# Cochell: The Early History of the Cornell Mathematics Department

5. A VIABLE GRADUATE PROGRAM

During the 1887–1888 academic year, there were eleven mathematics graudate students at Cornell. This represented one-seventh of the graduate work being done in all departments there [7,74]. Nevertheless, the graduate program in mathematics was still in a fledgling state. Oliver taught the theories of functions and probablility in addition to non-Euclidean geometry; George Jones offered advanced work in analytic geometry of two and three dimensions - lines and surfaces of first and second orders in addition to a course in modern synthetic geometry; and Lucien Wait covered advanced work in calculus - differential calculus. Two relatively new members of the department - Instructors Arthur Hathaway and James McMahon (1856-?) - were also involved in teaching in the advanced program.

Hathaway had done advanced work at Johns Hopkins from 1880 to 1884 and had specialized in the theory of numbers and quaternions. McMahon had earned an A.M. from the University of Dublin, focusing on the "mathematical functions needed in the solution of various physical, statistical and geometrical problems" [19]. At Cornell, Hathaway taught differential equations and a course on quaternions and vector analysis, while McMahon gave advanced work in analytic geometry of two and three dimensions - general theory of algebraic curves and surfaces and courses in integral calculus and the theory of invariants and covariants.

According to Cajori [18,184-185], books used in several of these courses reflected more or less current trends in Britian and on the Continent at the time. For example, in Oliver's course on the theory of functions, Broit and Bonquet's Theorie des fonctions elliptiques and Halphen's Traité des fonctions elliptiques were used. In teaching his class on the general theory of algebraic curves and surfaces McMahon adopted George Salmon's Treatise on the Analytic Geometry of Three Dimensions and Treatise on Higher Plane Curves while he used Salmon's Modern Higher Algebra in his lectures on the theory of invariants and covariants.

At the end of the 1887-1888 academic year, two students who followed this curriculum earned their Ph.D.'s: Cadwallader Edwards Linthicum wrote "On the Rectification of Certain Curves, and on Certain Series Involved" and Rollin Arthur Harris (1863-1918) explored "The Theory of Images in the Representation of Functions." Florian Cajori reported that "both of these are very creditable to the writers and to the university," goin on to say that the work of Harris "appears to us to fill a gap" [18,185].

The 1889-1890 academic year marked the beginning of yet another phase in the advancement of the graduate program at Cornell. James Oliver spent the year traveling abroad. He first visited Cambridge to see and hear Arthur Cayley, the inspriation behind much of his own mathematical research. Owing to Cayley's advanced age, however, Oliver's visit there was short. He moved on to Germany to observe both the mathematics taught and the methods of instruction used in higher learning there. In Germany, he mainly visited the university in Göttingen where he sat in on the courses of Felix Klein (1849-1925). As Oliver described his experiences in Göttingen, "My work here is likely to be of great service to me, including the trains of thought and plans it suggests, no very radically new plans, only as to the spirit, the aims, and the details of my Cornell work" [10,69]. Klein had made a deep impression on Oliver, and the two men, in fact, became friends. When Klein came to America for the Mathematical Congress associated with the World's Columbian Exposition of 1893, he paid both a personal and a professional visit to Oliver in Ithaca [10,69]. Klein wanted to see his American friend, but he also wanted a first-hand look at Cornell and its program. Parshall and Rowe sum up the impact of Klein on Oliver this way: "Cornell emerged as a prime sphere of Klein's influence in the United States" [46,213].

On Oliver's return to Cornell in 1890, several subtle changes began that helped solidify the graduate program over the next ten years. Almost immediately, Oliver organized a mathematical club patterned roughly on the German seminar. The "first regular meeting" of the Cornell Mathematical Club took place at Oliver's home on January 24, 1891 "with the business of organization" on the agenda [22]. In the constitution adopted at that first meeting, "mutual association, and discussion of mathematical questions of interest" defined the club's specific objectives [22]. Today known as the Oliver Club, this organization celebrated its centennial in 1991 and reconfirmed its original commitments:

The Mathematical Club of Cornell University was organized as a forum for discussion of mathematics outside the regular curriculum. The club met in faculty homes on a Friday or Saturday evening for a formal talk followed by discussion of the ideas presented. The Oliver Club is still functioning today, and continues to fulfill the primary goals of the original club. [36]

In founding the Mathematical Club, Oliver intended to get students and faculty involved in mathematics much in the way he saw German students involved in mathematics in their seminars.

