ABSTRACT
M uch of the stimulus for effective mathematical research comes from well-organized university departments of mathematics. This chapter will aim to summarize my own experience with
several departments. When I first became interested in mathematics in 1927 it was
generally agreed that the three leading American departments of mathematics were those at Harvard, Chicago, and Princeton (an unordered list). Harvard combined its venerable traditions with a long-standing attention to mathematics, going back to the days (1870) of Benjamin Peirce, who was noted especially for his 19thcentury research on linear algebra. From about 1900, William Fogg Osgood was the leading member of the Harvard department. He wrote the text for the Harvard calculus course (using infinitesimals instead of limits) and collaborated with his colleague W. C. Graustein in an undergraduate text on geometry. He was noted for his authoritative monograph on complex variable theory, written in German (his Ph.D. study had been in Germany). George Birkhoff assumed the leadership of the Harvard department, and had studied both at Harvard and at Chicago (with his Ph.D. from Chicago). As a young faculty member at Princeton he had proved Poincaré’s last geometric theorem, which Poincaré had published without a proof. This accomplishment led to his recognition as the best American mathematician, and to his appointment at Harvard. There, with decisive results on differential equations, he soon became the leading
figure in the department; for example, he guided a number of notable Ph.D. students, including Marston Morse, Marshall Stone, B. J. Koopman, and D. V. Widder. George Birkhoff was devoted to mathematics and clearly disliked administrative tasks, although he did once serve for a period as dean of the Harvard faculty. He was sharply critical of mathematicians who gave up research for administration, and so he was careful not to do that himself. The Harvard department, in the period of my membership there, had a close and effective social structure with clear social cohesion. The total effect was an air of excitement about new mathematical results.
