﬀ (29 December 1796–24 January 1877) was a German physicist who

undertook an ambitious plan to compile a catalog of scientists—that is, all who were recognized

in Europe. This Handbuch was the result.

1. PERSONNEL 47

long articles in the New York Times in 1918,

3

urged intervention to overthrow the

Bolsheviks. He appears among a group of social revolutionaries in a photograph

opposite page 34 of George Kennan’s book Russia Leaves the War (Atheneum,

New York, 1967). He died in New Canaan, CT on 20 August 1927. In 1952, the

Fred and Fanny Corse Professorship was established at UVM. There is also a Corse

fellowship, awarded annually to a UVM graduate holding a Bachelor of Arts degree

and planning to teach languages in a University.

Mr. Corse was followed by Allison Wing Slocum, who was actually a profes-

sor of physics but taught courses in the Department of Mathematics beginning

in 1894, leaving Prof. Daniels free to teach more advanced mathematics courses.

Slocum, who was born in Dartmouth, MA on 22 April 1866 and died in Boston on

15 December 1933, obtained a bachelor’s and master’s degree from Haverford, then

went on to Harvard to obtain a second master’s degree in 1891. He was Tyndal

scholar at Harvard in 1890–1891 and Morgan scholar at the University of Berlin in

1891–1892. Physics was beginning to come into its own at UVM at this time, even

though Slocum was its only professor. Williams Science Hall was built in 1895,

named for the industrialist Edward H. Williams

4

of the Baldwin Locomotive Com-

pany in Philadelphia, who donated $30,000 to equip the building, an assignment

that was carried out by A. W. Slocum.

Two other instructors in mathematics were hired during the 1890s: Warren

Gardner Bullard and Arthur Dexter Butterﬁeld. Bullard’s contact with UVM was

rather brief and superﬁcial on both sides. He was born in Hinsdale, NY on 25

February 1867 and graduated from Brown University in 1892. After spending one

year as an instructor at the Elmira (New York) Free Academy, he entered graduate

school at Clark University, where he received the Ph. D. in 1896 for a dissertation

“On the general classiﬁcation of plane quartic curves,” written under the direction

of W. E. Story, who was mentioned above. He spent four years as an instructor at

UVM, then left to become a faculty member at Syracuse University, where he rose

to the rank of full professor by 1909. He eventually published his dissertation and

was co-author of a textbook on college algebra, published in 1908. He died on 16

February 1927.

Arthur Dexter Butterﬁeld had a long and varied career, intersecting with UVM

over two periods. He was born on 13 October 1870 into an old and distinguished

family in Dunstable, MA. (He was the 15th generation to live in his house.) He

received the B. S. degree from Worcester Polytechnic Institute in 1893 and then,

after serving there as an instructor in civil engineering, an M. S. from the same

institution in 1898. In that year, he joined UVM’s faculty as an instructor in civil

engineering. He was named an assistant professor of mathematics in the Depart-

ment of Engineering in 1900, so that apparently UVM now had two mathematics

departments.

In this period of his career, he became the second UVM mathematician—the

ﬁrst, as noted above, was James Dean—to live in the Lucy Ann Abbot House at 41

3

See “Fred Merrit Corse returns to New York after 16-year sojourn in Russia, describes

conditions,” (New York Times, 29 April 1918, p. 6, col. 4) and “Describes conditions in Russia

and urges intervention against the Bolsheviki,” (New York Times, 23 June 1918, Sect. III, p. 4,

col. 1).

4

He was born in Woodstock, VT on 1 June 1824 and graduated from the UVM College of

Medicine. He eventually abandoned medicine to work in the railroad industry. He died in Santa

Barbara, CA on 21 December 1899.

48 4. THE BEGINNINGS OF GROWTH, 1885–1914

South Prospect Street, now Nicholson House, named after UVM Professor George

Nicholson (discussed below). He went on leave from UVM in 1904 to obtain an

A. M. from Columbia.

He left UVM in 1908 to be assistant professor of mathematics and geodesy at

Worcester Polytechnic Institute, which made him a full professor in 1914. During

this time, he showed considerable skill in fundraising and alumni relations. In

1917, during America’s participation as a belligerent in World War I, he joined

the Aviation Corps as a captain and was attached to General Pershing’s staﬀ.

He returned after the Armistice as a lieutenant colonel, having been awarded the

prestigious French L´egion d’honneur. He resigned from Worcester Polytechnic in

1920 to become director of education at the Norton company.

Returning to UVM in 1938, he became professor of mathematics and geodesy

and head of the mathematics department, a position he resigned in 1942. He seems

to have been a popular teacher, and his students referred to him aﬀectionately as

“Butt.” After World War II, he became director of Veterans’ Education at UVM,

having obtained a Doctor of Engineering degree from Worcester Polytechnic in 1945.

He resigned as director of Veterans’ Education in 1948 because of a desire to engage

in other work. He was an acquaintance of Atwater Kent, from whom he requested

money to build an observatory at UVM.

5

His vaunted fund-raising ability seems to

have failed in this case. The money was not forthcoming, and the observatory was

not built. He died of arteriosclerosis complicated by nephrosclerosis in Burlington

on 22 August 1955.

A. D. Butterﬁeld had broad intellectual interests, and his two publications re-

ﬂect an intense interest in the history of science. The ﬁrst was perhaps his master’s

thesis, a 57-page pamphlet bearing the title History and Development of Triangula-

tion in Massachusetts, published in 1898. The other is a 168-page work entitled A

History of the Determination of the Figure of the Earth from ARC Measurements,

published by the Davis Press in Worcester, MA in 1906. It is thus not surprising

that he eventually was named professor of mathematics and geodesy.

The resources mentioned above had increased during the 1890s, as shown by the

construction of the Williams Science Hall. The minutes of the Board of Trustees’

meeting of 1 December 1891 (Vol. IV, p. 224) note that

the bequest of ﬁfty thousand dollars to the University to found a

Professorship of Mathematical, Natural, or Technic Science, by the

will of the late Hon. Edwin Flint of Mason City, Iowa, and alumnus

of the class of 1836, was announced by the President.

Flint, born in Braintree, VT on 25 May 1814, was a lawyer and judge in Wis-

consin and Iowa. He died in Iowa on 15 October 1891. The ﬁrst Flint Professor of

Mechanics and Bridge Engineering was Volney Giles Barbour, who was mentioned

above. Only once has this professorship been held by a mathematician (Percy

Fraleigh, during the 1950s).

5

Arthur Atwater Kent, Sr. was born in Burlington on 3 December 1873. He was a ﬁrst-

year student at Worcester Polytechnic in 1895, which is probably where he met Butterﬁeld. He

patented the Unisparker automobile ignition coil, which was an industry standard for about 50

years. He is most famous for the Atwater Kent radios, which were wildly popular, despite being

expensive. He died in Hollywood, CA on 4 March 1949.

2. CURRICULUM 49

2. Curriculum

Daniels’s course on analytic function theory was supplemented with readings

from Dur`ege’s book on Riemann’s theory of complex variables.

6

This course, how-

ever, was oﬀered irregularly. Really, the best mathematics oﬀered during this period

was taught in the Department of Physics department. In 1899, Slocum oﬀered a

course in mathematical physics using as texts Riemann’s

7

Partielle Diﬀerentialgle-

ichungen—would we dare to use a textbook in a foreign language nowadays?—and

Fourier’s

8

Analytical Theory of Heat. He also used Maxwell’s Heat and Duhem’s

9

Potentiel thermodynamique. As mentioned above, Daniels reciprocated by oﬀering

a course in “Heat, Magnetism, and Electricity.”

For unknown reasons, Prof. Daniels ceased to teach the more advanced courses

after 1904. The academic students (exclusive of medical students) numbered about

350 at this time, of whom 164 were ﬁrst-year students. These ﬁgures suggest a high

dropout rate. Whether mathematics students contributed to this high failure rate

is unclear. Certainly, the admission standard for the University (as distinct from

the Agricultural College) in 1905 was rigorous enough, consisting of

(1) Arithmetic, including the metric system; (2) Algebra, includ-

ing the four species, factoring, largest common divisor and lowest

common multiple, fractions, theory of exponents, involution, ele-

mentary forms of binomial theorem, evolution, surds, simple [lin-

ear] equations with one, two and three unknown quantities, simple

quadratic equations. In the instruction the aim should be the for-

mation of the habit of clear and concise expression, and to this end

the class room work should be largely oral.

II. Solid and Spherical Geometry.

The word species has been used in diﬀerent senses in algebra. In the writings

of Diophantus, it means what we call the unknown in an equation. In those of

al-Khwarizmi, there are species of equations, since only positive coeﬃcients were

considered. Thus, one could have quadratic equations of the form ax

2

= bx + c,

ax

2

= c, ax

2

+ bx = c, ax

2

+ c = bx, each of which required a separate diagram

to illustrate its solution geometrically. Cases where a = 0 are linear equations, and

those with c = 0 have 0 as a root and become linear when divided by x.

The following year these requirements were expanded to include trigonometry,

simple permutations and combinations, determinants, linear equations, graphical

6

Heinrich Dur`ege (born in Poland on 13 July 1821, died in 1893) was a professor at the

University of Prague. His book went through at least four German editions before being translated

into English. Although the notation has changed considerably by using the language of manifolds,

the classical examples upon which an intuitive understanding of Riemann surfaces must be based

are discussed with great clarity in this book.

7

Georg Friedrich Bernhard Riemann (17 September 1826–20 July 1866), one of the greatest

geometers and analysts of the nineteenth century.

8

Jean-Baptiste Joseph Fourier (21 March 1768–16 May 1830), famous chieﬂy for this work,

which introduced Fourier series and integrals.

9

Pierre Duhem (10 June 1861–14 September 1916), best known for precisely this work.

50 4. THE BEGINNINGS OF GROWTH, 1885–1914

treatment of equations, Descartes’

10

rule of signs, and Horner’s

11

Method “but not

Sturm’s

12

functions or multiple roots.” Descartes’ rule of signs gives an upper bound

on the number of positive and negative roots a polynomial with real coeﬃcients can

have. Sturm’s functions, modiﬁcations of the remainders that arise in ﬁnding the

greatest common divisor of a polynomial and its derivative, can be used to ﬁnd

the exact number of real roots in a given interval, provided the polynomial has no

repeated roots.

Admission by high school certiﬁcation was supplemented by the College Board

Examination sometime during the ﬁrst decade of the twentieth century.

3. New Personnel

The engineering mathematics department began to grow in 1905, adding as-

sistant professor George Monroe Brett to the faculty. He was born in Auburn,

ME on 4 November 1875 and graduated from Bowdoin College in 1897. He came

to Burlington in 1903 as an assistant principal at Burlington High School. Local

newspapers reported in July 1910 that he and Prof. Butterﬁeld were surveying the

Winooski River. He must have gone abroad soon afterward, as he was listed as a

passenger on the Lusitania, which arrived in New York on 13 September 1912. Two

years later, now a professor at City College, he married Agnes Baldwin, a noted nu-

mismatist. He served in the army during World War I. His academic specialty was

accounting, and he is the author of Fundamental Accounting in the CCNY series,

published by Lancaster Publishing Company in 1928 (541 pages). He continued as

professor at City College until his death on 7 November 1941. He is buried at St.

Paul’s Episcopal Church in Newark, NJ.

In 1908, the engineering mathematics faculty gained professor Evan Thomas,

who is the author of many biographies and reminiscences of UVM mathematicians.

He was born on 25 August 1853 in Wales, as one would probably guess from his

names. In fact, he was born in the Rhondda Valley, made famous in the 1939 novel

How Green Was My Valley by Richard Llewellyn, which in turn was made into

a movie in 1941 starring Maureen O’Hara and Walter Pidgeon. In 1867, at the

age of 14, he was apprenticed to a ﬁrm of clothiers, and his parents emigrated to

Ohio. While visiting his parents at the age of 18, he decided to enroll in Dennison

University, where he obtained the B. S. degree in 1876. He became a Congrega-

tionalist minister at Vershire, VT in 1880, then spent 3 years as a pastor in the

Ludlow/Plymouth area, where he also managed the local newspaper. He came to

Essex Junction as pastor in 1886. In 1892 he taught a semester of mathematics at

UVM. Eventually, he became head of engineering mathematics and mechanics at

UVM, retiring in 1928, although he came back to teach for one semester in 1930.

He was the author of several articles on pedagogy, as well as Chapters XVII and

XVIII in the second edition of Walter Hill Crockett’s History of Lake Champlain

(McAuliﬀe Paper Company, Burlington, 1936). Prof. Thomas’s two chapters tell

of the raising of two of Benedict Arnold’s ships, which were sunk by the British

10

Ren´e Descartes (31 March 1596–11 February 1650), one of the inventors of analytic geom-

etry and calculus.

11

William Horner (1786–22 September 1837), inventor of a method of approximating roots

of an equation, although his claim to this honor is controversial. Besides the fact that there were

contemporaries who worked in this area, a method very like his was known to the ancient Chinese.

12

Jacques Charles Fran¸cois Sturm (29 September 1803–18 December 1855), famous for his

work on series expansions of solutions of second-order linear diﬀerential equations.

3. NEW PERSONNEL 51

in October of 1776, and of the construction of the bridges across Lake Champlain.

After he retired, he traveled in Europe and was horriﬁed by Kristallnacht in Ger-

many, which shattered many illusions about the superior civilization of Germany.

He wrote back to the United States that he was sure this was not typical of the

Germans and that the aberration would soon be corrected. He died in Burlington

on 3 September 1947.

Growth continued in the Department of Engineering Mathematics in 1914.

There seems to have been some general reorganization of UVM around this time.

After 1911 the catalogs refer to the “College of Arts and Sciences” and the “College

of Engineering,” where previously these units had been referred to as the “Depart-

ments of Arts and Sciences” and the “Department of Engineering.” In 1914, A. L.

Daniels retired from the Academic Mathematics Department, bringing an end to

the ﬁrst phase of what can be seen in retrospect to be UVM’s ﬁrst move to join the

worldwide mathematical community.

CHAPTER 5

Another Generation of Struggle, 1915–1954

A. L. Daniels’s successor, the fourth Williams Professor of Mathematics, was

Elijah Swift, like Daniels a part of the generation of young Americans who obtained

their education in Europe. Having obtained his European education a quarter-

century later than Daniels, however, he became a more prominent mathematician.

He was born in Buﬀalo, NY on 23 October 1882 and graduated from Harvard in

1903. In that year, he presented a paper before the American Mathematical Soci-

ety (which had been founded as the New York Mathematical Society in 1888), “On

the condition that a point transformation of the plane be a projective transforma-

tion.” This paper was published in the 1904 Bulletin of the American Mathemati-

cal Society. He then went to G¨ottingen, where he studied under the world-famous

mathematician David Hilbert (23 January 1862–14 February 1943). His notes from

Hilbert’s 1905–1906 course in integral equations, in which the now-standard con-

cept of a Hilbert space was introduced, were left in the mathematics department

and were turned over to the library’s Special Collections in 1990. He received the

Ph. D. degree magna cum laude in 1907 for a dissertation, “

¨

Uber die Form und

Stabilit¨at gewisser Fl¨ussigkeitstropfen,” (On the shape and stability of drops of

certain liquids). Then, like A. L. Daniels, he took up a position at Princeton, from

which he was hired by UVM.

Although he published a number of papers, we note here just two that are

typical:

• “Note on the second variation in an isoperimetric problem,” Bulletin of

the American Mathematical Society, XIV (1908).

