This history was written as part of the celebration of Union College’s 200 year anniversary by Theodore A. Bick in August 1993.

## The Early Days of the Department

Founders of early American colleges doubtless were aware of Plato’s admonition denying admission to anyone ignorant of geometry. They were also cognizant of the more general role of mathematics in the traditional *trivium* (logic, grammar and rhetoric) and *quadrivium* (arithmetic, geometry, astronomy and music), which constituted the liberal arts curricula of the time. Indeed, John Taylor, who came to Schenectady from New Jersey prior to 1793 to assume charge of the Schenectady Academy (which later became Union College), was appointed Professor of Mathematics and Natural Philosophy (Physics) at the College in 1797. Although such joint appointments were common at colleges during the early days of the Republic, even by the standards of the day, Taylor was an unusually versatile man. One account of his life mentioned that Taylor was “eminently fitted to advance (the academy)” and went on to say that “after taking charge of Union, was professor of all that was taught in the infant college”. Among other things, he had served with distinction during the Revolution, having risen from Captain to Colonel, and had taken part in the famous crossing of the Delaware with Washington.

Taylor was succeeded by Cornelius Van der Heuvel (1798-99); Benjamin Allen (1800-09); Ferdinand Hassler (1810-11), who later founded the U.S. Coastal Survey; Thomas Macauley (A.B. Union, 1804), who served as Tutor, 1805-06, Lecturer,1811-14, then Professor, 1814-22, and who, when he left the College, pursued a career in theology; Alonzo Potter (1822-26); and Benjamin Joslin, who graduated from Union in 1821, tutored at the College 1822-24, then graduated from the NYU College of Physicians and Surgeons in 1826. Throughout most of this period, the department consisted only of one professor, occasionally assisted by a tutor.

Doubtless the early curriculum in mathematics was influenced, at least indirectly, by Eliphalet Nott. The parallel curricula, which allowed students to “major” in classical or scientific courses, was introduced by Nott in 1828; that same year, differential and integral calculus were offered to seniors in the scientific curriculum. Engineering appeared in 1845 with the hiring, by Nott, of William Gillespie (about whom more later). Though he valued mathematics for its role in explaining science and engineering, Nott admired the subject as much for the mental discipline which its study demanded.

## The Jackson Years: 1826 – 1877

During the period from 1826 to 1877, the department contained, and for much of the time consisted of, Isaac Jackson. An 1826 graduate of Union, Jackson was an active publisher of textbooks himself – books on mechanics, optics, conic sections and trigonometry as well as notes on acoustics and electricity (his prescience evident there), magnetism and mineralogy bore his name. Although Jackson seems not to have sought to make any original contributions to mathematics, he maintained a lifelong friendship with the noted physicist Joseph Henry, and his texts and notes are evidence of his energy and love of mathematics and the teaching of it. Jackson was, as were many of the early faculty across the College, a man of many parts, as the article about him in this *Dictionary* attests. He retired in 1877, a year before Joseph Sylvester founded the first graduate program in mathematics in this country, at Johns Hopkins.

William Gillespie, a Columbia graduate, came to Union in 1845 as its first Lecturer in Civil Engineering. It is important to note that he also served for most of the rest of his career as Adjunct Professor of Mathematics. Gillespie not only stressed the importance of mathematics in engineering, he began a tradition of emphasizing the humanities for the engineers as well; this is a tradition that the College has wisely preserved to this day, to its enormous benefit. Gillespie was a poet, as well as the author of two successful textbooks, one on road-making, the other on surveying. It was through his efforts that the College acquired its copies of the Olivier models, which demonstrate three-dimensional surfaces by stringing threads on brass and wooden frames; some of these are now displayed prominently in the mathematics department, after having been restored during the 1970’s by Prof. William C. Stone. Stone’s monograph describes the models in detail.

Gillespie’s influence doubtless contributed to the study of mathematics at Union in its familiar role as “handmaiden of the sciences”. The *Catalogue* in 1882-83 listed, among many other things, a course in quaternions, which at the time was right at the frontier of mathematical research, and involved some of the biggest names in American mathematics (for example, Sylvester on one side and J. Willard Gibbs of Yale on the other). Although a comment in *Concordiensis* in November, 1880, claiming that only at Union and Johns Hopkins are courses in quaternions taught on this side of the Atlantic is probably an exaggeration, still the subject was in the air, and it is remarkable to find a course in that area, necessarily “voluntary”, taught at a small college. It is also worth noting that during the period 1883-1901, a series of papers on quaternions appeared under the pen of Charles Proteus Steinmetz.

