## History of the Department

The University of Chicago, and with it the Department of Mathematics, opened its doors in October of 1892. The first chair of the department was Eliakim Hastings Moore, who had been an associate professor at Northwestern. He immediately appointed Oskar Bolza and Heinrich Maschke, and the three of them became the core of the department during the period 1892-1908. R.C. Archibald has described this group as follows:

These three men supplemented one another remarkably. Moore was a fiery enthusiast, brilliant, and keenly interested in the popular mathematical research movements of the day; Bolza, a product of the meticulous German school of analysis led by Weierstrass, was an able, and widely read research scholar; Maschke was more deliberate than the other two, sagacious, brilliant in research, and a most delightful lecturer in geometry. During the period 1892-1908 the University of Chicago was unsurpassed in America as an institution for the study of higher mathematics.

One of the first projects undertaken by the newly formed department was the organization of an international congress of mathematicians in association with the World Fair held in Chicago in 1893. The success of this venture is indicated by the fact that it has inspired the organization of International Congresses of Mathematicians on a regular basis. The publication of the proceedings of this congress was undertaken with the help of the New York Mathematical Society, and shortly thereafter, with Moore's strong encouragement, it was concluded that the Society should be reorganized as the American Mathematical Society.

From 1892 to 1910, 39 students graduated from Chicago with doctoral degrees in mathematics. This group included such mathematicians as Leonard Dickson (Chicago's first Ph.D. in mathematics), Gilbert Bliss, Oswald Veblen, R.L. Moore, George D. Birkhoff and T.H. Hildebrandt. There was a shift in the character of the department beginning in 1908, when Maschke died, and this was accentuated in 1910 when Bolza returned to Germany. Along with Moore, the most influential members of the department became L.E. Dickson, G.A. Bliss and Ernst Wilczynski. The pace at which doctorates were granted accelerated: in 1910-1927, 115 Ph.D.s were granted. By the end of this period, Chicago had become a dominant source of mathematical Ph.D.s in the United States: in 1928, 45 Ph.D.s in mathematics were granted in the United States, and either 12 (according to the Bulletin of the AMS) or 14 (according to department records) of these were from Chicago. The nearest competitors in that year were Minnesota (with four) and Cornell and Johns Hopkins (three each). By virtue of sheer numbers, Chicago became a dominant force on the American mathematical scene, providing faculty for many departments in the nation. On the other hand, it is generally agreed that none of the graduate students in this period reached the same level of mathematical profundity as the best students in the earlier one. Saunders Mac Lane's sober assessment: "Chicago had become in part a Ph.D mill in mathematics."

In 1927, Gilbert Bliss succeeded Moore as chair of the department. He and Dickson were the dominant mathematical influences on the department during Bliss' chairmanship, which lasted until 1941. Together, they directed nearly 70 of the 117 theses written during this period. There was somewhat more success in producing mathematicians of depth in this period: Adrian Albert graduated in 1928, W.L. Duren in 1929, E.J MacShane in 1930 and Leon Alaoglu in 1938. Mac Lane (who was a student at Chicago during this period, though he soon left for Göttingen, with E.H. Moore's encouragement) makes this assessment: "In this period the department at Chicago trained a few outstanding research mathematicians and a number of effective members of this community - plus produced a large number of essentially routine theses."

Up until this point, it had been a pattern at Chicago to appoint Chicago Ph.D.s to the faculty. This predictably led to a certain narrowness of mathematical focus: the calculus of variations, projective differential geometry, algebra and number theory were the main topics of interest. During the latter part of Bliss' chairmanship, there were some efforts to appoint mathematicians in new fields and not from Chicago. Two of these included Saunders Mac Lane and Norman Steenrod, though both left after a few years.

Bliss retired in 1941, and was succeeded as chair by E.P. Lane. Lane's attempts to revive the department were largely unsuccessful, due primarily to the onset of World War II. President Robert Hutchins brought the Manhattan Project to the University of Chicago, and was housed in Eckhart Hall, while the mathematicians were moved into one of the towers of Harper Library. There were no new appointments until after the war; Irving Kaplansky was the first in 1945. There were however, some notable graduate students during the war, including George Whitehead in 1941.

At the conclusion of the war, Hutchins made an effort to retain some of the scientists who had come to campus as part of the Manhattan Project; a consequence of this was a need to strengthen the mathematics department. A professor at Harvard, Marshall Stone, was approached and asked if he would come to Chicago as chair. There were at the time five vacant senior positions which had accumulated during the war, which meant that the department had to be rebuilt almost completely, and there was a wish to match the level of appointments in the physical sciences which the university had been able to make through its involvement in the Manhattan Project.

Stone brought a considerable degree of ambition and vision to the project of rebuilding the department. The list of mathematicians appointed at Chicago through Stone's efforts is remarkable: André Weil, Antoni Zygmund, Saunders Mac Lane and Shiing-Shen Chern as professors, and Paul Halmos, Irving Segal and Edwin Spanier as assistant professors. Other appointments were attempted, but unsuccessful. The first offer Stone made was to Hassler Whitney. Stone's recommendation to appoint Whitney was initially rejected by the administration, and it required considerable effort to reverse this decision. When the offer was finally made, Whitney turned it down, and shortly later moved to the Institute for Advanced Study. In another case, an attempt was made to appoint Freeman Dyson; this failed when the Dean of the Division (a physicist) asked "Who is Dyson?"

Stone grew weary of the struggle with the administration for new resources, and stepped down as chair in 1952. He was succeeded by Mac Lane as chair from 1952-1958, and Adrian Albert from 1958-1962. This period presented new challenges, as Weil left in 1958, Chern and Spanier in 1959, Segal in 1960, and Halmos in 1961. But this account will end here, as the writing of recent history is too dangerous an occupation.

**Notes**: The material on this page has been stitched together from the following sources:

- In
*A Century of Mathematics in America*, Part II, Peter Duren, ed. (assisted by Richard A. Askey and Uta C. Merzbach), American Mathematical Society, 1988:- Saunders Mac Lane,
*Mathematics at the University of Chicago: A Brief History*. - Karen Hunger Parshall,
*Eliakim Hastings Moore and the Founding of a Mathematical Community in America, 1892-1902*, reprinted from the Annals of Science, vol. 41, 1984, pp. 313-333. - Marshall Stone,
*Reminiscences of Mathematics at Chicago*, reprinted from The University of Chicago Magazine. - Felix E. Browder,
*The Stone Age of Mathematics on the Midway*, reprinted from The University of Chicago Magazine.

- Saunders Mac Lane,
- The MacTutor History of Mathematics archive, including particularly the entry on Eliakim Hastings Moore.

An interesting account of life as a graduate student at Chicago in the 1920's, reprinted in the
*Century of Mathematics in America* volume mentioned above, is available online:

W.L. Duren, Jr., *Graduate
Student at Chicago in the Twenties* (access to JSTOR required).