• “Canonical forms for ordinary homogeneous linear diﬀerential equations

of the second order with periodic coeﬃcients,” American Journal of Math-

ematics, L (1928).

In Elijah Swift, UVM had found one of the best American mathematicians available

at the time. In 1931, he became Dean of the College of Arts and Sciences, retiring

from that position in 1948. He died on 21 July 1957. (In a 1990 interview, Professor

Nicholson said that Swift suﬀered from dementia for some time before he died.)

Despite Swift’s outstanding qualiﬁcations, the department was to be hard-

pressed to sustain the advances made under A. L. Daniels, mostly because of ﬁnan-

cial constraints, which at one point threatened the very existence of the university.

The curriculum declined over this period to a very elementary level, especially after

Elijah Swift left oﬀ teaching to become a dean.

1. New Personnel

During the period of “Coolidge prosperity” of the 1920s, UVM added a large

number of new faculty members, and was able to add even one more during the

53

54 5. ANOTHER GENERATION OF STRUGGLE, 1915–1954

Great Depression. The explanation for this seeming paradox will be given in Sect.

3 below. Right now, we merely note the additions.

Along with Prof. Swift, the Mathematics Department of the College of Arts and

Sciences hired James Edward Donahue, and these two were the core of the Mathe-

matics Department for the next 17 years. J. E. Donahue was born in Fairﬁeld, VT

on 25 April 1880. He graduated from Burlington High School in 1897 and from

UVM in 1902. He obtained the M. A. degree from Harvard in 1910 and remained

there until 1912, when he became an instructor at Washington University in St.

Louis. After three years at UVM he joined the Navy for the duration of America’s

participation in World War I, then returned to the Department of Mathematics. In

1930 he went on leave from UVM and obtained a doctoral degree from Columbia

University in 1931 for a dissertation “Concerning the geometry of the second de-

rivative of a polygenic function,” written under the direction of Edward Kasner (2

April 1878–7 January 1955). Tragically, he lived only one year after obtaining this

degree, dying of a cerebral hemorrhage while on vacation in Maine on 15 August

1932.

Swift and Donahue were joined by a succession of instructors, and gradually

more and more professors were added. Instructors Howard Guy Millington and

Fred Walter Householder were hired in 1920–1921; both of them later became as-

sistant professors. Millington’s appointment was in the Department of Engineering

Mathematics.

H. G. Millington was born 28 August 1887 and received the B. S. degree from

Rensselaer Polytechnic Institute. He became Assistant Coordinator of Civilian Pilot

Training at UVM in 1942. He retired from UVM in 1954 and died on 25 February

1965.

F. W. Householder, who had served in the Army Engineering Corps during the

last six months of World War I, was born in Jackson, TN on 7 April 1884. He

received the B. A., M. A., and LL. B. degrees at the University of Texas. He was

actually an historian who happened to know some mathematics. In those post-

War years, mathematicians were hard to ﬁnd. Householder seems to have worked

out well at ﬁrst, but suﬀered from “burn-out” in the 1930s. (Heath Riggs, who

took courses from him, conﬁrmed in a 1990 interview that this judgment, made by

Elijah Swift himself, is accurate.) Householder went to California to work in the

shipbuilding industry at the beginning of World War II, and Swift took advantage

of this situation, together with the University’s precarious ﬁnancial position (all

salaries had just been reduced by 25%) to urge him to resign. He died in Johnston,

RI on 3 June 1950.

Householder had been replaced by Instructor Douglas Tillman McClay in 1941.

McClay was born in Boston on 20 December 1915, graduated from Harvard in 1936,

and obtained a Ph. D. at Harvard in 1940. He remained at UVM until 1949 and

died in Burlington on 12 July 1982. Dean Swift expressed the opinion that McClay

was superior to Householder as an instructor.

The year 1923 saw the addition of the longest-serving member of the UVM

faculty. George Hubert Nicholson was born on Prince Edward Island on 12 March

1898 and attended Mount Allison University in New Brunswick, where he received

the A. B. in 1922. When the Canadian scholarship he had been hoping for was

preferentially awarded to a veteran of the war, he went to Harvard to obtain a

master’s degree. He taught at UVM, in some periods as much as 12 hours per

1. NEW PERSONNEL 55

week, for ﬁfty years, rising to the rank of associate professor, despite not having

a Ph. D. Although he oﬃcially retired in 1963, as required by UVM statutes, he

continued to teach as an adjunct until 1973.

Despite the sometimes-heavy teaching load, he found time to write a brochure

on mathematical instruments that is still in his ﬁle in the UVM Archives. Shortly

after he came to UVM, some students asked him to coach a hockey team. He

did so, spending $300 of his own money to ﬂood a ﬁeld near the site of what is

now the Bailey–Howe Library, and thus became the founder of the UVM Hockey

Team. As mentioned above, when he retired permanently in 1973, the Lucy Ann

Abbott House, which was the home of the Mathematics Department at the time,

was renamed Nicholson House in his honor. He died in Burlington on 24 January

1995.

Ceremony in 1974 honoring George Nicholson’s 50 years of ser-

vice to the University by renaming the Lucy Ann Abbot House

as Nicholson House. At left is N. James Schoonmaker, chair of

the Department. At right is Joseph Izzo, acting dean of the Col-

lege of Engineering Mathematics and Business Administration.

The woman in the photo is Margaret Essery (Peggy) Nicholson

(1 Feburary 1911–29 September 1994), wife of George Nicholson

and, like him, a native of Prince Edward Island.

Another instructor, added in 1924, was Horace Alpheus Giddings, who was

born in Farnworth, NH on 6 January 1902 and obtained the B. S. degree at the

University of New Hampshire in 1923. He remained at UVM until 1930, when

he entered graduate school at the Massachusetts Institute of Technology. He be-

came an instructor in mathematics there in 1933, while still working on a Ph. D.

He obtained the Ph. D. at MIT in 1937 and became an assistant professor at the

Armour Institute of Technology in Chicago, which became the Illinois Institute of

Technology in 1940 after merging with Lewis Institute. He died in Volusia, FL on

11 December 1984 and is buried in Tamworth, NH.

56 5. ANOTHER GENERATION OF STRUGGLE, 1915–1954

The Arts and Sciences Mathematics Department in 1925. Back

row, left to right: Nicholson, Householder, Donahue. Front row,

left to right: Swift, Giddings.

In 1928, Percy Austin Fraleigh became an assistant professor, bringing the total

faculty to 7 (four professors and three instructors). Fraleigh was born in Hyde Park,

NY on 12 April 1895 and received the degrees of A. B. (1917), A. M. (1918), and

Ph. D. (1927) at Cornell. He remained at UVM until 1963. As mentioned above,

during his last thirteen years at UVM he was the Flint Professor of Mathematics,

the only mathematician to occupy this endowed chair. He died in Burlington on 27

December 1980.

The next new professor, James Atkins Bullard, was appointed in both the Arts

and Sciences and Engineering Mathematics Departments, replacing Evan Thomas

in the latter. He was born in Parsippany, NJ on 3 February 1887 and received the

Ph. D. from Clark University in 1914,

1

as his namesake Warren Gardner Bullard

had done 18 years earlier. He was an instructor at Worcester Polytechnic Institute

until coming to UVM in 1928. He published his doctoral dissertation as the article

“On the structure of ﬁnite continuous groups” in The American Journal of Mathe-

matics, XXXIX, No. 4 (October 1917). He was co-author of a textbook on plane

and spherical trigonometry, published by D. C. Heath, Boston, in 1922 (revised edi-

tion 1930). He remained at UVM until 1953, becoming the ﬁfth Williams Professor

of Mathematics in 1944 upon the resignation of Dean Elijah Swift from the Mathe-

matics Department. He was the last person on whom this title was conferred until

it came to the present author in the year 2000. He came out of retirement for two

years in the mid-1950s to teach again. He died in Parsippany, NJ on 10 April 1959.

1

His thesis adviser was Henry Taber, born at Staten Island, New York on 10 June 1860. Taber

was a student of W. E. Story at Johns Hopkins, receiving the Ph. D. in 1888. He then joined Story

to form the core of the mathematics department at the newly founded Clark University. He died

on 6 January 1936.

2. CURRICULUM 57

The last of the new faculty, Myron Ellis Witham, a civil engineer, was hired

in 1932. He was born in Rockport, MA on 29 October 1880. He was a prominent

football player at Dartmouth, the hero of its 1903 team. In addition to teaching

mathematics at UVM through 1972, he also coached the UVM football team

2

and

taught physical education. He lived for a time in the late 1930s in what is now

Nicholson House. He died in Burlington on 7 March 1973.

The extended “Coolidge prosperity,” which had lasted all through the 1930s

at UVM, came to an abrupt end in 1941, for two reasons, one of which will be

discussed in the next section but one. The other reason was the attack on Pearl

Harbor on 7 December 1941. During the years of American participation in World

War II (1942–1945), when enrollment had shrunk to half of its normal level as

students enlisted in the armed services in large numbers, the faculty members just

listed barely managed to keep mathematics going at the University of Vermont.

2. Curriculum

Despite the large number of new faculty, there was little, if any, innovation in

curriculum during this time and essentially no research. Indeed, only ten courses

were oﬀered in the department at this time, and they were all elementary, with the

single exception of theory of functions. They were, however, heavily enrolled, so

that the ﬁve faculty members were kept quite busy teaching them. Although the

curriculum was revised when Swift and Donahue took over, it remained rudimen-

tary. Calculus was followed by Synthetic Geometry and Theory of Functions. That

was the entire curriculum. The Engineering Mathematics Department continued to

teach mechanics and diﬀerential equations and duplicated the teaching of analytic

geometry and calculus. (There was a great deal of duplication at this time; the

Engineering College even had its own English Department.)

The large growth in faculty during the 1930s discussed above reﬂects the growth

in the size of the student body rather than any growth in curriculum. The courses

that were added during this time, while of practical value to the students, no doubt,

were not by any means advanced mathematics courses. Mathematics of ﬁnance was

added in 1932, and a course in the teaching of algebra and geometry in 1934. The

admission requirements of 30 years earlier remained in the catalog unchanged. The

impression of stagnation created by this curriculum is conﬁrmed by a person who

actually took the courses. Heath Riggs, who graduated from UVM in 1940, stated

in a 1990 interview that he took mostly physics courses, since there wasn’t much

of interest in the Mathematics Department. He described Fraleigh and Nicholson

as excellent teachers and competent mathematicians, but conﬁrmed what other

sources suggest, that Householder was an incoherent lecturer.

In summary, this was a period when the University was overworking the teach-

ing faculty in order to serve a large number of students, leaving the faculty little

time to develop new courses and no time for research. It was only near the end

of World War II that some real updating of the curriculum began, and then very

slowly. Courses in advanced calculus, diﬀerential equations, complex variables, and

inﬁnite series were added in 1944. A course covering Lebesgue integration appears

for the ﬁrst time in 1946. The ﬁrst tentative step into graduate education appears

in 1947, with the addition of a master’s thesis course.

2

Football was abolished at UVM in 1974.

58 5. ANOTHER GENERATION OF STRUGGLE, 1915–1954

3. The Financial Situation

Despite the dismal economic situation in the United States during the Great

Depression of the 1930s, UVM’s thirteenth president, Guy Bailey,

3

seemed to be a

miracle-worker, prolonging the “Coolidge prosperity” of the 1920s, keeping salaries

up, and expanding the physical plant and the faculty. Only after his death was it

discovered that he had in fact been running huge deﬁcits, and that the University

was half a million dollars in debt. An emergency bailout of $260,000 was provided

by the legislature, with the stipulation that a certain amount of money (set at

precisely $68,880) was to be held in reserve each year to pay the interest on the

debt. This bailout came in early November 1941, just before Bailey’s successor,

John Schoﬀ Millis,

4

took oﬃce.

These events all took place less than a month before the attack on Pearl Harbor

took the United States into World War II. (I cannot resist pointing out that when

the legislature voted the bailout, it also voted a declaration of war on Germany

by the State of Vermont! That was a month ahead of the rest of the country.)

UVM students ﬂocked to enlist in the armed services, and by 1944, the enrollment

of 1300 students in 1942 had fallen by more than half. For an institution highly

dependent on tuition, this inevitably led to further deﬁcits. Millis, however, proved

to be a very capable president and managed to reduce the debt by nearly half a

million dollars before leaving oﬃce in 1949. This eﬀort was no doubt facilitated by

an inﬂux of returning veterans after the war.

4. The Mathematical Environment

Mathematics at UVM was a service discipline at this time. The department in

Arts and Sciences was merged with the Engineering Mathematics Department to

form a single Department of Mathematics and Mechanics in the College of Technol-

ogy in 1946. There were persistent rumors that this move was made because of the

terms of the Wilbur Fund, established by UVM trustee James Benjamin Wilbur.

5

It was asserted that this fund, which provided money for the College of Arts and

Sciences, speciﬁed that the College not grow beyond a ﬁxed number of students.

With mathematics majors being counted as engineers, the College had some room

to grow in other areas. This scenario sounds plausible, but some details need to be

added.

Wilbur left the money to the University of Vermont, not to the College of

Arts and Sciences. But, recall that when the institution known as the University

of Vermont and State Agricultural College was established, the portion of it that

bore the name University of Vermont was essentially only the College of Arts and

Sciences, together with the Medical School. According to his bequest,

6

3

Born in Hardwick, VT on 7 May 1876, died on 22 October 1940, he became president of

UVM in 1920 and remained in that oﬃce until shortly before his death.

4

Born in Palo Alto, CA on 22 November 1903, died in Cleveland Heights, OH on 1 January

1988.

5

Born in Cleveland on 11 November 1856, he apparently made his considerable fortune at

the Royal Trust Company in Chicago, which he founded in 1891. He gave money to UVM to build

the Ira Allen Chapel in 1925, and set up a trust for the money that is now in the fund. He died

on 28 August 1929.

6

Wilbur also speciﬁed that certain of his heirs were to have a lifetime claim on the money,

one of them being his son James Jr., who died in 1933. The widow and son of the latter sued the

University seeking to recover the money. Apparently UVM’s title to this money is now secure and

4. THE MATHEMATICAL ENVIRONMENT 59

The University of Vermont Trust, hereinabove referred to shall not

be created unless the Legislature of Vermont pass a law limiting

the number of students attending the University of Vermont in any

one year to one thousand, and no students from outside the State

to be admitted until after native born Vermont students, who ap-

ply and qualify, are admitted, or the Trustees of the University of

Vermont, if they have the authority to do so, pass a similar reso-

lution. This number of one thousand may be added to at the rate

of two hundred and ﬁfty for every one hundred thousand increase

in the number of inhabitants of the State over the United States

census taken in 1920, as determined by the best available informa-

tion obtainable in the State of Vermont. As soon as this provision

is carried out by the Legislature of Vermont or the Trustees of the

University, the Trustee shall constitute and set up the trust to be

known as the “UNIVERSITY OF VERMONT TRUST” for the

purposes and in the manner and on the conditions set forth in this

indenture.

The Wilbur Fund played a role in a charter change made in 1955. At that time,

UVM’s ﬁfteenth president, Carl Borgmann,

7

asked the legislature to stipulate that

the umbrella entity known as The University of Vermont and State Agricultural

College was an instrumentality of the State of Vermont and therefore eligible for

ﬁnancial support from the legislature. He had been disturbed by the fact that

students in the branch known as the University of Vermont had to pay $625 per

year in tuition, while students in the legislatively subsidized State Agricultural

College paid only $225. The ﬁve academic units of the combined entity (Arts and

Sciences, Medicine, Agriculture, Education and Nursing, and Technology) were left

just as they had been created under President Millis ten years earlier, so as to

protect the endowments, particularly the Wilbur Fund.

