Journal of Lie Theory 35 (2025), No. 1, 109--156
Copyright Heldermann Verlag 2025
Hellmuth Kneser: A Noteworthy Mathematician of the 20th Century
Karl Heinrich Hofmann
Fachbereich Mathematik, Technische Universitaet, Darmstadt, Germany
Dept. of Mathematics, Tulane University, New Orleans, U.S.A.
hofmann@mathematik.tu-darmstadt.de
Gerhard Betsch
Mathematisches Institut, Universitaet Tuebingen, Germany
gerhard.betsch@t-online.de
This text is a presentation of the mathematical biography of Hellmuth Kneser, 1898--1973. It contains a description of his substantial work in topology, including his pioneering work in low dimensional combinatorial theory of manifolds during the twenties, his influence on the work on the analysis of several complex variables, as well as his work on Lie groups and Lie algebras, and his later contributions to uncountable real analytic manifolds. It also gives an overview of diverse topics such as the teaching of mathematics in the years after 1945 as Kneser's efforts to compensate for losses suffered by German mathematics during 1933--1945.
One focus is Kneser's relation with Richard Courant whose activity at the university of Göttingen had contributed to its national and international reputation in mathematics during the nineteen-twenties, ending abruptly in 1933 with Courant's (and Emmy Noether's) dismissal in the course of the national socialist government takeover. Kneser was Courant's assistant in Göttingen from 1921 to 1924 and corresponded actively with him in 1933 from Greifswald, where he had held a professorship since 1925. He organized one of two direct appeals to the government protesting Courant's dismissal -- both in vain.
Keywords: Biography, cohomology, David Hilbert, Dehn's Lemma, Emmy Noether, Erich Kamke, fundamental group, Goettingen, Greifswald, Hauptvermutung, Hellmuth Kneser, Helmut Wielandt, Hopf algebra, John Milnor, Kneser's Conjecture, Lie group, Lie algebra, long
MSC: 01-00, 22E15, 57-03.
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