## The Turn of the Century: 1877 – 1930

Isaac Jackson retired in 1877, and was followed by Isaiah B. Price, who had graduated from Union in 1872 and served as Tutor from 1872-75. Upon the death of Jackson, Price became Professor of Mathematics (and Assistant Professor of Physics), 1878-84. He was succeeded by Thomas W. Wright, who served as Professor of Applied Mathematics and Chairman of the Department of Physics (1895-1904). Benjamin Ripton was appointed Adjunct Professor of Mathematics in 1886, and became Professor the following year. In 1894, he was appointed Professor of History and Government, a post he held until 1921. He also served as Dean from 1894-1919. Edwin H. Winans (A. B. Union, 1888) became an instructor in the department in 1889, and subsequently held the post of Assistant Professor for eight years. While teaching at Union, Winans also studied law and was admitted to the bar in 1892. He left to practice that profession in Rochester in 1899.

Since Steinmetz was the foremost electrical engineer in the world in the late nineteenth and early twentieth centuries, it was inevitable that his influence on the mathematics curriculum would be swift and powerful. Soon after his arrival at Union in 1895, that curriculum included, for the engineers, Advanced Calculus, Ordinary Differential Equations, and a choice between Geometry of Three- Space, Determinants, and Quaternions. More and more mathematics courses were offered by the Electrical Engineering Department, so that, for instance, by 1909-10, Charles F. F. Garis was the sole member of the “Academic” Mathematics Department, while “Engineering” Mathematics boasted a Professor (Garrison) and an Instructor (Mark).

By 1914-15, the Mathematics Department seems to have subsumed Engineering Mathematics, and its combined faculty now numbered five, with Garis at its head. It is interesting to note that in 1917, Assistant Professor Sidney Rowland took leave from the *College *to accept a commission as Lieutenant in the U. S. Army – and that he continued to be listed in the Catalogue as a member of the faculty. He returned to Union after the war and held the position of Assistant Professor of Mathematics until he left in 1924 to become head of the mathematics department at Ohio Wesleyan (and later held that post as well as being mayor of Delaware, Ohio). In 1919, Garis was named Dean of Students (and continued to hold his position as Professor and head of the Mathematics department). The previous year, David Sherman Morse had accepted a position as Instructor in the department. Morse left in 1920 to pursue studies toward the Ph.D. at Cornell. He obtained that degree in 1923 and rejoined the faculty at Union as Assistant Professor in 1924, the first person in the history of the department to hold the Ph.D. degree in mathematics.

## The Morse Years: 1933 – 1958

David Sherman Morse is the first Mathematics department chairman for whom there is significant living memory, of which this report makes heavy use. The record indicates that Morse rose quickly through the academic ranks, reaching Associate Professor in 1926, and Professor in 1931. Although Garis remained nominal head of the Mathematics department, he had been named Dean in 1919, and his office was in the Administration Building. It is not unreasonable to assume, and living recollection supports the assumption, that Morse became *de facto* head of the department as early as 1933. In any event, he was officially named Chairman in 1944, and was appointed to the Mary Louise Bailey endowed chair in 1952. He remained in the chair until his retirement in 1958.

During much of his time as head of the department, national economic conditions dictated that anyone who had a job did what he could to hang onto it. In addition, the tradition at Union and elsewhere was that people remained in department chairs more or less permanently. The result was that, if the chairman’s personality inclined him in that direction, there was little to prevent departments from becoming fiefdoms. According to available recollections, that is what happened at Union. Morse ran the department with an iron fist, telling instructors how to teach their courses, and even how to display the proofs of individual theorems. Moreover, Morse had decided that teaching and research were essentially antagonistic activities, and he developed and maintained an atmosphere in which professional growth was to take a distant second place to teaching. Moreover, teaching loads were high, and salaries were low, so that the temptation to teach graduate courses for extra compensation during the evening was difficult to resist, especially for faculty members with families. It is not surprising, then, that published research was in short supply in the Mathematics department during Morse’s years in charge.

Morse anecdotes, almost none complimentary, abound, and space does not permit an extensive recitation here. Perhaps one will suffice to indicate the nature of the man. When informed that the department’s water fountain was broken, Morse replied, “I never drink water between meals anyway”. The fountain remained unrepaired until a student fixed it on his own. On the other hand there is no evidence that he was anything but a man of consistent rectitude.