By 1946, the faculty in mathematics consisted of professors Bullard and Fraleigh

and assistant professors McClay, Millington, Nicholson, Witham, and Larrivee.

8

there are no more Wilbur heirs claiming it. The enrollment limit of 1,000 amounted to a little less

than one-third of one percent of the Vermont population of 353,000 in 1920. If that proportion

had been maintained, the allowable enrollment at UVM would now be slightly less than 2,000. In

fact, in-state enrollment alone at UVM is now about 4,000 and total enrollment is 13,000, which

is more than 2% of the population of the state. The conditions of the Trust are complicated,

however, and subject to varying interpretations, depending on how one deﬁnes the entity named

as The University of Vermont. By excluding the professional and graduate schools, one might be

able to argue that those conditions are being met. But it is also possible that the entire Trust

has been legally amended so that these conditions no longer apply at all. Moreover, the reference

in the trust to “native born Vermont students” appears to be of questionable legality. There are

various ways of establishing one’s eligibility for the Vermont-resident tuition rate at UVM, but

one that always works is having graduated from a Vermont high school. The fact that a student

may happen to have been born elsewhere is not an issue.

7

Born in Mount Washington, MO on 3 June 1905, he received a Ph. D. at Cambridge in

1934. He served as UVM’s sixteenth president from 1952 to 1958. He died in Livermore, CO on

29 November 1998.

8

Jules Alphonse Larrivee was born in Fall River, MA on 5 August 1909. His father, a

carpenter, had been brought there from Qu´ebec in 1883 at the age of 2. J. A. Larrivee received

the S. B. degree at MIT in 1930, an M. A. at George Washington University in 1935, and a Ph. D.

from the Catholic University of America in 1942. He is listed in the 1933 Washington, DC directory

as an astronomer, but in the 1950 census, where his address is again Fall River, his occupation

60 5. ANOTHER GENERATION OF STRUGGLE, 1915–1954

5. The Kenney Award

It becomes increasingly diﬃcult to trace the present whereabouts of UVM

alumni in the twentieth century, partly because of their large numbers, and partly

because the University has not published a general catalog of them since 1902. One

who absolutely must be mentioned, however, is John Francis Kenney (21 January

1897–4 May 1985) of the class of 1920, who was a professor at Northwestern and

the University of Wisconsin. He was a mathematical statistician who published

many articles in this area and wrote a two-volume textbook, The Mathematics of

Statistics, published by Van Nostrand, which went through three editions. After

retiring from the University of Wisconsin, he came to Brandon to live. In 1967, he

gave the University $5,000 to establish an annual prize in memory of his parents

for the best graduate work in mathematics.

9

The Kenney prize has been awarded

annually ever since.

is given as professor. In a 1990 telephone interview, Professor Fishback said that Larrivee left

UVM in 1953 to look for work on the west coast, having attained the rank of associate professor

at UVM. He is listed on the voting rolls in Los Angeles in 1960. He died in Benton, OR on 27

September 1974.

9

The careless use of the word “mathematics” to stand for “mathematics and statistics” must

now be guarded against, since the present title of the department contains both names. In the

mid-1980s, one mathematician objected to awarding the Kenney prize to a statistician, citing

the language of the bequest. At that time, it had been forgotten that Kenney was, in fact, a

statistician!

CHAPTER 6

Into the Mainstream: 1955–1975

In the years after World War II, the University expanded rapidly and has

continued to do so ever since. Because of the increase in the number of personnel

and the proliferation of courses and programs, we are forced to make rather drastic

selections in our discussion of this period. By no means all the people hired into

the department will be discussed, only those who remained for some time.

1. Personnel

The ﬁrst woman to teach mathematics at UVM arrived a few years after the

war. She was Ruth Gertrude Simond, who was born on 7 March 1904. She re-

ceived the B. A. and M. A. degrees from Boston University and the Ph. D. from the

University of Michigan. She then taught at Hampton Institute (a historically black

college in Hampton, VA), Berea College (Berea, KY), Heidelberg College (Tiﬃn,

OH), and Morningside College (Sioux City, IA) and served as a cryptanalyst for the

Navy during the war before coming to UVM as assistant professor of mathematics

in 1948. She died on 15 September 1958, having apparently resigned her position

because of ill health the previous June. She is buried in Franklin, NH.

In 1951, the University hired an assistant professor, William Thompson Fish-

back (born in Milwaukee, WI on 28 January 1922, received the Ph. D. at Harvard in

1952, died in Richmond, IN on 9 March 2014), and an associate professor, William

Scribner Kimball (born in Plainﬁeld, NJ on 26 August 1886, died in Burlington on

7 March 1963). I was able to contact Prof. Fishback through my colleague Prof.

Dan Archdeacon, who had been his student at Earlham College in Richmond, IN.

Prof. Fishback had moved there after leaving UVM. Although he was at UVM for

only two years, he was able to provide me with a few details about other ﬁgures in

the department.

Kimball was a Lieutenant Commander in the United States Navy who had

published about two dozen papers on physical chemistry, mechanics, and calculus

of variations from 1929 through 1947. He also wrote a textbook on the calculus

of variations, published in Britain. Already near the then-mandatory retirement

age of 65 when he arrived at UVM, he eloquently defended the rights of the older

worker, insisting on his right to be considered for tenure just like anyone else. (This

statement is based on correspondence found in Kimball’s ﬁle in the UVM archives.)

He retired from UVM in 1954.

The year 1954 saw the retirement of J. A. Bullard and H. G. Millington, along

with Prof. Kimball. It was also the last year for Assistant Professor Larrivee. It was

thus an opportune time for both expansion and renewal. From this point on, the

number of personnel in the department increases rapidly, and, as noted above, we

shall not be able to discuss any of them in any detail. We shall omit the instructors

entirely, although we will devote some space to the lecturers.

61

62 6. INTO THE MAINSTREAM: 1955–1975

The renewal of the faculty had begun with the hiring of Heath Kenyon Riggs

1

and Ivan Raymond Hershner, Jr.

2

in 1953. From this point on, mathematics courses

became both more numerous and more sophisticated. The following year, Julius

Solomon Dwork

3

was hired as associate professor. In 1955, Harry Lighthall, Jr.

4

was hired as an instructor, and in 1956, Joseph Anthony Izzo, Jr.

5

was hired as an

assistant professor.

In a telephone interview in 1990, Professor Hershner recalled that the major

task facing the Department was to rebuild the curriculum. Prof. Riggs was partic-

ularly interested in expanding the algebra oﬀerings. A course in groups, rings, and

ﬁelds was taught for the ﬁrst time in 1955. The following year, a senior problems

course was added, along with courses in computers and numerical analysis. At that

point, Prof. Hershner left to work at the Pentagon. His replacement as head of the

Mathematics Department was N. James Schoonmaker.

6

In 1959, Lighthall became

assistant professor, and Donald Eugene Moser

7

joined the Department as associate

professor. When Professor Fraleigh retired in 1963, Erling William Chamberlain, a

1

Born 28 October 1918, he was a 1940 graduate of UVM. He spent two years as a research

assistant in the Department of Mathematics, then served as Director of Admissions before depart-

ing for graduate study at the University of Chicago, where he received the Ph. D. in 1948. He

retired from UVM in 1985 and died on 20 April 2011, in Richmond, VT, the town where he was

born and lived his entire life.

2

Born 24 August 1916 in Lincoln, NE, he received the Ph. D. at Harvard in 1947. He died

on 31 January 2005 in Fairfax, VA. In a 1990 interview, Prof. Fishback, who also had a Ph. D.

from Harvard (1952) told me that he left UVM because he had heard that Hershner was coming.

Perhaps Hershner had a dubious reputation at Harvard. He went to work at the Pentagon when

he left UVM and retired from military service in 1980 at the rank of Colonel, after which he taught

at George Mason University until 1985. From speaking with him on the telephone in August of

1990, I had the impression of a very vigorous man; he was about to leave for a vacation in Moscow.

3

Born 19 October 1916. His listing in the Graduate College catalog asserts that he received

the Ph. D. at New York University, but calls to NYU made by the present author in preparing a

memorial resolution after his death revealed that they have no record of this degree. His ﬁle at

UVM indicates that he was hired with a recommendation from the outstanding mathematician

Martin Davis (b. 1928), who had contributed to the solution of Hilbert’s Tenth Problem (which

asks whether an algorithm exists for determining whether a given polynomial equation in several

variables with integer coeﬃcients has integer solutions—the answer is, “No”) and was at the Insti-

tute for Advanced Study in Princeton at the time. While Prof. Dwork’s knowledge of mathematics

was impressive, he refused to do any research or serve on any committees at UVM and was never

promoted to full professor. His most memorable academic contribution was writing discretized

diﬀerential equations that could be solved by electronic computers for weather prediction. He

retired in 1981 and died on 20 February 2002.

4

Born 7 January 1924 in New York, he served in the armed forces during World War II and

lost his left arm in that service. He went on leave from UVM to get a Ph. D. at Brown University in

1959. He was an enthusiastic champion of Aﬃrmative Action and diversity at UVM. He achieved

the rank of full professor, but died soon afterward, on 11 January 1975.

5

Born on 7 February 1917 in New York, he received a Ph. D. from Columbia University.

He served for one year as acting dean of the College of Engineering, Mathematics, and Business

Administration. He retired in 1981, but continued to teach at UVM until his death on 3 March

1996.

6

Norman James Schoonmaker was born on 24 December 1918 in Pennsylvania. He received

the Ph. D. in 1954 from the University of Pittsburgh for a dissertation on summability methods.

He died in Escondido, CA on 7 November 2008.

7

Born 22 June 1925, like Prof. Schoonmaker, he received the Ph. D. from the University of

Pittsburgh in 1956 for a dissertation on summability methods. (They had the same adviser.) He

died on 10 November 2001.

1. PERSONNEL 63

1962 Ph. D. at Columbia, was hired as an assistant professor. He is the ﬁrst math-

ematics professor hired at UVM who is still alive as of this writing (2018). The

following year, Bruce Meserve,

8

a specialist in mathematics education, was hired

as full professor. Mathematics education thereby became an important component

of the Department’s mission and was greatly strengthened a decade after Prof.

Meserve’s retirement, during the 1990s, by several initiatives undertaken by the

chair of the department, Kenneth Gross. Thus, UVM made extraordinary eﬀorts

to connect the University with elementary and secondary education in Vermont.

All of these professors had been educated at excellent graduate schools. They

began the task of moving UVM into the mainstream of contemporary mathematics,

a process that faltered during the 1970s, but resumed very strongly in the 1980s.

They began this eﬀort by increasing the number of professors. In the year 1966,

seven new assistant professors were hired, among them David Luther Sylwester,

9

who was a specialist in statistics. Over the next three years, four more professors

were to be hired, three of whom remained at UVM for several decades. The ﬁrst of

these three was Robert K. Wright, a 1966 Ph. D. at Columbia University (hired in

1966), followed by Roger L. Cooke (the present author), a 1966 Ph. D. at Princeton

(hired in 1968), and James A. Burgmeier, a 1969 Ph. D. at the University of New

Mexico (hired in 1969). The fourth and last who will be mentioned here was Paul

Brock (29 March 1923–2 February 1977, hired in 1970). Prof. Brock was intended

to be the senior research leader in a proposed Ph. D. program, as will be discussed

below.

When the University was reorganized in 1973, the faculty of the Department

resisted a proposal that Mathematics be moved into the College of Arts and Sci-

ences, preferring to remain part of the College of Technology, which was renamed

the College of Engineering, Mathematics and Business Administration. Since vari-

ous departments all over campus had found need of statistics and were hiring their

own statisticians to teach this subject, a program in statistics was organized, to

run in parallel with a program in computer science. In 1984, in an administrative

reorganization of the College, computer science was merged with electrical engi-

neering and statistics with mathematics, forming the Department of Electrical and

Computer Engineering and the Department of Mathematics and Statistics.

1.1. Computing at UVM. The story of computing at UVM deserves more

space and more prominent attention than it can get in the present narrative.

In brief, here is what happened: In 1955, IBM announced plans to build its 704

computer at MIT and share the time with other New England Colleges. One-third

of the time was reserved for IBM, one-third for MIT, and the remaining third was

apportioned among the other New England Colleges. Prof. Riggs spent some time

in Cambridge learning about computing in general and the 704 in particular. This

was in the days before FORTRAN, and programming had to be done in symbolic

8

Born 2 February 1917, he received the Ph. D. at Duke University and was the author of

many elementary textbooks on mathematics and the teaching of mathematics and also served as

President of the National Council of Teachers of Mathematics. He retired from UVM in 1981 and

died 14 November 2008.

9

Born in Roseburg, OR on 17 March 1936, he obtained the Ph. D. at Stanford in 1966. He

left UVM in 1984, dissatisﬁed that no Department of Statistics was to be created. He moved to

the University of Tennessee in Knoxville, where there actually is a Department of Statistics. He

died of Parkinson’s Disease on 26 April 2013.

64 6. INTO THE MAINSTREAM: 1955–1975

language, very close to machine language. Later, Prof. Dwork wrote a discretized

version of the diﬀerential equations that describe the movement of weather pat-

terns, and Prof. Riggs and the head of the Weather Service at Burlington took

these programs to MIT to run, thus carrying out some of the ﬁrst attempts at

computerized weather forecasting.

In 1960, UVM’s seventeenth president, John Theodore Fey,

10

oﬀered to buy an

IBM 1620 for the University, provided he could be assured the faculty would use it.

Prof. Riggs obtained statements from 35 faculty members asserting their intention

to use the proposed machine, which was accordingly bought. Prof. Riggs then gave

an Evening Division course in computing to a broad group of engineers, teachers,

and government workers from all over Vermont and thereby launched Vermont into

the computer era. From this beginning, the explosion of computer miniaturization,

the availability of aﬀordable individual computers, and the Internet, have combined

to ﬂood UVM with computers, just as in every other major educational institution

and business in the world.

Prof. Riggs spent a leave of absence studying computational mathematics at

the University of California at Berkeley in 1965–1966, afterwards creating a course

in numerical analysis that was for a long time one of the core elements of the com-

putational part of the curriculum. That curriculum expanded enormously during

the early 1960s, with courses being added on group theory, Galois theory, prob-

ability, topology, diﬀerential geometry, number theory, foundations of geometry,

computers, and numerical analysis.

2. Research. Graduate Degrees

Along with the modernization of the curriculum, UVM began to demand re-

search as a duty of the faculty. This movement was slow to develop, since research

had never been an important component of UVM’s educational mission. The Grad-

uate College at UVM was formed only in 1953. (It had previously been the Grad-

uate Council.) At that time, only the Medical College oﬀered a doctoral degree.

When Prof. Hershner arrived in 1953, there was only one master’s degree student

in mathematics. When he left in 1956, there were several. UVM began adding

Ph. D. programs in 1957 with biochemistry, and opened one new program each

year through 1960. By the time the program in mathematics and statistics was

opened in 1970, there were 13 others already in existence. The ﬁrst Ph. D. at UVM

was awarded in 1962, and the Graduate College began to publish its own catalog

in 1964. Master’s programs in mathematics continued to expand throughout the

1950s and 1960s, and planning was begun for a Ph. D. in applied mathematics and

statistics, a program that ultimately failed.

