**Richard Brauer** became interested in work on group characters. He formulated a method to classify all finite simple groups and spent the rest of his life working on this problem.

- Richard entered the Kaiser-Friedrich-Schule in Charlottenburg in 1907.
- Richard studied at this school until 1918 and it was during his school years that he developed his love of mathematics and science.
- When he graduated from the Kaiser-Friedrich-Schule in September 1918 the war was still in progress, and Brauer was drafted to undertake civilian war service in Berlin.
- Only two months later, in November 1918, the war ended, Brauer was released from war service and he resumed his education.
- At the University of Berlin Brauer was taught by a number of really outstanding mathematicians including Bieberbach, Carathéodory, Einstein, Knopp, von Mises, Planck, Schmidt, Schur and Szegő.
- Brauer was no exception to this, although he made only one visit during his studies, that being for a term to the University of Freiburg.
- He was increasingly attracted towards the algebra which Schur was presenting in his seminar (which was attended in the same year by Alfred Brauer).
- Schur suggested the problem that Brauer worked on for his doctorate and the degree was awarded (with distinction) in March 1926.
- Before his marriage Brauer was appointed as Knopp's assistant at the University of Königsberg and he took up this post in the autumn of 1925.
- Shortly after Brauer arrived in Königsberg, Knopp left to take up an appointment at Tübingen.
- The mathematics department at Königsberg was small, with two professors Szego and Reidemeister, and with Rogosinski and Kaluza holding junior positions like Brauer.
- It was in Königsberg that Brauer's two sons, George Ulrich Brauer and Fred Günter Brauer were born.
- Brauer taught at Königsberg until 1933 and during this period he produced results of fundamental importance.
- This group became known (to the author's embarrassment) as the "Brauer group" ...
- This was a desperate time for Brauer who realised that he had to find a post outside Germany.
- Fortunately action was taken in several countries to find posts abroad for German academics forced from their positions and a one year appointment was arranged for Brauer in Lexington, Kentucky for the academic year 1933-34.
- Following his year in Lexington, Brauer was appointed as Weyl's assistant at the Institute for Advanced Study in Princeton.
- Collaboration between Brauer and Weyl on several projects followed, in particular a famous joint paper on spinors published in 1935 in the American Journal of Mathematics.
- A permanent post followed the two temporary posts when Brauer accepted an assistant professorship at the University of Toronto in Canada in the autumn of 1935.
- This was a time when Brauer developed some of his most impressive theories, carrying the work of Frobenius into a whole new setting, in particular the work on group characters Frobenius published in 1896.
- Brauer carried Frobenius's theory of ordinary characters (where the characteristic of the field does not divide the order of the group) to the case of modular characters (where the characteristic does divide the group order).
- It was in joint work with Nesbitt, published in 1937, that Brauer introduced the theory of blocks.
- This he used to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work.
- Brauer spent 1941 at the University of Wisconsin having been awarded a Guggenheim Memorial Fellowship.
- In 1949 Brauer was awarded the Cole Prize from the American Mathematical Society for his paper On Artin's L-series with general group characters which he published in the Annals of Mathematics in 1947.
- We have mentioned a number of topics which Brauer worked on in the course of this biography.
- Brauer was to spend the rest of his life working on the problem of classifying the finite simple groups.
- (See the biography of Gorenstein for further details on the programme to classify finite simple groups.) Most important was Brauer's vital step in setting the direction for the whole classification programme in the paper On groups of even order where it is shown that there are only finitely many finite simple groups containing an involution whose centraliser is a given finite group.
- Brauer had announced these results and his programme for classifying finite simple groups at the International Congress of Mathematicians in Amsterdam in 1954.
- Despite his remarkable contributions to research, Brauer found time to act as an editor for a number of journals.
- We have mentioned above a number of honours which Brauer received.
- Brauer's interest in people was natural and unforced, and he treated students and colleagues alike with the same warm friendliness.
- Richard Brauer occupied an honoured position in the mathematical community, in which the respect due to a great mathematician was only one part.

Born 10 February 1901, Berlin-Charlottenburg, Germany. Died 17 April 1977, Belmont, Massachusetts, USA.

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Algebra, Group Theory, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive