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Schur is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.
Schur went to Latvia at the age of 13. In 1894 he entered the University of Berlin to read mathematics and physics. Frobenius was one of his teachers and was to greatly influence Schur. They collaborated on many papers.
In 1901 he obtained his doctorate with a thesis which examined rational representations of the general linear group over the complex field. Interest in the results of Schur's thesis continues today, for example J A Green published an account of these results in a modern setting in 1980.
In 1903 he became a lecturer at Berlin University and, from 1911 until 1916 he held the chair of mathematics, succeeding Hausdorff. He then returned to Berlin.
Between 1904 and 1907 Schur worked on projective representations of groups. In a series of papers he introduced the concept now known as the 'Schur multiplier'. This is an extremely important abstract concept which arose from the concrete problems that Schur was studying.
Schur was also interested in reducibility, location of roots and the construction of the Galois group of classes of polynomials such as Laguerre and Hermite polynomials.
In 1922 he was elected to the Prussian Academy by Planck, the secretary of the Academy. His address listing Schur's achievements had been written by Frobenius, at least five years before as he died in 1917.
From 1933 events in Germany made his life increasingly difficult. Schur saw himself as a German, not a Jew, and could not comprehend the persecution and humiliation he suffered under the Nazis. He left Germany for Palestine in 1939, broken in mind and body. He died two years later.
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