Issai Shur

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Issai Shur

Issai Shur (born January 10, 1875 in Mogilev , † January 10, 1941 in Tel Aviv ) was a Russian-German mathematician . As a student of Frobenius , he worked on representation theory of groups , but also in number theory and even in theoretical physics . A by-product of his work is best known, the Schur decomposition of matrices, which has important applications in numerical linear algebra .

Schur published both under the name I. Schur and J. Schur, the latter mainly in the journal for pure and applied mathematics . This has caused some confusion.



Issai Schur was born as the son of the merchant Moses Schur and his wife Golde Schur (née Landau) in Mogiljow on the Dnepr in what was then the Russian Empire . According to Vogt, Schur preferred the first name Schaia to Issai until his mid-twenties. Schur's father is said to have been a wholesale merchant.

In 1888, at the age of 13, Schur went to Libau ( Courland , now in Latvia ), where his married sister and brother-in-law lived at that time, 640 km northwest of Mogiljow. At that time Kurland was one of the three Baltic Governments of Tsarist Russia and since the Middle Ages the Baltic Germans (aristocracy and urban bourgeoisie) formed the leading social classes there. Most of the local Jewish community spoke German rather than Yiddish .

Schur attended the German-speaking Nicolai-Gymnasium in Libau between 1888 and 1894 and achieved the top grade in his final exam, as well as a gold medal. Here he learned fluent German, in his opinion he considered Yiddish to be his mother tongue.


In October 1894 Schur enrolled at the University of Berlin in mathematics and physics. In 1901 he received his doctorate summa cum laude under Ferdinand Georg Frobenius and Lazarus Immanuel Fuchs on a class of matrices that can be assigned to a given matrix , with this title concealing a theory of the representation of the general linear group . According to Vogt, he used his first name Issai for the first time in this work. According to a quotation, Schur assessed his chances in the Russian Empire as rather bad, and since he spoke German so perfectly that one could without a doubt assume that it was his mother tongue, he stayed in Berlin. He completed his habilitation in 1903 and became a private lecturer at the University of Berlin. For the ten years between 1903 and 1913, Schur held a position as a private lecturer at Berlin University.

In 1913 he accepted a position as associate professor and successor to Felix Hausdorff in Bonn. In the following years Frobenius tried in various ways to bring Schur back to Berlin. Among other things, the name Schur was mentioned in a letter dated June 27, 1913 from Frobenius to the President of the ETH School Board, Robert Gnehm , when the successor to Carl Friedrich Geiser had to be settled. Frobenius initially complained that his advice had never been followed elsewhere and then said: That's why I don't even recommend Prof. J. Schur (now in Bonn). It's way too good for Zurich and should be my successor in Berlin. As is well known, Hermann Weyl received the position in Zurich. Frobenius' efforts were not successful until 1916, when Schur succeeded Johannes Knoblauch as associate professor . One year later, on August 3, 1917, Frobenius died. In the faculty's application to regulate the succession, Schur and Carathéodory were named jointly in first place. But then Constantin Carathéodory was elected. In 1919 Schur finally received a personal professorship , and in 1921 he was able to take over the chair of the retired Friedrich Hermann Schottky . In 1919 he was elected a member of the Leopoldina . In the same year he was elected a corresponding member of the Göttingen Academy of Sciences . In 1922 he was also admitted to the Prussian Academy of Sciences . Since 1929 he was a corresponding member of the Soviet Academy of Sciences .

At the time of National Socialism

After the National Socialists came to power and the parliamentary opposition was eliminated, the law on the restoration of the civil service on April 7, 1933, decreed the dismissal of all politically unpopular civil servants who were regarded as "Jewish" by origin; According to a later regulation, this also applied to professors and therefore also to Schur. Schur was suspended and expelled from the university. His colleague Erhard Schmidt campaigned for his reinstatement, and since Schur had already been a Prussian civil servant before the First World War , he was again allowed to attend teaching with certain special lectures for the winter semester of 1933/1934. On this readmission, Schur withdrew his vacation request submitted to the Secretary of Science and turned down the offer of a visiting professorship at the University of Wisconsin-Madison for the academic year 1933/34. It is likely that the rejection of the offer also played a role in the fact that Schur no longer felt up to the demands that a new beginning in an English-speaking environment would have entailed.

In 1932, Schur's daughter Hilde married the doctor Chaim Abelin in Bern. As a result, Issai Schur visited his daughter in Bern several times. In Zurich he then met several times with George Pólya , with whom he had been on friendly terms since before the First World War.

On one such trip to Switzerland in the summer of 1935, Schur received a letter signed by Ludwig Bieberbach on behalf of the rector, saying that Schur should urgently visit him at the university in Berlin. There is an important matter to discuss with him. It is about Schur's release on September 30, 1935.

Schur remained a member of the Prussian Academy of Sciences after his dismissal as a professor, but a little later he also lost this last remnant of his official position. Due to an intervention by Bieberbach, he was forced in spring 1938 to resign from the Academy's commissions. His membership in the advisory board of the Mathematische Zeitschrift also ended in early 1939.


Grave in the Trumpeldor Cemetery in Tel Aviv

After many of his students had fled and were expelled from his previous place of work, the recognized scientist became lonely. Only Helmut Grunsky , Schur reported at the end of the 1930s, showed his immigrant pupil Max Menachem Schiffer to be friendly to him. The Gestapo was omnipresent. Since Schur had announced to his wife that he would commit suicide in the event of a summons to the Gestapo, his wife intercepted the letters and the summons with them in the summer of 1938, arranged for Issai Schur to recuperate in a home outside Berlin and provided him with a medical certificate instead of the husband to the Secret State Police. There they asked straight out why they were still in Germany. However, economic obstacles stood in the way of the planned emigration: Before leaving Germany, emigrating Germans had to pay a portion of their property as a flight tax - at that time a quarter of the tax value . Now Schur's wife had inherited a mortgage on a house in Lithuania, which could not be repaid due to the Lithuanian currency regulations. On the other hand, Schur was forbidden to forego it or to leave the mortgage to the German Reich. So the Schurs lacked liquid funds. In the end, the missing amount of money could be raised somehow, although it does not seem clear to this day who the financier was.

Schur was able to leave Germany in early 1939. His health was already badly affected. Accompanied by a nurse, he traveled to his daughter in Bern, where his wife followed him a few days later. They stayed there for a few weeks and then emigrated to Palestine . Just two years later, on his 66th birthday, on January 10, 1941, he died of a heart attack in Tel Aviv .


With many important works on group and representation theory, Schur continued the work of his teacher Frobenius. In addition, he published important results and elegant proofs for well-known theorems in almost all branches of classical algebra and number theory. His collected works are impressive evidence of this. His work on the theory of integral equations and on infinite series can also be found there.

Linear groups

In his doctoral thesis on a class of matrices that can be assigned to a given matrix , Issai Schur determines the polynomial representations of the general linear group over the field of complex numbers. The results and methods of this work are still relevant today. JA Green determines in his book the polynomial representations of the over infinite fields with arbitrary characteristics. In doing so, he is essentially based on Schur's dissertation. JA Green writes This remarkable work (of Schur) contained many very original ideas, developed with superb algebraic skill. Schur showed that these (polynomial) representations are completely reducible, that each one is "homogeneous" of some degree , and that es equivalence types of irreducible polynomial representations of , of fixed homogeneous degree , are in one-to-one correspondence with the partitions of into not more than parts. Moreover, Schur showed that the character of an irreducible representation of type is given by a certain symmetric function in variables, since described as a Schur function. According to Green, the methods of Schur's dissertation are still important today for the theory of algebraic groups.

In 1927, Schur gave new evidence for the main results of his dissertation in his work On the rational representations of the general linear group . If the natural -dimensional -vector space on which operates is and is a natural number, then the -fold tensor product is over a -module on which the symmetric group of degree also operates by permutation of the tensor factors of each generator of . By taking advantage of this - -Bimodul effect, Schur succeeds in finding elegant proofs for his propositions. This work by Schur immediately became very popular.

