# Cochell: The Early History of the Cornell Mathematics Department

4. JAMES EDWARD OLIVER AND

EARLY GRADUATE-LEVEL MATHEMATICS

Following Evan's death, the Cornell Mathematics Department underwent significant changes. From 1873 to 1895, it shifted from a department teaching only "undergraduate" mathematics to one actively engaged in training at the graduate level. The major influence toward this change was James Edward Oliver, chair of the department throughout this 22-year period.

Oliver is probably most noted in the general Cornell culture as the 'famous absent-minded professor'. For example, in a letter to the Cornell Alumni News in 1953, Walter F. Willcox (1861-1964), a statistician and former colleague, described this scene involving Oliver:

He was walking along East Avenue about noon towards his office in White Hall when he stopped to chat with a friend. When the friend started away, Oliver hesitated for a moment and then called out, "Which way was I going when we met?" The friend answered, "Toward your office, Professor Oliver." Having got that steer, he started off, calling out contentedly over his shoulder, "Thank you, that means that I have had my lunch." [58]

However interesting and amusing these stories are they do little to describe the true nature of James Edward Oliver. He was born in Maine on July 27, 1827 into a family with lineage to the first settlers in colonial Massachusetts. As a boy he was frail, and so spent much of his time indoors involved in books. The state of his health kept him from school in fact, until age seven, but he was nevertheless instructed at home by his mother, herself a teacher. By the time Oliver went to school he was far advanced in subjects usually not of interest to children his age, chief among them astronomy and literature.

Oliver also developed an ethical sense quite extraordinary for a youth. He was apparently very vocal in his positions against both slavery and the use of tobacco, on one occasion "standing upon the counter of his father's banking-room eloquently expostulating with a group of men addicted to tobacco-smoking or to too much wine" [10, 61]. His ethical convictions were not the mere folly of youth. In later years, "he was on terms of intimacy with the noted anti-slavery leaders of eastern Massachusetts, and was regarded by them as an efficient helper in forming the public sentiment which eventually compelled the removal of this peculiar institution from our country" [10,61].

At age seventeen Oliver entered Harvard as a sophomore. There, his interest in mathematics was stirred by Benjamin Peirce (1809-1880) who thought a great deal of his student's mathematical abilities [34, 141]. Horace Davis later president of the University of California and Oliver's roommate his last two years at Harvard, described him as "a remarkable man in many respects. He had a strong individuality, amounting almost to eccentricity. He was sturdy and independent in his thought and conscientious in his conviction, yet he was modest, retiring in his demeanor" [10,62]. As for mathematics, "...he devoured [it] with an eager appetite," Davis recounted. "[W]hen, in his senior year, he was given the Mécanique Céleste to study he would often become so absorbed as to prolong his work into the small hours of the morning, and I have many times waked up from my first nap to see him still poring over the ponderous volume long after midnight" [10,63].

Oliver graduated with an A.B.in 1849 and through the encouragement of his mentor, Peirce, took a position with the newly opened Nautical Almanac Office in Cambridge, Massachusetts. This federally funded organization was set up to compile a nautical almanac for the use of commercial as well as naval ships. However, it also became a haven for mathematicians and astronomers [31,14], and Oliver remained there until just after the office moved to Washington, D.C. in 1867. In fact, he "did not take kindly to the work necessitated by the publication of the American Ephemeris. . . . It soon became drudgery to him, and he would rather have devoted his energies to original research in higher algebra" [10,65]. Only because of the proximity to Harvard and the chance for the intellectual stimulation Peirce and the university offered did he stay with the Almanac Office so long.

In the three years from 1868 to 1871, Oliver's professional life was in flux. In 1871, however, he accepted an offer of an Assistant Professorship of Mathematics at Cornell. His professional life firmly took root there.

Harvard's Benjamin Peirce considerably influenced the development of mathematics at Cornell. Both Oliver (A.B. 1849) and Wait (A.B. 1870) had been Harvard graduates, with Oliver part of the advanced program at Harvard's Lawrence Scientific School "offered at that time by no other institution in the land" [18,178]. Moreover, the notable William Byerly (1849-1935) took both an A.B., 1871 and a Ph.D. (one of the first) in 1873 from Harvard, before moving on to a position at Cornell in 1873. Byerly stayed only for three years before returning to teach at Harvard, where he eventually became professor (1881-1913) and served as editor of the Annals of Mathematics. It was in the department animated by Oliver, Wait, and Byerly that the mathematics curriculum changed substantially from that of Cornell's earliest years. At its opening in 1868, Cornell offered

freshmen: Loomis's Trestise on Algebra and Elements of Geometry plus conic sections; sophomores: Loomis's T rigonometry and Analytical Geometry plus Church's Differential Calculus; juniors: Howison's Analytical Geometry and lectures on Modern Higher Geometry plus Church's Integral Calculus [24,135].

Beginning in 1874, however, the curriculum beyond calculus included courses in "differential equations, finite differences, quaternions, imaginaries, mathematical essays, seminary work, etc." for those students pursuing a degree in mathematics [18, 184]. The seminary work was given to those planning on careers in teaching. Following the departure of Byerly and Arnold in 1876, George Jones (1837-1911), a Yale A.B. (1859) and A.M. (1862), was hired as Assistant Professor, and Lucien Wait was promoted to Associate Professor to take some of the administrative burden off the shoulders of Oliver. These three men, Oliver, Wait and Jones, formed the core of the Mathematics Department for the next eighteen years. This triumvirate would slowly lead the department toward an active graduate program in mathematics.

As noted above, Cornell offered no graduate-level mathematics initially. By the mid-1870s, however, an "advanced course of study in Pure and Applied Mathematics ha[d] been established for resident graduates, and for such undergraduates as may elect . . ." [25,43]. This was the beginnings of graduate-level mathematics at Cornell. According to the catalog description:

Further instruction will be given in algebra and calculus; especially in the theories of imaginaries, elliptic integrals, differential equations, finite differences, and calculus of variations. Also in analytical and anharmonic geometry.

Instruction will also be given in analytic and celestial mechanics; and in quaternions, quantics, the theory of probabilities, least squares, insurance, and the theory of numbers [25,43].

At first, this program attracted few graduate students. In fact, no advanced degrees were awarded in mathematics (with the exception of Eddy's Ph.D. in 1872) until 1885 when Edward Charles Murphy (1859-1934) earned a Masters of Science degree. The next year Hiram John Messenger (1855-1913) took a Ph.D. under Oliver's direction. Murphy went on to study and teach civil engineering while Messenger ended up an actuary [19].

Within this same timeframe, 1872-1886, The Johns Hopkins University was founded, and James Joseph Sylvester, as chair in Mathematics, led the first extensive graduate mathematics program in America. From 1876 to1884, Hopkins had sixteen mathematics fellows and awarded nine Ph.D.'s [46,97]. Sylvester's departure for the Savilian Professorshi[ of Geometry at Oxford at the end of 1883, however, left a void to fill in American graduate level mathematics. Oliver wanted Cornell to take an active role in filling this void. He expressed this sentiment explicitly to the Cornell University President in an 1887 report:

yet one of our number, whose experience as a student, and as a teacher, enables him to judge,-- assures us that, now Professor Sylvester has gone back to England, the opportunities offered here to the average student of the higher pure mathematics are quite as good as those at any other university in the country. [6,59]

Unfortunately, several factors prevented Cornell from quickly stepping into a leadership role in the emerging American mathematical research community.

First, the backgrounds of the leaders of the Cornell Mathematics Department at this time hindered their overall effectiveness at the graduate level. Neither Oliver or Wait nor Jones had ever been primarily a research mathematician; none of them had a Ph.D. Although Oliver had the most advanced training of the three, given his work with Peirce at Harvard, he tended to do mathematics without a specific focus and for his own gratification. Arthur S. Hathaway (1855-1934), a former student of Sylvester at Johns Hopkins and a colleague of Oliver at Cornell put it this way: "Professor Oliver is a rare genius, powerful, able, but without the slightest ambition to publish his results. He works in mathematics for the love of it" [18, 179].

Second and perhaps more importantly, the foremost responsibility of Oliver, Wait, and Jones at Cornell was to the undergraduate mathematics program. For example, in 1880-81 Oliver taught an average of 18 1/3 hours per week, Wait 15 2/3 hours per week, and Jones 15 1/3 hours per week [1,12], with most of these hours devoted to undergraduate mathematics student. Little time remained for graduate level instruction of for publishing original research, even if Oliver, Wait, and Jones had been disposed toward research and publication. The thrust toward the production of original research was unprecedented in America before the founding of Hopkins and was as yet not felt at Cornell. There was a need to publish classroom textbooks, however, and the Cornell faculty did so under joint authorship. Two of their most important books were: A Treatise on Algebra (1887) and A Treatise on Trigonometry (1881). They wrote these books specifically to satisfy the needs of their undergraduate program.

The clash between teaching and research in the decade of the 1880s resulted in a crisis of identity in the Mathematics Department at Cornell. Oliver led a department still very much suited to teaching undergraduate mathematics, but nevertheless desirous of a graduate program. Reaching that new plateau would undoubtedly mean a struggle with the administration of the university. Oliver wanted additional faculty to allow his department time for more than just teaching; he wanted them to have the opportunity to do and to lead in research. Repeatedly in the 1880s, Oliver brought his arguments before the President of Cornell. In 1883, for example, he wrote in his annual report to the President:

. . . I now state that, whenever the income of the University will allow it, there ought to be appointed an additional mathematical professor of a high grade. We can go on satisfactorily and even creditably as we are going, for some time longer, but it should be borne in mind that the science of mathematics has been of late years greatly extended, and that as a consequence at the more important Universities of this and other countries there is a steady tendency toward an increase in the number of mathematical professors. A reason for joining in this movement whenever we shall be able to do so is seen in the fact that in no other department of study is there such an amount of talent scattered about our country and waiting to be developed. Mathematical geniuses are to be found in every part of our land, even among those who have enjoyed few advantages in instruction. To attract and develop this genius and talent should be one of our aims, and this can only be done by drawing into our Faculty more and more men recognized as leaders in various parts of this field of thought. [2,25]

Oliver was clearly aware that the development of the mathematical talent of American students required increased attention to advanced mathematical education, and that more resources would be needed to accomplish this goal at Cornell. Oliver also saw the need for these additional faculty to be trained to handle more advanced mathematics and to have the time to pursue original research. His annual report in 1887 underscored these points:

We are not unmindful of the fact that by publishing more we could help to strengthen the university, and that we ought to do so if it were possible. Indeed, every one of us five is now preparing work for publication or expect to be doing so this summer, but such work progresses very slowly because the more immediate duties of each day leave us so little of that freshness, without which good theoretical work cannot be done. [6,58]

He reiterated his position the next year as well:

Of course one important means toward this end is the publication of treatises for teaching, and of original work. A little in both lines has been done during the past year, though less than would have been but for the pressure of other University work, and less than we hope to accomplish next year. [7,75]

INTRODUCTION / NEXT SECTION / PREVIOUS SECTION / REFERENCES