Part of the reason for this failure of the ﬁrst attempt at a Ph. D. program was

na¨ıvet´e on the part of both faculty and administrators. They had never had to

administer such a program and did not understand what was involved in taking

on Ph. D. students. I write this not to criticize them. After all, UVM’s teaching

mission was a very useful and respectable enterprise. But it was not a propitious

time to begin such a program. Of the senior faculty members at the time, only Bruce

10

Born in Hopewell, VA on 10 March 1917, he served as president of UVM from 1958 to 1964

and returned as a member of the Board of Trustees from 1982 to 1985. He died on 29 April 2015.

2. RESEARCH. GRADUATE DEGREES 65

Meserve had more than one publication,

11

and his area was mathematics education,

which was not intended to be part of the Ph. D. program. Schoonmaker and Moser

had both published their doctoral dissertations, but had not gone beyond that.

Riggs had published one paper, a one-page review of work in computing. Lighthall,

Dwork, and Izzo had published nothing at all. The other faculty members, who

eventually did publish in some volume, were at the time all untenured assistant

professors. It would take more than one senior research leader to make such a

program viable, and even that one leader was not present.

In 1969, the sought-after research leader was found in the person of Paul Brock.

Prof. Brock received the Ph. D. from New York University in 1951. Most of his

career was spent working in private industry in California, at Electro Data Corpo-

ration, the Hughes Aircraft Corporation, and General Electric. Nine of his pub-

lications are listed in Mathematical Reviews, and undoubtedly there were others,

in outlets outside the scope of Mathematical Reviews. He appeared to be just the

kind of sophisticated researcher who could head up a Ph. D. program in applied

mathematics and numerical analysis. Unfortunately, he was not in good health

and had lost much of the vigor he surely must have had when younger. Although

he was extremely good at solving tricky mathematical problems, such as those on

the Putnam Examination, he was no longer doing original research. Moreover, he

had no experience of working inside a university administration, and was rather

naive as to what is needed to procure grant support. For all these reasons, the

Ph. D. program that was opened in 1970 was closed down around the time of his

death in 1977. The six Ph. D. students produced during the few years it was open

were all supervised by younger faculty members (Burgmeier, Cooke, Wright, and

Chamberlain).

Despite all these considerations, research, which had not previously been an is-

sue in tenure and promotion cases, was strongly weighted by Clinton Dana Cook,

12

the Vice-President for Academic Aﬀairs (now called the Provost) during the 1960s.

It has assumed increasing importance with every change of administration since.

Much of the impetus to this post-war expansion was due to the exceptional pros-

perity of the country during the 1950s and 1960s. The launching of Sputnik in

October of 1957 by the Soviet Union stimulated government support for educa-

tion and scientiﬁc research, and many mathematicians beneﬁted from the available

largesse, including the present author, who attended graduate school on a generous

National Science Foundation fellowship from 1963 to 1966. Seeing the readily avail-

able funds, administrators simply made the receiving of grants essentially the only

criterion for getting tenure and promotion. A number of assistant professors fell

afoul of this policy, which was all but openly proclaimed.

13

It was hidden behind a

11

This statement is based on a search in Mathematical Reviews. Since not every mathematics

journal was reviewed, it is possible that UVM faculty published more than appears here.

12

Born in St. Johnsbury, VT on 20 February 1921, he received the Ph. D. in chemistry from

New York University. He died of heart disease on 25 June 1969. The Cook Physical Sciences

Building is named in his honor.

13

When the present author interviewed for a position in 1968, Prof. Schoonmaker opened the

conversation on the way from the airport to the hotel by asking about my experience in getting

grants. When the position was oﬀered, he stated that the teaching load would be “six hours,

which is half time,” and that I would be expected to apply for grant support for half of my salary.

Not that the salary would not have been paid otherwise, but the point was that applying for (and,

by implication, receiving) grants was a serious obligation on my part, a sine qua non in getting

tenure.

66 6. INTO THE MAINSTREAM: 1955–1975

requirement of “signiﬁcant research,” but as Graduate College Dean Macmillan

14

frankly said,

15

the real test of signiﬁcance was whether the research was funded or

not. One professor, being told by the Dean of the College of Technology

16

that he

was being denied tenure because he had not done signiﬁcant research, asked the

dean to justify that claim and was told that “the procedures of the Dean’s Oﬃce

are not available for your inspection.”

At ﬁrst sight, this policy seems to make sense. After all, major universities are

able to oﬀer a much richer curriculum with the funds they generate from industrial

and government grants, and in the early 1960s, the portion of UVM’s budget pro-

vided by federal grants expanded from 16% to 26%. Most of that increase was in

the Medical College, however. In terms of grant-funding credibility, most depart-

ments at UVM were not on a level with the major universities, and mathematics

certainly was not. The mathematics Ph. D. was not the money-maker that had

probably been envisioned. The administrators involved did not suﬃciently take

account of the fact that the ability of a faculty member to obtain grants was very

much dependent on the reputation of the university itself, and that, in this time

before the information superhighway, professors at isolated universities like UVM

were liable to ﬁnd that their research had been anticipated elsewhere. In addition,

the University did not quite live up to its obligation to provide “matching funds”

for the research grants actually received. (The present author was supposed to have

“released time” for research while on NSF grants from 1970 to 1974. But in 1973,

faced with a need to cover the courses of Prof. Lighthall, who was ill, and unwilling

to ask any of the non-publishing faculty to teach 12 hours, the chair increased the

teaching load for the researcher in question from six hours to nine, that is, the same

teaching load given to professors who were not expected to engage in research.)

For all these reasons, the program was formally closed in 1976, the last can-

didate in the pipeline receiving the degree in 1978. Over the six years that it was

open, it produced six Ph. D.’s. (Prof. Burgmeier directed two of these, Prof. Cooke

another two, and Profs. Wright and Chamberlain each directed one.) A carefully

prepared plan for a renewed Ph. D. program was approved at all levels except the

Board of Trustees in 1990, but President Davis (1990–1991), engaged in planning

for ﬁscal austerity, refused to present it to the Board. The program was resur-

rected with great success two years later, but that portion of the story is reserved

for discussion in our ﬁnal chapter.

To end this chapter on a cheerier note, we remark that tuition at UVM in

1970 was $750 per year for Vermont residents and $2200 for non-residents. The

Good Old Days! In 2017, tuition for a normal course load of 12 to 18 hours per

semester was just under $16,000 for Vermont residents and just over $40,000 for

non-residents, roughly 20 times the 1970 level.

14

William Hooper Macmillan, born in Boston on 23 October 1923, received the Ph. D. in

pharmacology from Yale. He died on 4 April 2004 in Burlington.

15

And perhaps even believed. The deans of the College of Technology and the Graduate

College were both very nice men, and both very naive. A graduate-school classmate of the present

author, whom the mathematics department was hoping to recruit in 1972, was so disgusted after

his interview with Dean Macmillan that he immediately ruled out any position at UVM.

16

Warren Orvel Essler. He was born in Davenport, IA on 22 April 1924 and received the

Ph. D. in engineering from the University of Iowa. He left UVM in 1972 and took up a position

at Tennessee Technological University in Cookeville. He died in Sparta, TN on 23 June 2005.

2. RESEARCH. GRADUATE DEGREES 67

Mansﬁeld House, the former residence of UVM presidents, is

across Colchester Avenue from the main oﬃce in Lord House. It

provides very elegant oﬃces to many members of the faculty.

CHAPTER 7

Statistics Comes to UVM

At ﬁrst glance a statistics textbook appears to be ﬁlled with numbers and for-

mulas, just like a mathematics textbook, and indeed statistics has a strong mathe-

matical component. It is not, however, merely an area of mathematics. Its origins

are independent of mathematics, although of course numbers are involved. As

the name itself implies, it comes from the information collected by governments

(states) to be used in regulating their economies and social structure. Its basic

problem is to ﬁnd ways of making plausible inferences from large data sets. The

part of mathematics that grew alongside it is probability theory, which in turn

arose in the sixteenth and seventeenth centuries in connection with the analysis of

games of chance. Faced with a large data set, one can imagine selecting one piece

of data and asking how likely it is to have various properties. Statistical methods

of testing and revising hypotheses have made the subject an indispensable tool for

economists, scientists, and engineers.

The ﬁrst major works applying statistics to the real world were published in

the early eighteenth century. In 1710, Queen Anne’s physician John Arbuthnott

(1667–1735) published a note in the Transactions of the Royal Society, pointing

out what appeared to him to be an anomalous fact: Baptismal records for each

of the 82 years between 1629 and 1710 revealed that more boys than girls were

baptized in every single one of the years. This peculiar fact, he thought, required

an explanation. About the same time (1705), Jacob Bernoulli (mentioned above)

published the ﬁrst work on this subject, the Ars conjectandi (Art of Prediction),

which was published in 1713, after his death. He intended it to “apply to society,

morals, and economics.”

The subject of statistics was neglected by most mathematicians for a long time,

even though economists and engineers needed it. Courses in statistics at UVM were

for many decades taught in other departments, such as economics and the Medical

College. It was not until 1945 that the Department of Mathematics ﬁrst oﬀered a

course in statistics. Before that, in 1942, the Department of Home Economics in

the College of Agriculture had appointed an Assistant in Statistics, Margaret Mary

Eliza Openshaw.

1

Thus, the mathematics department got into the business of

teaching statistics rather late, the ﬁrst course in mathematical statistics appearing

in the catalog of 1945–1946. Courses in statistics continued to sprout all over

campus, in dental hygiene, nursing, psychology, economics, agronomy, engineering,

1

Born in Newport, RI on 4 December 1911 and graduated from the University of Rhode

Island in 1933, having been captain of the basketball team and manager of the hockey team there.

Except for a hiatus from 1943 to 1945, she served as Assistant in Statistics from 1942 to 1947,

then left to pursue other employment opportunities around Burlington. Eventually, she became

a vice-president at the Howard Bank, the position from which she retired. She died in Burlington

on 22 February 1992.

69

70 7. STATISTICS COMES TO UVM

and many other places. The word statistics appears about a dozen times in catalogs

from 1945, but about four dozen times in catalogs from the 1960s and over 100 times

in catalogs from the 1980s.

Eventually, a core of statisticians was assembled into a program in statistics,

which was announced in the catalog of 1973–1974, when the university underwent

a major reorganization.

The statistics program was in the newly-formed College of Engineering, Math-

ematics, and Business Administration. (Business Administration was moved from

the College of Arts and Sciences. In 1981, it became a school.) Chemistry and

Physics were moved from the now-defunct College of Technology into Arts and

Sciences, but strong preferences expressed by the mathematics faculty kept the

department under the same roof with the engineers. Eventually, the statistics pro-

gram was merged with mathematics, forming the Department of Mathematics and

Statistics that now exists.

A similar program in computer science was also announced in the 1973–1974

catalog. Like statistics, computer science has a strong mathematical component,

but is not mathematics. The computer science program was ﬁnally merged with

electrical engineering, to form the Department of Electrical and Computer Engi-

neering. For some time afterwards, the catalog did not actually specify academic

departments, but only indicated that B. S degrees were available in mathematics,

statistics, and computer science. The ﬁrst two of these degrees were labeled B. S.

in Mathematics, the third B. S. in Computer Science.

In the present-day College, called the College of Engineering and Mathemati-

cal Sciences, there are now two departments called the Department of Computer

Science and the Department of Electrical and Biomedical Engineering.

CHAPTER 8

UVM in the Worldwide Community: 1975–2000

In his magisterial 1893–1895 lectures on Russian history from the earliest time

down to his own day, the historian Vladimir Osipovich Klyuchevskii (16/28 January

1841–13/26 May 1911) broke the history of his country into periods, the fourth of

which he dated from 1613, which was the beginning of the Romanov Dynasty, to

1856, the year Aleksandr II came to the throne after the Crimean War. In that

connection, he wrote the following:

I repeat that this is not merely one period of our history. It is our

entire recent history. . . In studying the phenomena of this time,

one gets the feeling that, the farther one goes, the deeper one gets

into autobiography, that one is passing to the study of his own self,

his own spiritual content, to the extent that it is connected to the

past of our country. And all this concentrates one’s attention and

guards one’s thoughts from distraction.

Those words come to mind as I approach this ﬁnal chapter in the story. My own

career extends over this entire span of time, so that I ﬁnd it easy to assimilate the

facts but at the same time diﬃcult to be sure I am evaluating them objectively. As

I retired in 2003, I shall make no attempt to describe what has transpired after that

date, and I shall increasingly neglect detail as that date is approached. Still, certain

trends seem obvious to me. The Department of Mathematics and Statistics matured

through many diﬃculties during the 1980s and emerged stronger and conﬁdent of its

position as a respectable center of teaching and research excellence on the national

and international scale. I shall break this story into two pieces to illustrate how

both teaching and research were shaped into thriving enterprises in the last two

decades of the twentieth century.

1. Reorganization: Lecturers

With the Ph. D. program shut down, the Department needed to decide on the

best use of the faculty hired to staﬀ the program. The entry into the world of

publication and grantswinging was a trap door, and there was not any graceful way

to exit, even if there had been a desire to do so. (There was no such desire.) It

was necessary to move forward, even if research professors had to be paid out of

tuition-generated funds. How were the students who paid the tuition to be ade-

quately taught by faculty with two-course teaching loads? The answer was found

by an ingenious adaptation. Until 1972, the probationary period for faculty was

four years. Those at professorial rank were either given tenure (and sometimes

promoted) after that much time, or they were terminated. For those at the rank

of instructor, who did the heaviest teaching, only the second option was available.

Many talented teachers were lost to the University through this policy. The way

71

72 8. UVM IN THE WORLDWIDE COMMUNITY: 1975–2000

to solve both problems was found in the creation of the rank of lecturer, carefully

deﬁned in the handbook as a non-tenured position whose duties involved only teach-

ing, but did not have any term limits. Among the people hired as instructors in the

1973–1974 academic year were Larry Kost (9 January 1943–26 December 2015) and

David Morency (11 September 1938–27 June 2015). In the 1974–1975 year, they

were joined by John Lawlor. Holly Puterbaugh, who had been in the department

for several years at that time, was made a lecturer in 1976. In the following year,

Lawlor, Kost, and Morency were moved into the position of lecturer, and a former

instructor, Jan Johansson also assumed that position.

These ﬁve lecturers were the teaching backbone of the mathematics side of the

department for the next 30 years and more. Despite the wording in the handbook,

they did an immense variety of work that was not direct instruction, serving on

committees, organizing the high school mathematics competition, participating in

seminars, and engaging in many other activities essential to the smooth functioning

of the department. They were later joined by a number of other lecturers, of whom

we mention Karin Larson, who served from 1980 to 1997, Joanne Chandler Brown (9

February 1939–14 November 1998), who served from 1983 to 1997, and four others

who are still serving as of 2018: Karla Karstens, Helen Read, Tony Julianelle, and

Joan Rosebush. Statistician John Aleong, who had obtained the Ph. D. at Iowa

State University in 1975, was also appointed as a lecturer in 1976, but soon became

a research professor, and in 1996 a professor of statistics. Other lecturers have been

added in the 21st century, but these fall outside the scope of the present essay.

In statistics also, a large number of lecturers were hired, among whom were

Brian MacPherson (1980, retired 2009), Elizabeth Low (1985, retired 2004, origi-

nally appointed in School of Business Administration in 1982), and Sheila O’Leary

Weaver (1985).