In spite of the ethos that Morse installed, some research activity did occur. Orrin Farrell, who joined the department in 1931 with a Ph.D. from Harvard, published papers in 1932 and 1934, and in 1949, while on leave at the Institute for Advanced Study at Princeton, read two papers at a spring meeting of the American Mathematical Society. But it is worth noting that Farrell only resumed his publishing career after Morse retired. Charles Standish, who served in the department from 1954 until 1957, also produced published work during his time at Union. The case of Augustus Fox, however, must appear on the debit side of Morse’s record. Fox joined the department in 1929, and then, after a leave of absence, finished his Ph.D. at Yale in 1935. Fox was among the first Ph.D. students of Marshall H. Stone, one of the most prominent American mathematicians of the era, and so was at the forefront of what was then the new and exciting field of functional analysis. Fox, who retired in 1966, did publish three textbooks, but nothing in functional analysis. It is difficult not to conclude that much of his promise was unfulfilled, and that the Morse atmosphere was at least partly to blame.

Morse was, without question, one of the most influential figures in the history of the department, and as controversial as he was dictatorial. No doubt he was well intentioned, and in fact, may have been unaware of the frustration and anger felt by the many fine and intelligent men who served under him.

## After Morse: 1958 – 1967

The humorless, dreary Morse era did not end with his retirement in 1958. He was succeeded by Fox, Farrell as acting chairman in 1962, and Fox again from 1963 until his retirement in 1966. At that point, William C. Stone, (Union ’42), became chairman. Each of these men had spent most (and in Stone’s case, all) of his career under the chairmanship of David Morse and in consequence, had little or no experience with other models. But the mathematical times had changed – there was now a shortage of Ph.D.s, and a good part of the chairman’s job was to recruit quality people in an unfriendly market. Moreover, candidates for positions even at small colleges were now interested in sustaining their research interests as well as developing as teachers. Perhaps not surprisingly, Fox, Farrell and Stone had their principal recruiting success with former students who had recently earned their Ph.D.s.

Three Union alumni, Stewart Robinson (’55), Howard Bell (’58) and Theodore Bick (’58), were recruited back to the campus, Robinson in 1964 and Bell and Bick in 1966. They joined with Yel-Chiang Wu, who also arrived in 1966, in informal seminars. Inevitably, the talk turned from mathematics to a discussion of the future of the department under Stone’s leadership. These young men came to the conclusion that in the existing climate, the length of Stone’s absence from the professional mathematical world would make it impossible for him to do the necessary recruiting. At their request, Stone resigned the chair and was replaced for the academic year 1967-68 by James D. Palmer, Dean of Science and Engineering. Stone was an acclaimed teacher, a charming and decent man, and very popular across the campus. He saw himself, and here again the Morse influence is clearly discernable, as “a teacher rather than a mathematician.” Many faculty members inside and outside the department saw Stone’s removal from office as an unnecessary humiliation; the rebels who had asked for his removal received very bad press. Three of them (Bell, Robinson and Wu) left the College in 1967.

## The Seiken Years: 1967 – 1979

The Morse era was over. During Palmer’s acting chairmanship, a search was conducted for a new chairman, and the process yielded, in a stroke of good luck for the College, Arnold Seiken. Seiken had come to Union from the University of Rhode Island in 1967, where he had suffered under the reign of an autocrat not unlike Morse. He was shrewd enough to realize that among his other duties, he had to heal the serious wounds which the department had just endured. Stone was still in the department, as was his good friend Ingo Maddaus, himself an excellent teacher whose mathematical career had been harmed by Morse perhaps more than anyone else’s. Bick remained from the overthrow group. So Seiken developed a recruiting strategy which, it turned out, served the College well. He sought people who gave evidence of interest in both teaching and mathematical activity, but who would also not subvert the delicate truce which kept the department together. This last requirement was in no way subsidiary to the other two: there would be, if the new chairman could achieve it, harmony. One of Seiken’s early recruits, John Roulier, who arrived in 1969, personified this philosophy. An excellent teacher, Roulier quickly established himself as the most active researcher in the history of the department up to that point, publishing one or two papers each year.

Not that Seiken was universally successful; another early recruit, despite several warnings, elected to do no research, but concentrated on teaching alone, and he was very good. The result was predictable: the young man became very popular with the students, so that when he was denied tenure (on the grounds of no publications and no program under way), several of the best students demanded an explanation. These included, by the way, James Saxe, who had won the U.S. Mathematical Olympiad as a high school student, and who finished in the first five (these by tradition being listed in alphabetical order) in the prestigious Putnam mathematical competition open to all U.S. college and university mathematics students. Seiken’s performance in the meeting with the students was a masterpiece. He brought four calculus books, one from each of the preceding four decades, to the meeting, and he used them to make it clear that since a tenure offer commits the College to perhaps forty years, someone who had crystallized four decades earlier could have serious trouble being either an effective teacher or a successful researcher. The students, to their credit, were convinced. After Edwin Gillette (a veteran of the Morse era) served in 1973-74 as acting chairman while Seiken was on leave, Roulier left to accept a position at North Carolina State University, which had a medical facility which could provide the care which his daughter required.

