Towering Figures in American Mathematics, 1890-1950

The state of American mathematics in the year 1890 was quite bleak. Only two schools offered true graduate education, The Johns Hopkins University and Clark University. Both were new, Hopkins having been founded in 1876 and Clark in 1889. When compared to their counterparts in Europe, the courses taught at the vast majority of American universities were paltry, the spirit of research almost nonexistent, and the quality of the faculty vastly inferior. Most established universities and colleges in America emphasized a classical education that featured rhetoric and classical languages to the exclusion of the sciences. By 1950, just 60 years later, a dramatic revolution had completely altered the mathematical landscape. American students could now obtain an excellent grounding at dozens of first-rate institutions before pursuing doctoral degrees at several world-class departments led by an international cast of outstanding researchers. A who’s who list from 1890 might feature Thomas Craig and Fabian Franklin (both then at Johns Hopkins), William Story (at Clark), William Byerly (Harvard), G. B. Halsted (Texas), and Hubert Newton (Yale)—hardly a sextet of household names today even among historians of mathematics. The hypothetical list would surely include J. Willard Gibbs and George Hill, two individuals who had ascended to high ranks in the scientific community but who were peripheral players on the American mathematical scene. By 1950 a snapshot of one department alone might capture Andre Weil, Antoni Zygmund, S. S. Chern, and Saunders Mac Lane centered on Marshall Stone. This photo might be captioned “the fab five”, whereas the list from 60 years earlier could be dubbed “the sad six”. Although few other names could be added to the “sad six” list, 3 × 5 shots of A. A. Albert, Paul Halmos, Magnus Hestenes, Irving Kaplansky, John Kelley, and Irving Segal could accompany the 8 × 12 photo of the “fab five”. The revolution from 1890 to 1950 occurred in several evolutionary stages. It began with a few isolated individuals and ended with a mature community. We recount here the main features of this development using the lives of six mathematicians to illustrate some of the major changes that occurred. These six figures—E. H. Moore, O. Veblen, G. D. Birkhoff, R. L. Moore, N. Wiener, and M. Stone—towered over the mathematical landscape and ushered in a completely new generation of American mathematicians. This account describes their achievements in an attempt to provide us with a clearer picture of our heritage.