2. Reorganization: Research Groups, 1975–1988

Meanwhile, to keep researchers active, it was realized that a critical mass of

at least two or three professors would be needed in whatever areas were chosen as

specializations. As a general disclaimer, we state at the outset that the following

description of the researchers in these areas is incomplete, mostly because this essay

is conﬁned to the twentieth century. All of the research areas below have added

talented people since the twenty-ﬁrst century began. (And, it is now more than

one-sixth gone! It is well that none of these research areas has chosen to rest on its

reputation.)

In statistics, which had close connections with many other units in the Univer-

sity, especially the Medical College, a number of new people were hired during the

period in question. The ﬁrst of these, hired in 1973, was Takamaru Ashikaga, a

1973 Ph. D. at UCLA. He was followed in 1975 by Larry Haugh, a 1972 Ph. D. at

the University of Wisconsin, and then in 1976 by John Aleong, mentioned above, in

1983 by Ruth Mickey, a 1984 Ph. D. at UCLA, and Mun Son, also a 1984 Ph. D., at

Oklahoma State University. Thus a substantial staﬀ of statisticians was assembled

for both teaching and research.

As for the mathematicians, in the mid-1960s, Professors Chamberlain and

Wright, both graduates of Columbia, collaborated in work on the asymptotic theory

of diﬀerential equations. The two hires from the late 1960s, Cooke and Burgmeier

3. THE PH. D. PROGRAM: THE ROCKY ROAD TO RENEWAL 73

specialized in areas that had a common point of contact in what is called func-

tional analysis, so that collaborative research would have been possible. In the end,

however, Burgmeier’s interests turned to computational and numerical methods,

and Wright joined him in that area. Chamberlain also turned toward numerical

methods, supervising a Ph. D. dissertation in this area in the mid-1970s. The areas

that eventually deﬁned the department’s research interest turned out to be alge-

bra/number theory, combinatorics, analysis, and numerical analysis. To form these

groups, a sizeable contingent of young faculty was assembled during the early 1980s.

In combinatorics, Jeﬀrey Dinitz was hired, fresh from his Ph. D. at Ohio State

University, in 1980. In 1982, he was joined by his classmate Dan Steven Archdeacon

(11 May 1954–16 February 2015), also a 1980 Ph. D. These two brought in many

visiting professors, conducted a lively seminar every semester, and published an

impressive number of papers.

Algebra/number theory was built up beginning in 1981 with the hiring of

Richard Foote, a 1976 Ph. D. at Cambridge (UK) University. In 1984, he was

joined by David Dummit, who had received the Ph. D. at Princeton in 1980. This

group was ﬁlled out in 1986 by the addition of Jonathan Sands, a 1982 Ph. D. at

the University of California at San Diego. The group was expanded enormously by

outreach to nearby Middlebury College, St. Michael’s College, and McGill Univer-

sity in Montr´eal, forming a group known as the Vermont–Qu´ebec Number Theory

Seminar, which issued its own proceedings in the form of a periodic journal.

In 1986, analysis, the area in which Cooke had been the sole researcher, acquired

James Michael Wilson, who had received the Ph. D. at UCLA in 1981. These two

conducted several seminars in orthogonal series expansions during the 1990s and

supervised the doctoral dissertations of two students, both of whom graduated in

1999.

Numerical methods, as already remarked, were the province of Professors Burg-

meier and Wright and various of their associates. In addition, Prof. Burgmeier

specializes in mathematical software and had a long collaboration with lecturer

Larry Kost in this area. While these four groups had active research programs,

conducted regular seminars, and published papers that attracted notice from a

wide audience, the absence of a Ph. D. program would have limited what they

could achieve in terms of recognition in the academic world. These researchers

were all rather young, most of them in their 30’s and only two or three in their

40’s. Especially after the death of Prof. Brock, there was no experienced “elder

statesman” to organize a coherent research program that would involve the whole

department. A search was therefore begun for such a person, and we now turn the

page to explore the ﬁnal episode of this history.

3. The Ph. D. Program: the Rocky Road to Renewal

Professor Schoonmaker announced his retirement from the position of depart-

ment chair in 1977 and was succeeded by Prof. Moser. While the latter was a

superb administrator, he was not well-versed in research, as he himself realized. A

search for a senior research leader to chair the department was begun in 1983, and

appeared to have turned up a suitable person, namely James C. Becker, a topologist

with a Ph. D. from the University of Michigan, currently teaching at Purdue Uni-

versity. He was oﬀered the position and accepted, subject to the condition that he

would postpone his arrival for a year due to family commitments in West Lafayette.

74 8. UVM IN THE WORLDWIDE COMMUNITY: 1975–2000

The University found this arrangement acceptable, Professor Moser went on leave

for the academic year 1984–1985, and the present author was named acting chair

for that year.

Candor compels me to admit that I have no administrative skills whatever. I

can carry out assignments with great zeal, but I have no ability to make a cogent

argument for a policy, and I loathe having to refuse requests. Worst of all, I

am hopeless when it comes to resolving interpersonal conﬂicts between two other

parties. The result was that, by the time Professor Becker arrived to take up

his position in the fall of 1985, morale in the department was low.

1

Nevertheless,

everyone was hopeful that a new day had arrived along with Prof. Becker. That

hope was dashed very quickly. Having dipped his toe into the waters at UVM,

Professor Becker decided he did not wish to take the plunge. After only one semester

in place, he submitted his resignation, eﬀective as of May 1986. The department

was once again without a leader.

Fortunately, Professor Moser was willing to return and set matters on an even

keel once again, serving as chair through 1988. The search for a research leader

resumed and this time was crowned with stunning success. The University was

able to hire Kenneth I. Gross, a 1966 Ph. D. from Washington University in St.

Louis, who had taught at the University of North Carolina, served as chair of the

department at the University of Wyoming, and had travelled to many countries to

collaborate with others. He was working at the National Science Foundation at the

time. He had the experience, the contacts, the creative ideas, and the interpersonal

skills to forge a superb Department of Mathematics and Statistics when he assumed

the role of chair in January 1989.

Recent chairs of the Department. Jeﬀ Dinitz (1999–2004), James

Burgmeier (2004–2014), John Lawlor (Spring 2008), Kenneth

Gross (1988–1992), Roger Cooke (1984–1985).

Professor Gross took several immediate and dramatic steps toward resurrect-

ing the Ph. D. program. First, he hired another senior research leader, William D.

1

Lest you think me capable of learning from experience, I will say that I was once again

drawn into administration in the years 1994–1998, and the eﬀect on department morale was no

better than it had been a decade earlier. My excuse, such as it is, is that my daughter was a

student at Bryn Mawr during those years, and I needed the extra pay.

3. THE PH. D. PROGRAM: THE ROCKY ROAD TO RENEWAL 75

Lakin, a 1968 Ph. D. at the University of Chicago, to assist him in building a re-

search group in applied mathematics. A group of excellent applied mathematicians,

both junior and senior faculty, was assembled. The task was facilitated by giving

joint appointments to four of the engineering faculty: George Pinder, a 1968 Ph. D.

from the University of Illinois, dean of the college, and formerly chair of civil en-

gineering at Princeton University; electrical engineer Kenneth Golden, who earned

the Ph. D. at the University of Paris in 1964; electrical engineer Kurt Oughstun,

a 1978 Ph. D. from the University of Rochester; and computer scientist Robert

Snapp, whose 1987 Ph. D. is from the University of Texas. All that took place in

1990. Promising young people were then hired, beginning in 1992 with Jun Yu, a

1988 Ph. D. from the University of Washington; in 1994, Jianke Yang, who received

the Ph. D. at MIT in that year; and ﬁnally, in 1995, Daniel Bentil, a 1990 Ph. D.

from Oxford (UK) University.

In 1993, the statisticians added one more young person, namely Jeﬀ Buzas,

a 1993 Ph. D. at North Carolina State University and the present chair of the

Department of Mathematics and Statistics.

As already stated, in 1990, President Davis had refused to submit the proposal

for a renewed Ph. D. to the board of Trustees. But the department persisted, and

the program was approved by the Board of Trustees in 1992. It has been ﬂourishing

ever since and has produced, as of 2018, 20 Ph. D.’s, starting in 1997.

An indication of the new, livelier intellectual atmosphere was provided in 1990,

when the combinatorics and algebra/number theory research groups collaborated

to organize an international conference on coding theory and combinatorial design

to take place 13–18 September. This conference was proposed and organized with

superhuman energy by Professors Dinitz and Foote, and had been planned to cele-

brate the 80th birthday of Professor Marshall Hall on 17 September. Unfortunately,

Prof. Hall died on 4 July that year, and the conference was consequently dedicated

to his memory.

Participants in the 1990 Marshall Hall Conference, photographed

in front of the Waterman Building.

Not satisﬁed merely to add applied mathematics to the department’s areas

of specialization, Prof. Gross also took an interest in mathematics education at

the kindergarten-to-high-school level. He developed contacts with the Vermont

Department of Education and founded the Vermont State Mathematics Coalition

in 1989, the Vermont High School Summer Mathematics Institute in 1993, and

the Vermont Mathematics Initiative in 1999. He procured funding for all these

programs from the National Science Foundation, the US Department of Education,

and the Vermont Department of Education. Thus, mathematics education became a

76 8. UVM IN THE WORLDWIDE COMMUNITY: 1975–2000

strong sixth area of concentration for the Department. In fact, at least ten members

of the current department list mathematics or statistics or computer education as

areas of expertise.

Prof. Gross had named Prof. Dinitz associate chair in 1992, and the following

year, he relinquished the chair of the department, being replaced by Prof. Lakin,

who (as related above) took on the present author as associate chair. In 1999, Prof.

Lakin relinquished the chair to Prof. Dinitz, who took Prof. Burgmeier

2

as associate

chair.

4. The Year 2000 and Beyond

The large footprint that the Department of Mathematics and Statistics has in

the University and in Vermont is well described in a snapshot of the mathematics

portion of the department written in 2000 by then-chair Dinitz. This portion of

the faculty consisted of twelve full professors, two associate professors, one assistant

professor, ﬁve senior lecturers, ﬁve additional full-time lecturers, four part-time lec-

turers, and three graduate teaching fellows. Collectively, they taught 4668 students,

a total of 14,608 credit hours. Unlike the majority of mathematics and statistics

departments, the UVM department does not use the large lecture/recitation sec-

tion method. All courses are taught as independent sections, and even in the very

crowded calculus sequence, section sizes are normally held down to 35 students

each. The seriousness of the approach to teaching is reﬂected in the fact that two

members of the department up to that time had won the George V. Kidder Out-

standing Faculty award (one more has won since 2000), and ﬁve others had won

the Kroepsch–Maurice award for outstanding teaching. Although service courses

are a large portion of the teaching mission, with a variety of courses being oﬀered

to meet the various needs of students in Engineering, Physical Sciences, and Social

Sciences and Humanities, the Department nevertheless oﬀers majors leading to the

Bachelor of Science degree in the College of Engineering and Mathematical Sciences

(21 majors in the year 2000) and the Bachelor of Arts in the College of Arts and

Sciences (24 majors in the year 2000). In addition, it oﬀers three master’s degrees

(Master of Science, Master of Science in Teaching, Master of Arts in Teaching)

and the Ph. D. The impact of these programs in Vermont is considerable. Norwich

University, for example, has two UVM Ph. D’s on its staﬀ, as well as several faculty

members with master’s degrees from UVM.

As for research, the quality of the Department’s faculty is shown by the fact that

a professor with an appointment in the Department of Mathematics and Statistics

was named one of the three University Scholars every year from 1994 to 2000.

In service to the State of Vermont and the nation as a whole, the Department

provides a number of programs, several of which were mentioned above as creations

of Prof. Gross. In addition, the Department conducts the annual High School

Mathematics Contest every year during Mathematics Awareness Month (March)

and gives a luncheon and awards ceremony with a mathematics lecture to the

winners. Faculty members also give frequent lectures at other institutions in the

state. On the national level, the Department participates in the NASA Space Grant,

2

Prof. Burgmeier became chair of the department in 2004, when Prof. Dinitz resigned the

position, and continued through 2014, with John Lawlor serving as interim chair during Prof.

Burgmeier’s leave of absence in the spring semester of 2008.

4. THE YEAR 2000 AND BEYOND 77

which was administered by Prof. Lakin until his retirement. On the university level,

mathematics faculty served on 40 committees in 2000–2001.

It is now, I hope, clear that the Department of Mathematics and Statistics has

a large, talented, and hard-working faculty, who would under any circumstances

have produced outstanding work. In that sense, one cannot name any one person

or factor that has led to this rapid development. Still, it must be said that Prof.

Gross was at least the catalyst, if not the main ingredient in the progress the

Department has made over the past generation. He worked tirelessly to give the

department a higher proﬁle, constantly nominating faculty members for academic

honors (and incidentally, winning a number of prestigious awards himself). All this

took a terrible toll on his health, yet he continued to cope for nearly three decades

before retiring in 2016. His death on 10 September 2017 was widely mourned, and

he will always be remembered as an outstanding teacher and scholar and a kind

and generous human being.

While Prof. Gross’s contributions were enormous—I think greater than those of

any other mathematician in UVM’s history—he would be the ﬁrst to minimize their

eﬀect and give the credit to the talented and energetic researchers and teachers who

have made the Department of Mathematics and Statistics into the shining jewel in

the crown of UVM that it now is. After all, he would say truly, they all contributed

creative ideas and worked eﬃciently to implement those ideas. And on that note

of optimism, our narrative comes to an end.

Faculty of the Department of Mathematics and Statistics, April

1994, in front of the Lord House. Standing in front, left to right:

J. Michael Wilson, William Lakin, John Lawlor, Jeﬀrey Dinitz,

Jozef Siran, Jan Johansson, Erling Chamberlain, Dan Zwick,

John Aleong, Takamaru Ashikaga, Mun Son. First step, left

to right: David Morency, Holly Puterbaugh. Second step, left

to right: Janet Ferguson, Helen Read, David Dummit. Third

step, left to right: Joseph Izzo, James Burgmeier, Dan Archdea-

con. Fourth step: Larry Haugh. Standing on porch, left to

right: Larry Kost, Mary Betty Burnard, Robert Wright, Joanne

Brown, Jun Yu, Karin Larson, Richard Foote, Roger Cooke, Pe-

ter Rodney, Jonathan Sands.

UVM Mathematics and Statistics Faculty,

1800–2000

In the two charts that follow, the solid line indicates the period of full-time

service. The dashed lines indicate the portion of the person’s life before and/or

after service at UVM. If there is no dashed line, the person was still alive as of

March 2018.

The ﬁrst chart below gives the time of service for faculty hired before 1970

whose service ended before the year 2000. It should be possible, for example, by

holding a straight edge at right angles to the text, passing through the heading

corresponding to a given year, to determine who was in the department that year.

The second chart shows the time of service for faculty who were either hired

after 1970 or continued beyond the year 2000 or both. This chart is far from

complete. It omits about a dozen faculty members who were in the department

for a period of one to several years between 1970 and 2000, and it omits all the

faculty hired after the year 2000. The latter now constitute about half of the

present faculty. I regret the incompleteness and I hope no one feels slighted by

being omitted; but, since I have not been present in the department since 2003

and am a classical analyst, I thought this story should be told by a more modern

annalist.

79

80 UVM MATHEMATICS AND STATISTICS FACULTY, 1800–2000

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.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

1800 1850 1900 1950 2000

James Dean

.................................. ..............

Ebenezer Burgess

.......