## Recent Years: 1975 – 1990

In 1975, Seiken recruited two young set theorists, Alan Taylor and William Zwicker. Their mathematical ability and energy became quickly apparent. For example, they began, immediately upon their arrival, the biennial Union College Set Theory Conference. This conference continues to the present, although the name has gone through several changes which have reflected the specialties of various persons added to the department; it is unique among small, essentially undergraduate colleges. International mathematical luminaries – among others, Paul Erdös, Saunders MacLane, and Stanislaw Ulam – have spoken at the conference (MacLane also received an honorary degree from the College in 1990).

By 1979, Seiken had served as chairman for eleven years, and although there was no dissatisfaction in the department with his performance, he decided to relinquish that post. William Fairchild, who had come to Union in 1970, succeeded to the chair, and at about that time, the College began the policy of having department chairs rotate among the tenured faculty, the usual period being three years. In 1981, Susan Niefield and Karl Zimmermann joined the department, and, following the example of Taylor and Zwicker, quickly demonstrated that excellence in either research or teaching does not imply neglect of the other.

Bick followed Fairchild as chairman in 1982; that same year, Julius Barbanel and Kimmo Rosenthal, who had previously served as temporary Assistant Professors, returned in tenure track positions. By this time, the critical mass of active young mathematicians and the existence of the conference had put Union on the mathematical map, with the result that the mathematical as well as the pedagogical expectations in the department had become very high. Student evaluations and research outputs which had previously been regarded as unusually high had now become the norm. Yet all six, Taylor, Zwicker, Niefield, Zimmermann, Barbanel and Rosenthal made it successfully through the tenure process. Bick’s three year term as chairman ended in 1985; he was succeeded by Taylor. In 1987, the College acquired the services of Michael Frame, who brought a high level of computer expertise to the department, along with a driving energy which impressed even the dedicated group already in place. Frame had an immediate and powerful impact on the department; he was also instrumental in persuading the College to place a personal computer on the desk of everyone in the department. Frame quickly advanced through the tenurability process; Taylor was succeeded as chairman in 1988 by Zwicker, who went on leave in 1989, Taylor serving as acting chair for 1989-90. Zwicker reassumed the chair in 1990.

## Conclusion

Space considerations do not permit a detailed discussion of the curricular changes which have occurred since the beginning of the Seiken chairmanship. For the most part, such a discussion would reveal that the department, with its influx of active professionals, has kept up with or ahead of its competition. As one example, the course in set theory and abstract systems, Mathematics 199 (formerly Math 99, formerly Math 18), was created in 1967 – and it was probably the first “introduction to the upperclass curriculum” of its kind in the country. In 1970, with the arrival of Fairchild, the department had the authors of perhaps the only two textbooks in existence suitable for that course (Bick is the other). It remains to the present time the prerequisite for every theoretical upperclass course, and often serves as a primary indicator of success as a mathematics major.

The department has benefitted from a pretty constant supply of excellent students, too many, of course, to mention here by name. As one example, of the four mathematics majors in the class of 1958, all went on to advanced degrees in mathematics, three of them to the Ph.D.. More recently, two must be recalled: James Saxe (’76), who went on to the Ph.D. in computer science at Carnegie Mellon; and Cynthia Curtis (now Budka) (’87), who compiled a straight A average at Union, completed her Ph.D. at Yale and is now on the faculty at Princeton. These are clearly exceptional, but the department can boast of many others of rank nearly equal to theirs. Almost every year, two or three graduates are accepted at the foremost graduate schools in the country.

By any reasonable measure – quality and quantity of publication, student evaluations of teaching, participation in or sponsoring of professional conferences, or success of its graduates in the most challenging graduate programs – the Union College Mathematics Department stands, in 1990, in the front rank of mathematics departments at American small colleges.

## References

- Smith, D.E. and Jekuthiel Ginsberg, “A History of Mathematics in America Before 1900” (Carus Mathematical Monographs #5), Mathematical Association of America (Open Court Publishing Co.), Chicago, 1934.
- Somers, Wayne, “Perseverance Conquers Much”, Friends of the Union College Library, Schenectady, N.Y., 1990.
- Stone, William C., “The Olivier Models”, Friends of the Union College Library, Schenectady, N.Y., 1969.
- Bell, Howard E., Private Communication, July, 1993.
- Standish, Charles J., Private Communication, July, 1993.
- Craig, Edward J., Personal Interview, July, 1993.
- Huntley, C. William, Telephone Interview, July, 1993.
- Maddaus Jr., Ingo, Personal Interview, July, 1993.