Fifty years as a mathematician

Abstract

During the height of the great German Inflation, I began my university studies in the autumn of 1923 at the University of Frankfurt. I remained there for three semesters, and then, in the spring of 1925, went to the University of Gottingen. Although there was only a small number of students in the Mathematics Department at Frankfurt, it had outstanding teachers, the Professors Dehn, Hellinger, Epstein, Szasz, and Siegel. From Siegel I learned most, particularly in analytic number theory and related parts of function theory. He introduced me to Diophantine equations and approximations, and, in his great paper of 1929, to transcendental numbers. Gottingen, during my stay from 1925 to 1933, had a much larger mathematical department, and it was at that time a centre of world mathematics, with many distinguished visitors from abroad. Of particular relevance for my later research was what I learned from Courant about direct methods in the calculus of variations, and from Emmy Noether about modern algebra and in particular about fields with valuations and padic numbers. After the coming of Hitler in 1933, I left Giittingen where, since my Frankfurt doctorate in 1927, I had been doing research, chiefly on transcendental numbers and Diophantine approximations. On the invitation of Mordell, I spent the session of 1933-1934 at the University of Manchester. Then, on the invitation of van der Corput, I went for the next two years 1934 to 1936 to the University of Groningen in the Netherlands. After another year’s leave of absence, due to illness, I returned to the University of Manchester in the autumn of 1937 and was to stay there until 1963 when I went for the next live years to the Australian National University at Canberra until my retirement at 65. Between 1968 and 1972 I held a professorship at the Ohio State University at Columbus, Ohio. Finally I returned in 1972 for retirement to the Australian National University in Canberra.