**Issai Schur** is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.

- In 1894 Schur entered the University of Berlin to read mathematics and physics.
- Frobenius was one of his teachers and he was to greatly influence Schur and later to direct his doctoral studies.
- This theory proved a very powerful tool in the study of groups and Schur was to learn the foundations of this subject from Frobenius.
- Schur then made major steps forward, both in work of his own and work done in collaboration with Frobenius.
- In 1901 Schur obtained his doctorate with a thesis which examined rational representations of the general linear group over the complex field.
- Functions which Schur introduced in his thesis are today called SSS-functions, where the SSS stands for Schur.
- In 1903 Schur became a lecturer at Berlin University and then, from 1911 until 1916, he held a professorship in mathematics at the University of Bonn.
- Schur is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory, analysis and other topics described below.
- One of the most fundamental results which he discovered at this time is today called Schur's Lemma.
- 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.
- They were unaware at that time that the second cohomology group with coefficients in the nonzero complex numbers is the Schur multiplier, and therefore that Schur had made some of the first steps forty years earlier.
- Around 1914 Schur's interest in representations of groups was put to one side while he worked on other topics but, around 1925, developments in theoretical physics showed that group representations were of fundamental importance in that subject.
- Schur returned to work on representation theory with renewed vigour and he was able to complete the programme of research begun in his doctoral dissertation and give a complete description of the rational representations of the general linear group.
- 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.
- The school which Schur built at Berlin was of major importance not only for the representation theory of groups but, as indicated above, for other areas of mathematics.
- Schur's charismatic leadership inspired those around him to push forward with research on group representations.
- Schur's own impressive contributions were extended by his students in a number of different directions.
- There were others who worked under Schur such as Kurt Hirsch, Walter Ledermann, Hanna Neumann and Menahem Max Schiffer.
- In 1922 Schur was elected to the Prussian Academy, proposed by Planck, the secretary of the Academy.
- Planck's address which listed Schur's outstanding achievements had been written by Frobenius, at least five years earlier, as Frobenius died in 1917.
- From 1933 events in Germany made Schur's life increasingly difficult.
- And Bieberbach did this quite nicely and then he said 'A drop of remorse falls into my joy because my dear friend and colleague Schur is not allowed to be among us today'.
- The next day Erhard Schmidt started his lecture with a protest against this dismissal and even Bieberbach, who later made himself a shameful reputation as a Nazi, came out in Schur's defence.
- Schur went on quietly with his work on algebra at home.
- Schur saw himself as a German, not a Jew, and could not comprehend the persecution and humiliation he suffered under the Nazis.
- Schur's dismissal was revoked and he was able to carry out some of his duties for a while.
- By November 1933 when Walter Ledermann took his Staatsexamen he was examined by Schur together with Bieberbach who was wearing Nazi uniform.
- There were invitations to Schur to go to the United States and to Britain but he declined them all, unable to understand how a German was not welcome in Germany.
- For example Ledermann obtained a scholarship to go to St Andrews in Scotland in the spring of 1934 and he tried unsuccessfully to persuade Schur to join him in St Andrews.
- Schur continued to suffer the humiliation that was heaped on him.
- Pressure was put on Schur to resign from the Prussian Academy to which he had been honoured to be elected in 1922.
- Just over a week later, on 7 April 1938, Schur resigned from Commissions of the Academy.
- Schur left Germany for Palestine in 1939, broken in mind and body, having the final humiliation of being forced to find a sponsor to pay the 'Reichs flight tax' to allow him to leave Germany.

Born 10 January 1875, Mogilev, Russian Empire (now Belarus). Died 10 January 1941, Tel Aviv, British Mandate for Palestine (now Israel).

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Algebra, Group Theory, Origin Belarus, Puzzles And Problems

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive