Richard Brewer

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Richard Brauer with his wife Ilse Brauer, 1970

Richard Dagobert Brauer (born February 10, 1901 in Charlottenburg , † April 17, 1977 in Belmont , Massachusetts ) was a German-American mathematician .

Childhood and youth

Brauer was the son of the leather goods dealer Max Brauer and his wife Lilly Caroline. He was the youngest of three children, and his brother Alfred , who was seven years older than him , also became a mathematician.

Richard Brauer attended the Kaiser-Friedrich-Schule in Charlottenburg from 1907 to 1918, at that time an independent community just outside Berlin, and during this time he developed a passion for mathematical problems, although the influence of his brother was more decisive than the quality of the educators . Only one of the teachers who had received his doctorate from Frobenius could convince him.

The last four years of his school attendance took place during the First World War , but Brauer was too young to be drafted. After graduating in September 1918, he was only used for community service in Berlin and in November - after the end of the war - he was able to continue his training.


His childhood dream was to become an inventor , and so in February 1919, despite his devotion to mathematics , he began studying at the Technical University of Charlottenburg, which later became the Technical University of Berlin . But after just one semester he noticed that he liked the theoretical direction more than the practical. He therefore went to the Berlin Kaiser Wilhelm University .

Some of the most important mathematicians and natural scientists taught at the Berlin University: Ludwig Bieberbach , Constantin Carathéodory , Albert Einstein , Konrad Knopp , Richard von Mises , Max Planck , Erhard Schmidt , Issai Schur and Gábor Szegő . Brauer describes Schmidt's lectures as follows:

It is not easy to describe their fascination. When Schmidt was at the blackboard, he never used notes and was rarely well prepared. He made you feel like he was developing the theory here and now.

In keeping with the tradition of German students to change places at university, Brauer also left Berlin. He studied at the University of Freiburg , but returned to Berlin after just one semester. Here he attended seminars by Bieberbach, Schmidt and Schur. He was now drawn more and more to algebra , as presented by Schur in his seminars:

[Schur] was always well prepared in his teaching and presented very quickly. If you weren't careful all the time, it was easy to lose context. There was barely enough time to take notes, it had to be done at home ... He had weekly practice sessions and almost every time it was a difficult problem. Some of these exercises had already been used by his teacher Frobenius. Sometimes he mentioned problems that he was unable to solve himself.

In fact, it was one of those open problems that Richard and his brother were able to solve in 1921, leading to an initial publication. It was also Schur who suggested the topic for Brauer's dissertation . Richard Brauer received his doctorate with this work in 1926. It dealt with an algebraic approach to characterize irreducible representations of the real orthogonal group .

Before completing his doctorate, Brauer had got a position as assistant to Konrad Knopp in Königsberg and married his fellow student Ilse Karger. In autumn 1925 he took up his position in East Prussia. Shortly after his arrival, however, Knopp went to the University of Tübingen and since the faculty for mathematics in Königsberg was not very large, Brauer had a lot of tasks and freedom. There were two professors, Gabor Szegö and Kurt Reidemeister , as well as two assistants in addition to Brauer. Brauer taught in Königsberg until the spring of 1933, when he lost his position after the transfer of power to the National Socialists and had to go abroad, where he was gratefully received.

In 1932 he published with Helmut Hasse and Emmy Noether an important theorem in the arithmetic theory of algebras (theorem of Brauer-Hasse-Noether), in competition with simultaneous experiments by American mathematicians.

Emigration to the USA

Brauer first went to Lexington (Kentucky) for a year . After this engagement, he became Hermann Weyl's assistant , which was a long-cherished wish of Brauer. In 1935 the two published a joint paper on Spinore in the American Journal of Mathematics . This paper formed the mathematical basis for Dirac's concept of electron spin within quantum mechanics .

In the fall of 1935, Brauer was appointed to a permanent position as an assistant professor at the University of Toronto , on the recommendation of Emmy Noether . It was here that Brauer developed some of his most impressive theories, taking the work of Ferdinand Georg Frobenius in a new direction. Together with C. Nesbitt he developed the theory of blocks, with the help of which he obtained results for finite groups, especially the finite simple groups . A plan for a textbook on algebra, which should appear in the basic doctrines of the mathematical sciences and which should bring a simpler and more concrete, more suitable approach for beginners than Modern Algebra by Bartel Leendert van der Waerden and realize an old plan of the school of his teacher Issai Schur should, failed in 1935 (despite support from Emmy Noether and Richard Courant). Such a textbook on algebra by Brauer would never appear later. Also partly for political reasons, Brauer's already finished article on the theory of algebras was rejected for the new edition of the Encyclopedia of Mathematical Sciences (it was finished in 1936 and actually already accepted for publication).

After a year at the University of Wisconsin in 1941, he returned to the United States for good in 1948, to the University of Michigan at Ann Arbor . In 1949 he received the coveted Cole Prize from the American Mathematical Society for his work On Artin's L-series with general group characters , which he published in the American Journal of Mathematics in 1947 . In 1954 he gave a plenary lecture at the International Congress of Mathematicians in Amsterdam ( On the structure of groups of finite order ).

In 1951 he received a call to Harvard University , which he accepted in 1952. He stayed here until his retirement in 1971. At Harvard he began to classify all finite simple groups. The first step was a group theoretical characterization of the PSL (2, q). Brauer now devoted the rest of his creative time to classification work. However, he died a few years before this project was temporarily completed.

In 1954 Brauer was elected to the American Academy of Arts and Sciences , 1955 to the National Academy of Sciences , 1965 to the Göttingen Academy of Sciences and 1974 to the American Philosophical Society . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Blocks of characters ) and in 1962 in Stockholm ( On finite groups of even order ).

Editorial activity

In addition to his university activities, he found time to work as an editor of numerous magazines:

  • Transactions of the Canadian Mathematical Congress (1943-1949)
  • American Journal of Mathematics (1944-1950)
  • Canadian Journal of Mathematics (1949-1959)
  • Duke Mathematical Journal (1951–1956, 1963–1969)
  • Annals of Mathematics (1953-1960)
  • Proceedings of the Canadian Mathematical Congress (1954–1957)
  • Journal of Algebra (1964-1970)


  • On the modular representations of groups of finite order, University of Toronto Press 1937
  • Paul Fong, Warren J. Wong (editors): Richard Brauer-Collected Papers, MIT Press 1980

See also

Web links

Individual evidence

  1. ^ Obituary for Brauer by JA Green, Biographical Memoirs Nat. Acad. Sci.
  2. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 48.
  3. ^ Member History: Richard D. Brauer. American Philosophical Society, accessed May 18, 2018 .