Some Mathematical Reminiscences

Abstract

2. Cambridge, Massachusetts Harvard is where I received my basic training: a bachelor's degree in 1925, two years as a part-time instructor in 1925-27, and a Ph.D. in 1928. In those days the mathematics department was relatively small so that there was a close relationship between students and faculty. My first account concerns three Harvard faculty members, William F. Osgood, George D. Birkhoff and Julian Coolidge; and one visitor, Constantin Caratheodory. Professor Osgood was a tall, black-bearded man, an 1886 graduate of Harvard College. In those days a young American desiring to pursue mathematics further had to go to Europe since mathematics in America was still in its infancy. Osgood chose Gottingen and Erlangen, Germany, where in 1890 he obtained a Ph.D. under the renowned Felix Klein. Returning to the United States and a position at Harvard, he made some distinguished contributions to complex variable theory, including results on conformal mapping and a two-volume treatise entitled, Lehrbuch der Funktionentheorie. By the way, this treatise was written in German, because English was not as yet regarded as an appropriate language for a mathematical treatise. I met Osgood in 1920. I was a 15-year-old high school junior, eager to take advantage of the anticipatory examinations which a student could take if he were entering with more subjects than needed for regular admission to Harvard. The student could, thereby, earn in advance up to a year's college credit. I resolved to do just that, in particular to cover by myself the Harvard freshman course in analytic geometry and calculus. Osgood, then the mathematics department chairman, advised me as to the texts used in the course. I did well on the examination and was given an A. This success, plus Osgood's apparent interest in me, then persuaded me at age 16 to aspire to become a mathematician. Osgood served as my college advisor, invited me to his home and visited me in the student infirmary. He was a superb teacher who struck a good balance between giving complete details and leaving matters to the student's initiative and intuition, frequently motivating a new subject through physical applications. My last meeting with him was during September 1932 in a Harvard Square cafeteria. Greeting me there was a clean shaven man whose voice I recognized as Osgood's. Since that was only a few days before my marriage, I invited him and his new young wife to the wedding, and both came. Professor Birkhoff had the distinction of being among the first American-trained mathematicians to receive international recognition. As a sophomore I was hired to be problem reader in his calculus course, and subsequently took his various courses on differential equations, including one on the three-body problem. His lecture style was