## Download PDF by Peter L. Duren, Richard Askey, Uta C. Merzbach: A Century of mathematics in America (History of Mathematics,

By Peter L. Duren, Richard Askey, Uta C. Merzbach

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So does his early introduction to Harvard of functional analysis, through his 1922 paper with O. D. Kellogg on "Invariant points in function space", his probable influence on Stone and Koopman, and his "pointwise ergodic theorem" of 1931. But deepest was probably his creative research on the dynamical systems of celestial mechanics. It was to present this research that he was made AMS colloquium lecturer in 1920, and to honor it that he was awarded the first Bocher prize in 1922. It is interesting to consider my father's related work on celestial mechanics as a continuation of the tradition of Bowditch and Benjamin Peirce, which George David Birkhoff MATHEMATICS AT HARVARD, 1836-1944 29 was carried on by Hill and Newcomb, and after them by E.

These included Joseph Slepian (inventor of the magnetron), Marston Morse, H. J. Ettlinger, J. L. Walsh, R. E. Langer, Carl Garabedian (father of Paul), D. V. Widder, H. W. Brinkmann, Bernard Koopman, Marshall Stone, C. B. Morrey, D. C. Lewis, G. Baley Price, and Hassler Whitney. Four of them (Morse, Walsh, Stone, and Morrey) would become AMS presidents. In retrospect, my father's role in bringing topology to Harvard (as Veblen did to Princeton), at a time just after L. E. J. Brouwer had proved some of its most basic theorems rigorously, seems to me especially remarkable.

My acquaintance with general topology was broadened by reading Frechet's The- sis (1906), which introduced me to function spaces, and his book Les Espaces Abstraits. It was also deepened by reading the fundamental papers of Urysohn, Alexandroff, Niemytski, and Tychonoff (Math. , vols. 92-95). I was fascinated by Caratheodory's paper "on the linear measure of sets" and Hausdorfl's fractional-dimensional measure, so brilliantly applied to fractals by Benoit Mandelbrot in recent decades. This reading was guided and monitored by Marston Morse; like all faculty members, his official duties included talking with each of his `tutees' for about an hour every two weeks.