Gamaliel Olds

.......

George Huntington

..............

George Benedict

..............

Farrand Benedict

..............................................................................

McKendree Petty

......................................................................................................

Archibald Daniels

..................................................................................................

Fred Corse

...........

Allison Slocum

...............................................................................................................

Warren Bullard

..............

Arthur Butterﬁeld

.................................. ..................................

George Brett

.................

Evan Thomas

....................................................................

Elijah Swift

...........................................................................................................................................

James Donahue

.....................................................................................

Fred Householder

...........................................................................

Howard Millington

...................................................................................................................

George Nicholson

.........................................................................................................................................................................

Douglas McClay

............................

Horace Giddings

.....................

Percy Fraleigh

.......................................................................................................................

James Bullard

........................................................................................

Myron Witham

..........................................................................................................................................

Jules Larrivee

........................

William Fishback

.......

Ruth Simond

..................................

William Kimball

...........

Ivan Hershner

...........

Heath Riggs

.............................................................................................................

Julius Dwork

............................................................................................

Harry Lighthall

....................................................................

Joseph Izzo

........................................................................................

James Schoonmaker

.....................................................................................

Donald Moser

..................................................................................................

Bruce Meserve

.............................................................

Erling Chamberlain

.............................................................................................................

David Sylwester

.............................................................

Paul Brock

........................

...... ........... .................................

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UVM MATHEMATICS AND STATISTICS FACULTY, 1800–2000 81

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............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

1900 1950 2000 2050

Robert Wright

....................................................................................................................................

Roger Cooke

.......................................................................................................................

James Burgmeier

............................................................................................................................................................

Larry Kost

..............................................................................................................................................

David Morency

..............................................................................................................................................

John Lawlor

........................................................................................................................................

Holly Puterbaugh

.............................................................................................................................

Takamaru Ashikaga

........................................................................................................................................................

Larry Haugh

..........................................................................................................

Ruth Mickey

...................................................................................................................

Mun Son

.......................................................................................................................

Jeﬀrey Dinitz

.................................................................................................................................

Dan Archdeacon

................................................................................................................

Richard Foote

.............................................................................................................................

David Dummit

.............................................................................................................

Jonathan Sands

.............................................................................................................

J. Michael Wilson

.............................................................................................................

Jun Yu

........................................................................................

Jianke Yang

..................................................................................

Daniel Bentil

..............................................................................

William Lakin

.............................................................

George Pinder

...............................................................................................

Kurt Oughstun

...............................................................................................

Kenneth Golden

........................................................................................

Kenneth Gross

..................................................................................................

Jeﬀ Buzas

.....................................................................................

John Aleong

..................................................................................................................................................

Brian MacPherson

..................................................................................................

Sheila Weaver

................................................................................................................

Elizabeth Low

.................................................................

Karla Karstens

.........................................................................................................

Helen Read

......................................................................................................

Joan Rosebush

...............................................................................................

Tony Julianelle

...........................................................................

Jan Johansson

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Karin Larson

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Joanne Brown

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Bibliography

[1] L. Diana Carlisle. Champlain Glass Company: Burlington’s ﬁrst manufacturing enterprise.

Vermont History, 68 (Summer/Fall)):133–161, 2000. 14

[2] George F. Houghton. A biographical sketch of the late Prof. James Dean, LL. D. Journal of

the Vermont Historical Society, XI (October):599–601, 1867. 5, 19

[3] Julian Ira Lindsay. Tradition Looks Forward. The University of Vermont: A History 1791–

1904. University of Vermont, Burlington, Vermont, 1954. iv, 2, 4, 26, 38

[4] Otto Neugebauer. History of Anciant Mathematical Astronomy. Springer-Verlag, New York,

1975. 3

[5] Jules Older. The University of Vermont: the First Two Hundred Years, chapter 17, pages

313–332. University Press of New England, Hanover, NH, 1991. 43

[6] Marius B. P´eladeau. Royall Tyler and the University of Vermont. Vermont History, 42

(winter):22–33, 1974. 7

[7] Helena Pycior. The History of Modern Mathematics, volume I, pages 125–156. Academic

Press, Boston, 1988. 22

[8] William Ragan Stanton. The Great United States Exploring Expedition of 1838–1842. Uni-

versity of California Press, 1975. 14, 15

[9] John Wheeler. Historical Discourse. Free Press Print, Burlington, Vermont, 1854. 4, 5

[10] Edward H. Worthen. McKendree. Published by the author, South Hero, VT, 2004. 35