In the first year, 1890-1891, the club's membership numbered twenty-two. Among the graduate students, the names of Virgil Snyder (1869-1950), John Tanner (1861-1940), and Paul Saurel (1841-1934) stand out on the list [22]. Snyder left Cornell for Göttingen where he earned a doctorate under Felix Klein; he then returned to a long and successful career back at his alma mater. Tanner also left Cornell to pursue his studies in Germany, while Saurel proceeded to Bordeaux. In the 1890s, the Mathematical Club provided an avenue for students and faculty to share their mutual interests in mathematics outside the usual classroom setting. Moreoever, it apparently stimulated the students enough to interest several of them in programs of note in Europe.

The decade of the 1890s was, in fact, a time that found many Americans traveling to Europe to study mathematics, and Oliver had much to do with sending Cornell students there to further their mathematics education. In addition to Snyder, Tanner, and Saurel , others, like Annie Louise MacKinnon (1868-1940), first earned her Cornell Ph.D. (1894) and then went on to study in Göttingen. An American Collegiate Alumnae (ACA) European Fellow during the 1894-95 year, MacKinnon credited Oliver explicitly for her knowledge of this opportunity. In a letter to Felix Klein she wrote "[l]ast winter [1893] I heard through Prof. Oliver that you had obtained permission for certain women to attend your lectures" [29,238].

Not only were American students going off to study in Europe, but European mathematics was being imported more actively into the United States. This was true at Cornell during the 1890s. Through the German connection started by Oliver, the Mathematics Department sent Tanner to Germany to study (1894-96) and to secure a young German professor for Cornell. In May, 1895, Tanner persuaded Ernst Ritter (1867-1895) to come to Cornell. Ritter had earned his doctorate in 1891 at Göttingen under Felix Klein and had gone on to serve as Privatdozent and assistant to Klein there. Unfortunately, Ritter caught typhoid fever on the trip to American and died before arriving in Ithaca [34,43]. Wait expressed his grief to Klein in a letter dated December 23, 1895:

I cannot tell you the grief and disappointment that I experienced at the death of Dr. Ritter. As you know, we never saw him as he died in New York. He would have had a great future here for I feel sure that I could have secured advances in salary as often as he should have merited such increase. I have been corresponding with and exchanging cablegrams with Mr. Tanner with regard to Ritter's body. I have nearly all the information to lay before our Board of Trustees. I shall either send it back to Germany or bring it to Ithaca. [38]

This setback did not dissuade Cornell from getting someone with German training into their department. They persuaded Virgil Snyder, who was finishing his doctorate in 1895 under Klein, to come back to Cornell as an Instructor.

Another untimely death occurred during Tanner's stay in Germany. The leader of the Department, James Oliver, took ill and died. The front page of the Cornell Daily Sun announced that "[o]n Thursday, March 28th, [1895] Professor James Edward Oliver, whose serious illness has since January kept the whole university world in suspense, breathed out his last life" [21,1]. Fortunately Oliver's death did not slow the progress the Department had made. Lucien Wait, who had handled most of the administrative work of the Department for the previous eighteen years, formally took over as department and continued to guide Cornell mathematics in the direction defined by Oliver. Wait sketched the Department's contours in the same letter to Klein in which he lamented Ritter's death:

We have nearly 1800 students this year and there are 167 teachers. We shall get from $100,000 to $150,000 from an estate just settled, which the Trustees are thinking of devoting to pensions for superannuated Professors. I am desirous of bringing a leading German mathematician to America to assist us here at Cornell. I desire to have ONE advanced course of mathematical lectures delivered in the German language so that our students will be able to take hold of work in Germany without so much delay. Mr. Tanner has promised to continue to assist me in this plan. The coming of Ritter was due to a commission that I gave Mr. Tanner when he left for Germany. We shall send two of our graduate students to Europe for an extended course of mathematical study next Summer. . . . I desire to express my grateful appreciation for what you are doing for our students in Göttingen. They not only enjoy your work but they all speak of you with a great deal of affection personally. [38]

As his letter suggests, Wait was committed to the ideals Oliver had embraced; he sought help from Europe, and especially Germany, to strengthen Cornell's graduate program in mathematics.

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