# Cochell: The Early History of the Cornell Mathematics Department

7. CONCLUSIONS

The graduate program in the Cornell Mathematics Department crystallized in the final decade of the nineteenth century. Its young faculty, animated by a commitment to research, teaching, and service to the broader mathematical community, carried out this transformation. Five of them earned stars in American Men (and Women) of Science during their careers; several of them went on to be very active in the AAAS and AMS; a number of them held offices in these associations, culminated by Virgil Snyder's presidency of the AMS in 1927-1928. As trainers of future researchers, they put together a curriculum that was modern by the standards of the day and that incorporated some of the latest contemporary mathematical developments. In the decade from 1900 to 1909 15 students earned their doctorates in this environment with 16 more following in the years from 1910 to 1919. During the twenty-year period between 1900-1919, in fact, Cornell ranked sixth among American institutions in mathematics Ph.D. production behind the University of Chicago, The Johns Hopkins University, Harvard, Yale, and Columbia [47,203].

The Cornell Mathematics Department also showed leadership on a key issue in the last years of the nineteenth century: the education of women. Both Ezra Cornell and Andrew White had shown great interest in the education of women. As Rudolph put it: "The revolutionary reputation of Cornell was greatly advanced by the university's inevitable but delayed adherence to a policy of coeducation in 1872, a delay that had been prompted by the absence of a suitable dormitory" [49, 124]. On a national level, however, obstacles were more difficult to overcome. In her work on the history of women in American science, Margaret Rossiter characterized the situation this way:

When all the attempts by women to gain higher degrees at universities in the United States and Germany over three decades (1870 to 1900) are viewed together, they can be seen as a process of infiltration, a kind of educational 'guerilla warfare' or slow 'war or attrition' against the universities. Under this almost military strategy, individual women sought to test the repressive system on as many fronts (departments and universities) as possible, probing for weak points and using what friends they had to help them evade the rules informally, and, when enough 'exceptional' women had been admitted in this way and had surpassed their fellow students without the imagined disruptiion, to push for a change in policy, which then could be seen as harmless, 'only fair,' and long overdue, and could be enacted quietly. Thus over several decades a series of women eventually accomplished their objective, but at great human cost. [48,31]

At Cornell, women found a friendly place in the 1890s. In fact, Cornell's Mathematics Department granted three of the first six Ph.D.'s earned by women in American institutions. Ida Martha Metcalf (1856-1952) earned her doctorate in 1893, followed by Annie Louise MacKinnon (Fitch) in 1894 and Agnes Sime Baxter (Hill) (1870-1917) in 1895. From all indications, they seemed to write their dissertations under James Oliver [29,235]. As noted above, MacKinnon also pursued her studies in Göttingen under Klein, yet it was characteristic of the times that none of these women realized their full potential in careers in mathematics. As Rossiter argued, "Sex discrimination was so widespread in academic hiring that there was no incentive for the women at these colleges to do any more research. They already held the best jobs open to women, and even with outstanding research accomplishments they were not going to be called to a major graduate school, as the better men at these colleges often were" [48, 23].

After Metcalf received her Ph.D. she worked for a time as a security analyst in a banking house in New York City. She then won a job in the Comptroller's Office of New York City on the basis of her performance on a civil service examination; she remained in this post until her retirement. It should be noted, however, that "In view of her own hard struggles to find positions commensurate with her ability, Miss Metcalf, throughout her life had a very cynical view of higher education for women." [35]. Agnes Baxter Hill's post-graduate experiences were more typical, however. She followed her husband and his career, and spent her time raising their children and battling a serious illness that cut her life short. Of the three Cornell women Ph.D's Annie MacKinnon Fitch had a short career in mathematics. After her return to America in 1896 from her post-doctoral studies in Germany, she took a position at Wells College in Aurora, New York. She taught there for five years until her 1901 marriage to Dr. Edward Fitch, Professor of Greek at Hamilton College in Clinton, New York, forced her to leave her position. After her marriage there seems to be no evidence of mathematical activity, although she apparently became somewhat of a community activist.

Cornell granted degrees to two other notable women in the 1890s: Estella Kate Wentz (1866-1938) and Anna Helene Palmie (1863-1946). Wentz earned an M.S. in mathematics from Cornell in 1894, while Palmie took an undergraduate Ph.B. in 1890 and was a graduate fellow in mathematics until 1892. Both women went on to similar careers, taking the sorts of teaching positions that were more the norm for women in that era. Palmie taught at the Women's College of Western Reserve University in Cleveland, Ohio from 1892 until 1928, while Wentz taught at Emmerich Manual Training High School in Indianapolis, Indiana, from 1895 until 1931 [57,7-10].

In concluding their study of the emergence of the American mathematical research community, Parshall and Rowe give the following assessment of the forces at work during the final quarter of the nineteenth century:

Individuals both at home and abroad, educational institutions both domestic and foreign, general developments in science and its social and cultural status, broader philosophies of education, political rivalries, and the encroachment of modernity in its several guises, these were among the factors that formed the matrix in which research-level mathematics evolved in the United States . . . [46,453]

The forces they listed certainly acted on Cornell during this period. Andrew White and Ezra Cornell founded Cornell University to give students more freedom in choosing their studies, to provide them with a more utilitarian education. In so doing, they created a model for other American universities to follow. However, this had little immediate effect on the mathematics taught at Cornell. Initially, it was very much the mathematics of the colonial American colleges - - algebra, geometry, and some calculus with applications to astronomy, navigation and surveying. There was no significant advanced mathematical training until the German model of research education started to gain favor in the Cornell Mathematics Department in the late 1880s and early 1890s. Still, the best and brightest students went to Europe for their Ph.D.'s or to do post-doctoral study. It was not until the turn of the twentieth century, after a nucleus of European-trained faculty were themselves training graduate students, that the Cornell Mathematics Department became a leader in the American mathematical research community.

The development of the Cornell Mathematics Department thus paralleled that of the American mathematical research community as a whole. In 1868 Cornell University opened its doors as a place where anyone could study any subject they wanted, but at an undergraduate level. By 1900, Cornell students could study the latest research-level mathematics of Europe. The vision and leadership first of James Oliver and latter of Virgil Snyder guided the Cornell Mathematics Department's transformation from a strictly undergraduate program to a full-scale, research-oriented department.

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