As a student of Ferdinand Georg Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics.

[4] In 1888, at the age of 13, Schur went to Liepāja (Courland, now in Latvia), where his married sister and his brother lived, 640 km north-west of Mogilev.

[7] Schur attended the German-speaking Nicolai Gymnasium in Libau from 1888 to 1894 and reached the top grade in his final examination, and received a gold medal.

In 1901, he graduated summa cum laude under Frobenius and Lazarus Immanuel Fuchs with his dissertation On a class of matrices that can be assigned to a given matrix,[9] which contains a general theory of the representation of linear groups.

Schur thought that his chance of success in the Russian Empire was rather poor,[11] and because he spoke German so perfectly, he remained in Berlin.

Among other things, Schur's name was mentioned in a letter dated 27 June 1913[13] from Frobenius to Robert Gnehm (the School Board President of the ETH) as a possible successor to Carl Friedrich Geiser.

The efforts of Frobenius were finally successful in 1916, when Schur succeeded Johannes Knoblauch as adjunct professor.

In 1919 Schur finally received a personal professorship, and in 1921 he took over the chair of the retired Friedrich Hermann Schottky.

[citation needed] After the takeover by the Nazis and the elimination of the parliamentary opposition, the Law for the Restoration of the Professional Civil Service on 7 April 1933, prescribed the release of all distinguished public servants that held unpopular political opinions or who were "Jewish" in origin; a subsequent regulation[15] extended this to professors and therefore also to Schur.

His colleague Erhard Schmidt fought for his reinstatement, and since Schur had been a Prussian official before the First World War,[16] he was allowed to participate in certain special lectures on teaching in the winter semester of 1933/1934 again.

Schur withdrew his application for leave from the Science Minister and passed up the offer of a visiting professorship at the University of Wisconsin–Madison for the academic year 1933–34.

[17] One element that likely played a role in the rejection of the offer was that Schur no longer felt he could cope with the requirements that would have come with a new beginning in an English-speaking environment.

[22] Schur remained a member of the Prussian Academy of Sciences after his release as a professor, but a little later he lost this last remnant of his official position.

[24] Schur found himself lonely after the flight of many of his students and the expulsion of renowned scientists from his previous place of work.

Only Dr. Helmut Grunsky had been friendly to him, as Schur reported in the late thirties to his expatriate student Max Menachem Schiffer.

Now Schur's wife had inherited a mortgage on a house in Lithuania, which because of the Lithuanian foreign exchange determination could not be repaid.

In his doctoral thesis Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen Issai Schur determined the polynomial representations of the general linear group

Green writes, "This remarkable work (of Schur) contained many very original ideas, developed with superb algebraic skill.

According to Green, the methods of Schur's dissertation today are important for the theory of algebraic groups.

[citation needed] In 1927 Schur, in his work On the rational representations of the general linear group, gave new proofs for the main results of his dissertation.

[citation needed] Schur lived in Berlin as a highly respected member of the academic world, an apolitical scholar.

A leading mathematician and outstanding and very successful teacher, he held a prestigious chair at the University of Berlin for 16 years.

[32] Schur made fundamental contributions to algebra and group theory which, according to Hermann Weyl, were comparable in scope and depth to those of Emmy Noether (1882–1935).

[34] By the efforts of his colleague Erhard Schmidt Schur was allowed to continue lecturing until the end of September 1935.

[37] On behalf of the Mathematical Seminars chief Michel Plancherel, on 12 December 1935[38] the school board president Arthur Rohn invited Schur to une série de conférences sur la théorie de la représentation des groupes finis.

At the same time he asked that the formal invitation should come from President Rohn, comme le prof. Schur doit obtenir l'autorisation du ministère compétent de donner ces conférences.

[43] In Berlin, meanwhile, mathematician and Nazi Ludwig Bieberbach, in a letter dated 20 February 1936, informed the Reich Minister for Science, Art, and Education on the journey of Schur, and announced that he wanted to find out what was the content of the lecture in Zurich.

Heinz Hopf, who had been in Berlin before his appointment to Zurich at the ETH Privatdozent, held – as is clear from oral statements and also from letters – Issai Schur as a mathematician and greatly appreciated man.

Here, this appreciation was based entirely on reciprocity: in a letter of 1930 to George Pólya on the occasion of the re-appointment of Hermann Weyl, Schur says of Hopf: Hopf is a very excellent teacher, a mathematician of strong temperament and strong effect, a master's discipline, trained excellent in other areas.

The testimony of Hopf is in accordance with statements of Schur's former students in Berlin, by Walter Ledermann and Bernhard Neumann.