83

Subject Index

1620 computer, 64

704 computer, 63

A Chronological History of the

World, 13

A Complete Descriptive and

Statistical Gazetteer of the

United States of America, 13

“A Foot-Note to John Todd’s Long

Lake”, 28

A History of the Determination of

the Figure of the Earth from

ARC Measurements, 48

“A method of determining the

temperature of the mercury in a

siphon barometer, from the

observed upper and lower

readings; and of testing the

accuracy of the instrument”, 27

A New and Complete System of

Universal Geography, 4

abolitionists, 18, 26, 35

Academy of Sciences, 15

accounting, 50

actuary, vii

Adirondack Mountains, 27

Adrain’s Hutton, 22

Advocates for Exceptional Children,

41

Aeneid, 2

African-Americans at UVM, 40

Agricultural and Mechanical College

of Alabama, 30

Agricultural College of Pennsylvania,

29

agriculture, 38

agronomy, 69

Airy functions, 31

Airy’s equation, 31

Alabama, 16

ALANA, 41

algebra, 2, 22, 28, 29, 39, 42, 45, 47,

57, 62, 73, 75

teaching, 57

alligation (mixture) problems, 22

alligation alternate, 22

alligation medial, 22

American Academy of Arts and

Sciences, vii, 20

American Baptist Education Society,

45

American Colonization Society for

Africa, 8

American exploring expedition,

14–15

American Journal of Mathematics,

46, 53, 56

American Journal of Science, vii, 21

American Mathematical Society, 53

American Philosophical Society, vii

American Quarterly Register, 26

American Revolution, 10

Amherst College, 8

An Exposition of the System of

Instruction and Discipline

Pursued in the University of

Vermont, 26

analysis, v, 73

analytic function theory, 46, 49

Analytic Theory of Heat, 49

Andover Theological Seminary, 8

angle trisection, 23

Ann Arbor, MI, 38

apogee, 20

applied mathematics, 64, 65

apportionment, 15

85

86 SUBJECT INDEX

Arbela, 3

Ariel, 36

arithmetic, 2, 22, 39, 49

arithmetical progression, 22

Arizona, 38

Arkansas, 7

Arkansas Weekly Gazette, 7

Armistice, 48

Armour Institute of Technology

(Illinois Institute of

Technology), 55

Army Engineering Corps, 54

Ars conjectandi, 69

astronomy, vii, 22, 28

geometric, 20

spherical, 2

Atheneum Press, 47

Athens, Greece, 40

Atwater Kent radios, 48

Auburn, AL, 30

Auburn, ME, 50

aurora borealis, 20, 21

autumnal term, 21, 28

Aviation Corps, 48

avversiera, 31

Back Log Camp Press, 28

Bailey–Howe Library, iv, 8, 21, 22,

25, 55

Special Collections, 40, 53

Baldwin Locomotive Company, 47

Baltimore, MD, 17

basketball, 69

battery, 4

Benton, OR, 60

Berea College, 61

Berea, KY, 61

Berkeley, CA, 64

Berlin, v, 42, 45

binomial theorem, 49

biochemistry, 64

Biographisch-Literarisches

Handw¨orterbuch zur Geschichte

der exacten Wissenschaften, 46

Biot–Savart law, 31

Board of Overseers, 12

Bolsheviks, 47

Bonnycastle’s Algebra, 28

Boston Journal of Philosophy, 21

Boston University, 61

Boston, MA, 3, 47, 54, 56, 66

Bowditch’s Practical Navigator, vii

Bowdoin College, 50

Braintree, VT, 48

Brandon, VT, 40, 60

Brooklyn Institute, 46

Brown University, 8, 37, 47, 62

Brunswick, ME, 40

Bryn Mawr College, 45, 74

Buﬀalo, NY, 19, 27, 30, 53

Bulletin of the American

Mathematical Society, 53

Burlington Free Press, 17, 18, 21, 26,

39

Burlington High School, 41, 50, 54

Burlington, VT, v, 6, 13, 14, 17–19,

25, 26, 29, 30, 36, 38, 39, 41, 48,

50, 51, 55–57, 61, 64, 66, 69

calculus, 3, 22, 26, 28, 31, 37, 50, 57

advanced, 57

diﬀerential, 28, 36

integral, 28

multi-variable, 37

one-variable, 37

vector, 37

calculus of variations, 61

Caledonia County, VT, 11

California, 16, 54, 65

Calvinism, 8

Cambridge Course, 28

Cambridge University, 30, 73

Cambridge, England, 59

Cambridge, MA, 63

Canaan, CT, 37

Canada, 10

“Canonical forms for ordinary

homogeneous linear diﬀerential

equations of the second order

with periodic coeﬃcients”, 53

Canton, CT, 38

“Carden’s formula”, 23

Carrickfergus, Ireland, vii

Carthage, 3

Castleton, VT, 35

Catholic Church, 43

Catholic University of America, 59

Catholics at UVM, 43

SUBJECT INDEX 87

Center for Cultural Pluralism, 41

Champaign–Urbana, IL, 29

Champlain Glass Company, 14

chapel, 43

Chauncey Goodrich Printers, 26, 30

Chelsea, VT, 12

chemistry, vii, 26, 28, 65, 70

agricultural, 38

analytical, 38

laboratory, 26

physical, 61

Cherokee tribe, 15

Chicago, IL, 29, 55, 58

Chinese mathematicians, 50

Chittenden County, VT, 18, 20, 46

Christie’s, 4

Cicero’s orations against Cataline, 2

Circleville, OH, 8

City College of New York, 50

City University of New York, 37

civil engineering, 28, 29, 36, 38, 47,

57, 75

Civil War, v, 30, 36, 37, 45

Civilian Pilot Training, 54

“civilizing and christianizing”, 10

Claremont, NH, 40

Clark University, 45, 47, 56

Clarke County, VA, 40

Classical College, 21

classical languages, 26, 41

classics, 37

Cleveland Heights, OH, 58

Cleveland, OH, 58

Clifton, NJ, 1

climate change, 15

Colchester Avenue, 66

College Board Examination, 50

College Ediﬁce, 7, 13, 25

College of Agriculture, 46, 69

College of Arts and Sciences, 51, 53,

56, 58, 63, 70, 76

College of Engineering, 51, 56, 58

College of Engineering and

Mathematical Sciences, 70, 76

College of Engineering,

Mathematics, and Business

Administration, 62, 63, 70

College of Technology, 58, 63, 66, 70

Columbia University, 22, 46, 48, 54,

62, 63, 72

combinations, 22, 49

combinatorics, 73

cometarium, 20

Committee on Naval Aﬀairs, 15

complex numbers, 22, 23

complex variables, 49

compound interest, 22

compound magnet, 4

Comptes rendus, 32

computational mathematics, 64

computer science, 63

program, 63, 70

computing, 62–64

“Concerning the geometry of the

second derivative of a polygenic

function”, 54

Concord, VT, 32

Congregational Church, 1, 8, 37, 40,

43, 50

Congress, 38

conic sections, 2, 28, 29

Connecticut River, 10

Constitution, 42

Continental Congress, 10

Cook Physical Sciences Building, 65

Cookeville, TN, 66

“Coolidge prosperity”, 53, 57, 58

Cornell University, 56

Corning, NY, 14

Corruption, 4

Corse fellowship, 47

Creek tribe, 1

Crelle’s Journal, 32

Crimean War, 71

cryptic puzzles, iv

crystallography, 28

Curator of Buildings, 46

curriculum, 26, 28, 37, 46, 49–50, 57,

62

D. C. Heath Publishers, 56

Dallas, TX, 19

Dartmouth College, v, vi, 5, 9–13, 30

trustees, 10, 13

Dartmouth University, 12, 13, 45, 57

trustees, 13

Dartmouth, MA, 47

88 SUBJECT INDEX

Davenport, IA, 66

Davis Press, 48

Dean’s Method, 21

Declaration of Independence, 10

Dedham, MA, 8

Democratic OK Clubs, 18

Democratic Party, 17

Democratic-Republican Party, 12

Denio and Phelps Publishers, 8

Dennison University, 50

dental hygiene, 69

Department of Academic

Mathematics, 51

Department of Computer Science, 70

Department of Electrical and

Biomedical Engineering, 70

Department of Electrical and

Computer Engineering, 63, 70

Department of Engineering, 47, 51

Department of Engineering

Mathematics, 51, 54, 57

Department of English, 57

Department of Home Economics, 69

Department of Mathematics, 54–56,

62, 69

Department of Mathematics and

Mechanics, 58

Department of Mathematics and

Statistics, 41, 63, 70, 71, 74, 75

Department of Physics, 49

Departments of Arts and Sciences,

51

Derby, CT, 39

Descartes’ rule of signs, 50

determinants, 26, 49

dialling, 2

Dictionary of National Biography, 4

diﬀerential equations, 22, 57, 62, 64

asymptotic theory, 72

ordinary, 46

partial, 46

second-order linear, 50

Director of Admissions, 62

Doctor of Philosophy, 64–65, 73–75

Du calcul des d´erivations, 30

Duke University, 63

Dunstable, MA, 47

Duquesne University, 23

Earlham College, 61

Easton, NY, 42

eclipse, 2

lunar, 3

solar, 3, 20

´

Ecole Polytechnique, 3, 30, 31

economics, 69

Edinburgh Review, vi

Edinburgh Royal Society, vii

Edinburgh, Scotland, vii

electric generator, 4

electrical cannon, 4

electrical engineering, 63, 75

electricity, 26, 46

Electro Data Corporation, 65

electromagnetic induction, vi, 21

Eleven Point, Arkansas, 8

elliptic functions, v, 46

Elmira Free Academy, 47

Elmira, NY, 47

Elmwood Cemetery, 19

end-of-semester potlucks, iv

engineering, 38, 69

engineering mathematics, 50

England, 43

equation of time, 20

equations, 22, 26

approximate solution, 50

cubic, 23, 31

irreducible case, 23

graphical solution, 49

linear, 49

quadratic, 22, 39, 49

Erbil, Iraq, 3

Escondido, CA, 62

Essex County, VT, 32

Essex Junction, VT, 50

Euclid or Einstein?, 23

Euclid’s Elements, 2

“Eulers”, iv

evolution (extraction of roots), 22, 49

exponents, 49

factoring, 49

Fair Representation, 21

fair representation, 15–16

Fairfax, VA, 62

Fairﬁeld, VT, 54

fall picnic, iv

SUBJECT INDEX 89

Fall River, MA, 59

Faraday’s law, vi

Farnworth, NH, 55

Federalist Party, 12, 13

Fine Hall, 46

“Finer Hall”, 46

First Amendment, 42

First Calvinist Congregational

Society, 13

Fisk University, 40

Fleischmanns, NY, 28

Flint Professorship, 48, 56

ﬂuxions, 22

ﬂying saucers, 14

football, 57

forcing pump, 20

FORTRAN, 63

Foucault pendulum, 2

four species, 49

fractions, 49

Franklin County, VT, 18

Franklin, NH, 61

Fred and Fanny Corse Professorship,

47

Free Press Association, 23

Free Soil Party, 18, 19

French and Indian War, 9

French-Canadians at UVM, 43

friction, 21

functional analysis, 73

Fundamental Accounting, 50

Galois theory, 64

gauging, 2

General Catalogue of the University

of Vermont, 1791–1890, 23, 42

General Electric, 65

geodesy, 48

geography, 2, 4, 39

geology, vii

geometric function theory, 46

geometry, 2, 23, 28, 29, 54

analytic, 29, 50, 57

diﬀerential, 64

foundations, 64

hyperbolic, v, 23

projective, 46

solid, 28, 49

spherical, 2, 28, 49

synthetic, 57

teaching, 57

George Mason University, 62

George Washington University, 59

Georgia, 15

German universities, 45

Germany, 51

Glastonbury, CT, 8

globes, 4

Gospels, 2

G¨ottingen, v, 45, 53

Graduate College, 66

graduate degrees, 64–66

graduate education, 57

Grafton, MA, 12

grammar, 39

Grand Isle County, VT, 18

Granville, MA, 8

Great Depression, 53, 58

Greek philosophy, 6

Green Mount Cemetery, 26

Greenﬁeld, MA, 8

Greenwich, England, 3

Greenwich, NY, 41

Gregorian calendar, 9, 31

Groton Academy, 20

Groton, MA, 20

Guilford, VT, 5

Hadley, MA, 37

Hamilton College, 27

Hampton Institute, 61

Hampton, VA, 61

Hannover, Germany, 29

Hanover, NH, 9, 12

Hardwick, England, 28

Hardwick, VT, 58

Harvard University, v, vi, 1, 4, 28,

45, 47, 53, 54, 61, 62

Haverford College, 47

Heat, 49

heat, 46

Hebron, CT, 12

Heidelberg College, 61

helix, 21

henry (unit of electrical inductance),

vii

Herschel’s Astronomy, 28

90 SUBJECT INDEX

High School Mathematics Contest,

76

Hilbert space, 53

Hilbert’s Tenth Problem, 62

Hinesburg, VT, 19

Hinsdale, NY, 47

Historical Catalogue of Brown

University, 8

History and Development of

Triangulation in Massachusetts,

48

History of Lake Champlain, 50

History of the Indian Wars with the

First Settlers of the United

States, 1

hockey, 69

hollow earth theory, 14

Hollywood, CA, 48

Hopewell, VA, 64

Horner’s method, 50

Houghton–Miﬄin Publishers, 30

House of Representatives, 15

How Green Was My Valley, 50

Howard Bank, 69

Howard Street, 38

Hudson River, 27

Hudson, MI, 45

Hughes Aircraft Corporation, 65

humanities, 39

Hungary, 45

Hutton’s Algebra, 22

Hutton’s Arithmetick, 22

Hutton’s Conick Sections, 22

Hutton’s Geometry, 22

Hutton’s Trigonometry, 22

Hyde Park, NY, 56

hydrogen, 4

hypothesis testing, 69

IBM, 63

Illinois Industrial University

(University of Illinois), 29

Indian Removal, 17

Indonesia, 7

inﬁnite series, 57

inﬁnitesimals, 31

Ingham University, 40

Institute for Advanced Study, 62

Instituzioni analytiche, 30

Instructor in Mathematics, 46

Instructor in Political Economy, 46

instructors, 71

integral equations, 53

Internet, 64

involution (raising to power), 22, 49

Iowa State University, 72

Ira Allen Chapel, 58

Iraq, 3

Iroquois language, 7

irrational numbers, 31

J. H. Colton Publishers, 13

J. T. White Publishers, 1

Jackson, MO, 7

Jackson, TN, 54

Jacksonian democracy, 15

Jeﬀersonian democracy, 15

Jersey City, NJ, 39

John Dewey Lounge, 26, 36

John Low Publishers, 4

Johns Hopkins University, 45, 56

Johnston, RI, 54

Journal de math´ematiques pures et

appliqu´ees, 32

Journal f¨ur die reine und

angewandte Mathematik, 32

Journal of the Franklin Institute, 21

Julian Calendar, 31

junior exhibition, 39

Jupiter, moons of, 3

Kappa Alpha Theta, 39

Kenney Award, 60

Kentucky, 17

Kentucky College, 23

Kidder Award, 76

Kinderhook, NY, 18

Knoxville, TN, 63

Kristallnacht, 51

Kroepsch–Maurice Award, 76

La Crosse, WI, 42

Lake Champlain, 14, 51

Lambda Iota fraternity, 35, 36

Lancaster Publishing Company, 50

land-grant institutions, 38

Lanesboro, MA, 21

largest common divisor, 49

SUBJECT INDEX 91

latitude, 2

Lawrence County, AR, 8

Lawrence, KS, 35

Lebanon, CT, 9

Lebesgue integration, 57

lecturers, 71–72

Legendre’s Geometry, 28

L´egion d’honneur, 48

Legislative Acts of Vermont, 11

Leipzig, 45

Leroy, NY, 40

Lessons in Astronomy, 13

levelling, 2

Lewis Institute, 55

LGBT community at UVM, 40

LGBTQA Coalition, 41

Liberty Party, 18

librations, 20

Lincoln, NE, 62

Liouville’s Journal, 32

literature, 26

Livermore, CO, 59

Locofocos, 18

logarithms, 2, 22

London, England, v, 4

longitude, 2–3, 31

Lord House, 66

Lorillard Institute, 35

Lorillard Tobacco Company, 35

Los Angeles, CA, 60

Louisiana, 35

Lousiana State University, 35

lowest common multiple, 49

Lucasian Professorship, 30

Lucy Ann Abbot House, 6, 47, 55

Ludlow, VT, 50

Lusitania, 50

“Luther and Loyola”, 39

machine language, 63

magnetism, 46

Maine, 54

manifolds, 49

Mansﬁeld House, 66

Maple Street, 14

Maricopa County, AZ, 38

Marshall Hall Conference, 75

Massachusetts, 17, 43

Constitutional Convention, 1

Massachusetts Historical Society, 20

Massachusetts Institute of

Technology, 55, 59, 63, 75

Master of Arts in Teaching, 76

Master of Science, 76

Master of Science in Teaching, 76

master’s degree, 64

master’s thesis, 57

Mathematical Reviews, 65

Mathematical Tracts on Physical

Astronomy, 30

Mathematics Awareness Month, 76

mathematics education, 63, 65,

75–76

mathematics of ﬁnance, 57

Maxwell laws, vii

McAuliﬀe Paper Company, 50

McGill University, 73

M´ecanique c´eleste, vii, 3

mechanical drawing, 39

mechanical engineering, 29

mechanics, 28, 50, 57, 61

Medﬁeld, MA, 1

Medical College, 21, 64, 66, 69, 72

Memoirs of the American Academy

of Arts and Letters, 20, 21

mensuration, 2

mephitic air (carbon dioxide), 4

metallurgy, 38

meteor, 26

meter, 31

Methodist Church, 35

metric system, 49

Mexican War, 18, 19

microscope, 4

Middlebury College, 8, 9, 37, 38, 73

Middlebury, VT, 1

military aﬀairs, 22

Milwaukee, WI, 61

mining, 38

Minneapolis, MN, 38, 42

Mississippi River, 15, 42

Missouri, 7

mixed (applied) mathematics, 42

Montgomery, VT, 41

Montpelier Academy, 5

Montpelier High School, 41

Montpelier, VT, 5, 21

92 SUBJECT INDEX

Montr´eal, Qu´ebec, 73

moon phases, 3

Moor’s Charity School, 9, 10, 12

Morgan scholars, 47

Morningside College, 61

Morrill Act, 38

Moscow, Russia, 62

Mount Allison University, 54

Mount Tambora, 7

Mount Washington, MO, 59

multiple roots, 50

NASA Space Grant, 77

Nashville, TN, 40

national bank, 17, 18

National Council of Teachers of

Mathematics, 63

National Cyclopedia of American

Biography, 1, 5, 8

national debt, 19

National Science Foundation, 65, 66,

74, 75

National Weather Service, 64

Native Americans, 40

natural philosophy, vii

Naval Observatory, 45

navigation, vii, 2, 28

Nazis, 45

New Brunswick, Canada, 54

New Brunswick, NJ, vii

New Canaan, CT, 47

New England, 4

New England colleges, 63

New Hampshire, 9, 10, 12

New Haven, CT, 8

New Haven, VT, 30

New Jersey, 39

New London, NH, 41

New York, 4, 10, 18, 50, 62

New York Free Academy (City

College of New York), 29

New York Life Insurance Company,

46

New York Mathematical Society, 53

New York Times, 47

New York University, 62, 65

Newark, NJ, 50

Newburgh, NY, 25

Newport, RI, 69

Newton’s Principia, vii, 29, 31

Nicholson House, 6, 48, 55, 57

“Nihil humani alienum”, 20

normal (Gaussian) distribution, vii

North Carolina State University, 75

North Dorset, VT, 35

North Stamford, CT, 25

Northern Paciﬁc Railroad, 30, 38

Northwestern University, 60

Norton Publishers, 48

Norwich University, 38, 76

“Note on the second variation in an

isoperimetric problem”, 53

Nova Scotia, 45

number theory, 64, 73

numerical analysis, 62, 64, 65, 73

numismatics, 50

nursing, 69

oblique coordinates, 29

Ohio, 40, 50

Ohio State University, 73

OK, 18

Oklahoma State University, 72

Old Mill, 26, 36

Old Monkland, 11

On Air, 4

“On the condition that a point

transformation of the plane be a

projective transformation”, 53

“On the diameter of screws”, 21

“On the general classiﬁcation of

plane quartic curves”, 47

“On the sections of a plane, with the

solids formed by the revolution

of the conic sections, about axes

situated in their planes”, 27

“On the structure of ﬁnite

continuous groups”, 56

Onondaga, NY, 27

optics, 28

Oration on Curiosity, 5

orbits, 29

“Orful Konﬂagration”, 18

Orleans County, VT, 18

Oxford University, 42, 75

oxygen, 4

Palo Alto, CA, 58

SUBJECT INDEX 93

Pan-American Exposition, 30

Paradise Lost, 2

parallel lines, 23

parallel postulate, 23, 29, 37

Paris, v

1900 Exposition, 30

Parsippany, NJ, 27, 28, 56

particles, 29

Partielle Diﬀerentialgleichungen, 49

Paternoster Row, 4

Pearl Harbor, 57, 58

pendulum, 21

Pennsylvania, 62

Pentagon, 62

permutations, 22, 49

Petersburg, Russia, 46

pharmacology, 66

Phelps, NY, 21

Phi Beta Kappa, 39

Philadelphia, PA, 19, 47

Philosophical Chamber, 4

physics, 28, 70

piezometer, 20

Pike Cemetery, 32

Plainﬁeld, NJ, 61

planetarium, 4

Plattsburgh, NY, 14

Plymouth, VT, 50

Poisson distribution, 32

Poland, 49

polar coordinates, 29

pole star, 2

Portsmouth, NH, 10

Potentiel thermodynamique, 49

power-series expansions, 31

prediction, 69

Presbyterian Church, 37

Preston, CT, 13

Prince Edward Island, 54, 55

Princeton University, vi, 21, 46, 53,

63, 73, 75

Princeton, NJ, 20, 62

probability, 64, 69

projections, 28, 39

Protestant worship, 43

Providence, RI, 8

psychology, 69

Purdue University, 73

pure mathematics, 42

Purple Mountain Press, 28

Putnam Examination, 65

Putnam’s Monthly, 28

quadrants, 4

Qu´ebec, 59

Queen’s College (Rutgers), 22

Raquette River, 28

rectangular coordinates, 29

Redwood Glass Company, 14

Registrar, 46

Rensselaer Polytechnic Institute, 54

Republican Party, 19

research, 45, 64–66, 72–73

released time, 66

research professor, 72

revenue tariﬀ, 19

Rhondda Valley, 50

Richmond, IN, 61

Richmond, VT, 62

Riemann surfaces, 49

Rochester, NY, 37

Rock Island, IL, 42

Rockingham, VT, 29

Rockport, MA, 57

Romanov Dynasty, 71

Roseburg, OR, 63

Rowley, MA, 30

Royal Frederick University, v

Royal Irish Academy, vii

Royal Military Academy, 22, 28

Royal Society Catalogue of Scientiﬁc

Papers, vii, 20, 26, 27

Royal Trust Company, 58

Royalton, VT, 30

Rule of Double Position, 23

Russia Leaves the War, 47

Russian Revolution, 46

Ryegate, VT, 11

Salem, MA, 4

Samuel Mills Press, 6, 7

San Francisco, 42

Santa Barbara, CA, 47

Saxton’s River, VT, 39

Scandinavia, 43

Schenectady, NY, 1, 13

94 SUBJECT INDEX

School of Business Administration,

72

scientiﬁc instruments, 4

Scituate, RI, 37

Scotland, 11

Scottish Society for Propagating

Christian Knowledge, 9

scripture, 43

Secretary of State for the Colonies, 9

Secretary of the Faculty, 46

semicubical parabola, 31

senior exhibition, 39

series expansions, 50

Seven Years’ War, 9

Sheﬃeld, England, 32

Sherman and Smith Publishers, 13

shipbuilding, 54

sidereal day, 2

Silliman’s Journal, vii, 21, 26, 27

Singer company, 46

Sioux City, IA, 61

Sketches of the History of Dartmouth

College and Moor’s Charity

School, with a Particular

Account of Some Late

Remarkable Proceedings of the

Board of Trustees from the Year

1771 to the Year 1815, 12

slave auction, 35

slavery, 17–19, 26, 40

Slough, England, 29

Sobail, NY, 28

solar time, 20

mean, 20

sophomore exhibition, 39

South Carolina, 15, 17

South Prospect Street, 6, 47

South Willard Street, 14

Soviet Union, 65

history, 46

Sparta, TN, 66

species, 49

sphere, projections of, 2

spherical solids, 29

spring term, 21

Sputnik, 65

St. Albans, VT, 5, 37

St. Johnsbury, VT, 65

St. Louis, MO, 30, 54, 74

St. Michael’s College, 73

St. Paul’s Episcopal Church, 50

Stanford University, 63

State Agricultural College, 38, 39,

49, 59

“Statement of Facts Relative to the

Appointment of the Author to

the Oﬃce of Professor of

Chemistry in Middlebury

College and the Termination of

his Connexion with that

College”, 8

Staten Island, NY, 56

statistics, 60, 63, 64, 69–70, 72

program, 63, 70

STEM, 39

Strasbourg, 30

student awards, iv

Sturbridge, MA, 1

Sturm functions, 50

summability methods, 62

summer term, 21, 28

Supreme Court, 13, 15

surds, 49

surveying, 2, 28

Syracuse University, 47

Tammany Hall, 18

Tamworth, NH, 55

tariﬀs, 17

taxation, 39

telegraph, 26

telescope, 4

Tennessee Technological University,

66

tenure, 71

Texas, 18

textbooks, 4, 28–29

The Mathematics of Statistics, 60

“The Puritans and Art”, 39

“The Wilds of Northern New York”,

28

theory of equations, v

theory of ﬁelds, 62

theory of functions, 57

theory of groups, 62, 64

theory of rings, 62

Tiﬃn, OH, 61

SUBJECT INDEX 95

tobacco, 35

topology, 64, 73

Torricellian experiment, 4

Townsend Acts, 9

Trail of Tears, 15

Transactions of the Royal Society,

32, 69

Transcendentalists, 1

trial-and-error, 23

tribalism, 41

trigonometry, 2, 49

plane, 28, 56

spherical, 2, 20, 22, 28, 56

Troy, NY, 26

“True Excellence: Conformity to

Principle”, 39

Trustees of Dartmouth College v.

Woodward, 13

Tyndal scholars, 47

“

¨

Uber die Form und Stabilit¨at

gewisser Fl¨ussigkeitstropfen”, 53

UCLA, 72, 73

UFOlogists, 14

Underhill, VT, 28

Union College, 1, 13, 38

Unisparker ignition coil, 48

Unitarian Church, 1

United Irishmen, vii

United States, 26

United States Department of

Education, 75

United States Military Academy, 28

United States Navy, 15, 54, 61

Universal Geography, 4

University Grammar School, 8

University of Berlin, 47

University of California, 64

University of California at San

Diego, 73

University of Chicago, 45, 62, 75

University of Georgia, 8

University of Illinois, 75

University of Iowa, 29, 66

University of Kazan, v

University of Michigan, 23, 26, 38,

45, 61, 73

University of New Hampshire, 55

University of New Mexico, 63

University of North Carolina, 74

University of Oslo, v

University of Paris, 75

University of Pittsburgh, 62

University of Prague, 49

University of Rhode Island, 69

University of Rochester, 75

University of Tennessee, 63

University of Texas, 54

University of Vermont, 1, 15, 26,

37–39, 58

alumni, 23, 29, 60

archives, 35, 55, 61

Board of Trustees, 13, 32, 33, 39,

48, 59, 64, 66, 75

minutes, 1, 4, 6, 9

by-laws, 43

catalog, 21, 70

College of Medicine, 47

commencement, 28, 32

endowments, 39

enrollments, 38, 49, 57, 58

gifts, 39

Graduate College, 64

Graduate Council, 64

hockey team, 55

library, 4, 26, 30–32, 37

observatory, 48

religious rules, 42–43

student expenses, 23, 59, 66

tuition, 39

Veterans’ Education, 48

University of Vermont and State

Agricultural College, 38, 39, 58

“University of Vermont Trust”, 59

University of Washington, 75

University of Wisconsin, 60

University of Wyoming, 74

University Scholar Award, 76

Uranus, 29

US census, 39

Van Nostrand Publishers, 60

Vergennes, VT, 1

Vermont, 1, 3, 10, 11, 17, 18, 21–23,

33, 35, 37–40, 43, 59, 63, 64, 66,

76

Council, 11

Declaration of Independence, 10

96 INDEX

declaration of war on Germany, 58

Department of Education, 75

General Assembly, 10–12, 14

Governor, 11

legislature, 1, 5, 39, 58, 59

origin of the name, 10

population, 7

Republic, 10

Constitution, 10

Supreme Court, 12

Surveyor General, 11

Vermont Academy, 39

Vermont Baptist Convention, 39

Vermont high school mathematics

competition, 41–42, 72

Vermont High School Summer

Mathematics Institute, 75

Vermont Historical Society, 5

Vermont Mathematics Initiative, 75

Vermont–Qu´ebec Number Theory

Seminar, 73

Vermont State Mathematics

Coalition, 75

Vershire, VT, 50

versiera, 31

Vice-President for Academic Aﬀairs

(Provost), 65

Virginia, 12

Volusia, FL, 55

Wales, 50

War of 1812, 1, 6

Wareham, MA, 8

Washington County Grammar

School, 5

Washington University in St. Louis,

54, 74

Washington, DC, 18, 45, 59

water pump, 4

Waterman Building, 75

wave theory of light, 31

weather prediction, 62, 64

West Lafayette, IN, 73

West Roxbury, MA, 42

Westﬁeld, MA, 25

Academy, 25

Westminster, VT, 10

Wheelock, VT, 11, 12

Whig Party, 17, 18

Wilberforce University, 40

Wilbur Collection, iii, 8, 21

Wilbur Fund, 58

Willard Street, 38

Williams College, v, vi, 8, 25, 37

Williams Professorship, 32–33, 35,

45, 46, 53, 56

Williams Science Hall, 47, 48

Wilmington, OH, 14

Windham, CT, 9

Windsor, VT, 5, 10, 19

Winooski River, 50

witch of Agnesi, 31

women at UVM, 39–40, 61

Women’s Studies, 40

Woodbury, CT, 27

Woodstock, VT, 12, 30, 47

Woolwich, 22, 28

Worcester Polytechnic Institute, 47,

48, 56

Worcester v. Georgia, 15

Worcester, MA, 8, 48

World War I, 45, 48, 50, 54

World War II, 48, 54, 57, 58, 61, 62

World’s Columbian Exposition, 29

Xenia, OH, 40

Yale University, vii, 4, 8, 13, 40, 45,

66

Yale University Press, 21

Zoonomia, 4

Name Index

Abel, Niels Henrik, v

Adams, John, 12, 26

Adams, John Quincy, 15

Adrain, Robert, vii, 22

Agnesi, Maria, 30

Airy, George, 30

al-Khwarizmi, 49

Aleong, John, 72, 77

Allen, Ethan, 10

Angell, James, 37

Arbogast, Louis-Fran¸cois, 30

Arbuthnott, John, 69

Archdeacon, Dan, viii, 61, 73, 77

Archimedes, 31

Arnold, Benedict, 50

Ashikaga, Takamaru, viii, 72, 77

Austin, Samuel, 8, 13

Bailey, Guy, 58

Baldwin, Agnes, 50

Balinski, M. L., 21

Barbour, Volney, 38, 48

Bartels, Johann, v

Becker, Howard, 28

Becker, James, 73

Benedict, Farrand, 27–29, 38

Benedict, George, 22, 25–27, 30

Benedict, Joel, 29

Bentil, Daniel, 75

Bernoulli, Jacob, 30, 69

Bernoulli, John, 30

B´ezout,

´

Etienne, 26

Billings, Frederick, 30, 38

Biot, Jean-Baptiste, 30

Blow, David, iii

Bonnycastle, John, 28

Borgmann, Carl, 59

Bowditch, Nathaniel, vii, 3, 21

Brett, George, 50

Brock, Paul, 63, 65, 73

Brooks, Preston, 35

Brown, Joanne, 77

Buck, Daniel, 11

Buckham, Matthew, 29, 38

Bullard, James, 56, 59, 61

Bullard, Warren, 47, 56

Burgess, Ebenezer, 8

Burgmeier, James, viii, 63, 65, 66,

72–74, 76, 77

Burnard, Mary Betty, 77

Butler, Caleb, 20

Butterﬁeld, Arthur, 6, 47, 50

Buzas, Jeﬀ, 75

Cadbury, Warder, 28

Calhoun, John, 17

Callahan, Jeremiah, 23

Cardano, Girolamo, 23

Carlisle, L. Diana, 14

Carnot, Lazare, 30

Cayley, Arthur, 46

Chamberlain, Erling, 62, 65, 66, 72,

77

Chamberlain, Jason, 7

Cicero, 2

Clay, Henry, 17, 18

Colson, John, 30

Cook, Clinton, 65

Cooke, Andrew, viii

Cooke, Roger, viii, 33, 63, 65, 66,

72–74, 77

Corning, Charles, 14

Corse, Fred, 46

Cotes, Roger, 30

Cox, Emily, iv

Craig, Thomas, 45

97

98 NAME INDEX

Crelle, August, 32

Crockett, Walter Hill, 50

Crowell, Albert, 21

Dallas, George, 19

Daniels, Archibald, 45, 47, 49, 51, 53

Daniels, Robert, 46

Darwin, Charles, 4

Darwin, Erasmus, 4

Davies, Charles, 28

Davis, George, 66, 75

Davis, Martin, 62

Dean, Abigail, 5, 20

Dean, Eleanor, 5

Dean, James, vii, 4–21, 30, 47

Dean, John, 5

Dean, Nathaniel, 5

Dean, Noah, 5, 20

Dean, Parnell, 5

Dean, Willard, 5

Delambre, Jean-Baptiste, 30

Dinitz, Jeﬀrey, iii, viii, 33, 73–77

Diophantus, 49

Donahue, James, 54, 57

Drew, Charles, 41

Duhem, Pierre, 49

Dummit, David, viii, 73, 77

Durant, Lettie, 41

Dur`ege, Heinrich, 49

Dwork, Julius, 62, 64, 65

Einstein, Albert, 23

Essler, Warren, 66

Euclid, 2, 23

Euler, Leonhard, 3, 30

Faraday, Michael, vi

Fenwick, James, viii

Ferguson, Janet, iv, 77

Fey, John, 64

Fillmore, Millard, 17

Fine, Henry, 46

Fishback, William, 60, 61

Flint, Edwin, 48

Foote, Richard, 73, 75, 77

Foster, John, 14

Fourier, Jean-Baptiste Joseph, 49

Fraleigh, Percy, 48, 56, 57, 59, 62

Franklin, Fabian, 45

Galileo, 3

Gauss, Carl Friedrich, v, vii, 30

George III, 12

Giddings, Horace, 55

Golden, Kenneth, 33, 75

Gross, Kenneth, 33, 63, 74

Gunning, Robert, 46

Hall, Marshall, 75

Hamilton, Ellen, 39

Harrison, William Henry, 17, 18

Haskel, Daniel, 13, 21

Haugh, Larry, 72, 77

Hayne, Robert, 15

Henderson, George, 40

Henry, Joseph, vi, vii, 20, 21

Herschel, William, 28

Hershner, Ivan, iv, 62, 64

Hilbert, David, 53

Hodge, Helen, 40

Hodge, Lydia, 40

Hodge, Steven, 39

Horner, William, 50

Houghton, George, 5, 19, 30

Houghton, Henry Oscar, 30

Householder, Fred, 54, 57

Howard, John, 38

Hubbell, Lucas, 21

Huntington, George, 27

Huntington, Samuel, 38

Hutchinson, Titus, 11, 25

Hutton, Charles, 22, 23, 29, 32

Izzo, Joseph, iv, 55, 62, 65, 77

Jackson, Andrew, 1, 15, 17, 19

Jeﬀerson, Thomas, 7, 12, 26

Johansson, Jan, 72, 77

Johnson, Joseph, 4

Julianelle, Tony, 72

Karstens, Karla, 72

Karstens, William “Sandy”, viii

Kasner, Edward, 54

Kennan, George, 47

Kenney, John, 60

Kent, Atwater, 48

Kimball, William, 61

Klein, Felix, 45

Klyuchevskii, Vladimir, 71

NAME INDEX 99

Kost, Larry, viii, 72, 73, 77

La Croix, Sylvestre, 30

Lafayette, Marquis de, 26

Lagrange, Joseph-Louis, 3

Lakin, William, 74, 76, 77

Laplace, Pierre-Simon, vii, viii, 3

Larrivee, Jules, 59, 61

Larson, Karin, 77

Lawlor, John, iv, viii, 72, 74, 76, 77

Legendre, Adrien-Marie, 28, 29, 37

Leibniz, Gottfried Wilhelm, 31

Lenin, Nikolai (Vladimir Il’ich

Ul’yanov), v

Lighthall, Harry, 62, 65, 66

Lincoln, Abraham, 19

Lindsay, Julian, 2–4, 26, 38

Liouville, Joseph, 32

Llewellyn, Richard, 50

Lobachevskii, Nikolai Ivanovich, v

Loomis, Elias, 37

Lord Dartmouth (William Legge,

2nd Earl of Dartmouth), 9

Lorillard, Pierre, 35

Low, Elizabeth, 72

Maclaurin, Colin, 30

Macmillan William, 66

MacPherson, Brian, 72

Maltby, Richard, iv

Marlow, Jackie, iv

Marshall, John, 13

Mason, Lida, 39

Maxwell, James Clerk, vi, 49

McClay, Douglas, 54, 59

Meserve, Bruce, 63, 64

Mickey, Ruth, 72

Millington, Howard, 54, 59, 61

Millis, John, 58, 59

Milton, John, 2

Moor(e), Joshua, 9

Morency, David, 72, 77

Morrill, Justin, 38

Moser, Donald, 62, 65, 73

Mr. Pickwick, 29

Neumann, Carl, 45

Newcomb, Simon, 45, 46

Newton, Isaac, v, 29, 31

Nicholson, George, iv, 6, 48, 53, 54,

57, 59

Nicholson, Margaret, 55

O’Hara, Maureen, 50

“Old Kinderhook” (Martin Van

Buren), 18

Olds, Gamaliel, 8–9

Openshaw, Mary Eliza, 69

Oughstun, Kurt, 75

Parker, Charles, 28

Payne, John, 4

Peabody, Selim, 29

Pease, Calvin, 37

Peck, John, 14

P´eladeau, Marius, 7

Pershing, John, 48

Petty, McKendree, 29, 35–38, 45

Phillips, John, 12

Pidgeon, Walter, 50

Pinder, George, 75

Poggendorﬀ, Johann, 46

Poisson, Sim´eon-Denis, 30

Polk, James K., 17–19

Pomeroy, John, 38

Priestley, Joseph, 4

Prince, John, 4

Ptolemy, Claudius, 3

Puterbaugh, Holly, 41, 72, 77

Pycior, Helena, 22

Pythagoras, 6

Queen Anne, 69

Rathvon, Henry, iv

Read, Helen, 72, 77

Reynolds, Jeremiah, 14

Riemann, Bernhard, 49

Riggs, Heath, iv, 54, 57, 62, 63, 65

Rockefeller, John D., 45

Rodney, Peter, 77

Sanders, Daniel Clarke, 1, 6

Sands, Jonathan, viii, 73, 77

Schoonmaker, N. James, iv, 55, 62,

65, 73

Schwarz, Hermann, 45

Sherman, Ethel, 41

Silliman, Benjamin, vii, 8

100 INDEX

Simon, Lloyd, viii

Simond, Ruth Gertrude, 61

Siran, Jozef, 77

Slocum, Allison, 47, 49

Smith, John Calvin, 13

Smith, Otis, 30

Smith, Rev. Sydney, vi

Smith, Worthington, 37

Snapp, Robert, 75

Son, Mun, 72, 77

Stanton, William, 14, 15

Story, William, 45, 47, 56

Sturm, Jacques, 50

Sumner, Charles, 35

Swift, Elijah, 53–54, 56, 57

Sylvester, James, 45

Sylwester, David, 63

Symmes, John, 14

Taber, Henry, 56

Taylor, Zachary, 17, 19

Terence, 20

Thomas, Evan, 50, 56

Thompson, William, 41

Tolstoy, Leo, v

Torrey, Augustus, 42

Torrey, Joseph, 30, 37

Tsar Aleksandr II, 71

Tyler, John, 17, 18

Van Buren, Martin, 15, 17, 19

Weaver, Sheila, 72

Webster, Daniel, 13, 15, 17

Weierstrass, Karl, 45, 46

Wentworth, Benning, 10

Wheeler, John, 4, 5, 30

Wheeler, Mary, 41

Wheelock, Eleazar, 9

Wheelock, John, 10, 12

Whitelaw, James, 11

Wilbur, James, 58

Williams, Azarias, 32

Williams, Edward, 47

Williams, George, 23

Wilson, J. Michael, 73, 77

Witham, Myron, 6, 57, 59

Woodruﬀ, Frank, 40

Woodruﬀ, Mary, 40

Woodward, William, 12

Worthen, Edward, 35

Wright, Karen, iv

Wright, Robert, 63, 65, 66, 72, 73, 77

Yang, Jianke, 75

Young, Thomas, 30

Young, Y. Peyton, 21

Yu, Jun, 75, 77

Zwick, Dan, 77