Professorship in Berlin

Schur lived in Berlin as a highly respected member of the academic world, a scholar far removed from politics. A leading mathematician and an outstanding and very successful teacher, he held a prestigious chair at the University of Berlin for 16 years. By 1933, his working group at the University of Berlin had an excellent reputation beyond Germany. With Schur at the center, his teaching staff dealt with representation theory, which his students expanded in various directions (solvable groups, combinatorics, matrix theory). Schur made fundamental contributions to algebra and group theory which, according to Hermann Weyl , were comparable in scope and depth to those of Emmy Amalie Noether (1882–1935) .

When Schur's lectures were canceled in 1933, there was an outcry among the students and professors who valued and liked him. Through his colleague Erhard Schmidt, Schur was able to continue his lectures until the end of September 1935 for the time being. At that time, Schur was the last Jewish professor to lose his post.

Zurich lecture

In Switzerland, Schur's colleagues Heinz Hopf and George Pólya were informed of Issai Schur's dismissal in 1935. They tried to help as best they could. On December 12, 1935, on behalf of the Mathematical Seminar, its head, Michel Plancherel, applied to the President of the School Council, Arthur Rohn , to invite Issai Schur to une série de conférences sur la théorie de la représentation des groupes finis in January . At the same time he asked that the formal invitation should come from President Rohn, comme le prof. Schur doit obtenir du ministère compétent l'autorisation de donner ces conférences. George Pólya also informed the Conference of the Department of Mathematics and Physics on December 16 of this proposal from the Mathematics Seminar. Meanwhile, on December 14th, President Rohn's official letter of invitation to Issai Schur had already been sent. In it, Schur was offered a fee of CHF 500 for his guest lecture.

Schur did not reply until January 28, 1936 that on that day he had obtained the necessary approval from the local authorities . He would be happy to accept the invitation. He also announced that the lecture would begin on February 4th. Schur spent most of February in Switzerland. Before returning to Germany, he visited his daughter in Bern for a few days, and on February 27th he returned to Berlin via Karlsruhe, where his sister lived. He closes a letter to Pólya from Bern with the words: I say goodbye to Switzerland with a heavy heart .

In Berlin, Ludwig Bieberbach had meanwhile drawn the Reich Minister for Science, Art and Education to the attention of Schur in a letter dated February 20, 1936, and announced that he wanted to find out what the content of the lecture in Zurich was.

Eminent students

Schur had a total of 26 doctoral students, some of whom achieved world renown in mathematics. Among them are

and Karl Dörge (1925), Felix Pollaczek (1922), Wolfgang Hahn (1933), Rose Peltesohn (1936), Arnold Scholz (1928), Rudolf Kochendörffer (1937), Roberto Frucht (1931) and Hans Rohrbach (1932).



According to Issai Schur, u. a. named the following


In his commemorative speech, Alfred Brauer (PhD student Schurs) commented on Issai Schur as follows: Schur was an excellent lecturer. His lectures were extremely clear, but not always easy and required cooperation. - In the winter semester of 1930, the number of students who wanted to take Schur's number theory was so large that the second largest lecture hall at the university was too small with a little over 500 seats. His most outstanding human qualities were arguably his great humility, helpfulness and human interest in his students.

Heinz Hopf, who had been a private lecturer in Berlin before his appointment to the ETH in Zurich, - as can be seen from oral statements and letters - greatly appreciated Issai Schur as a mathematician and person. This appreciation was based entirely on reciprocity: in a letter from 1930 to George Pólya on the occasion of the refilling of the position of Hermann Weyl, Schur says about Hopf: Hopf is a very excellent lecturer, a mathematician with a strong temperament and strong impact, a master of his Discipline that has also been excellently trained in other areas. - If I am still to characterize him as a person, it may be enough to say that I am genuinely happy to meet him every time.

However, Schur was known for attaching importance to correct distance in personal dealings. Corresponding statements by Hopf are in agreement with statements by Schur's former Berlin students, Walter Ledermann and Bernhard Neumann . One must imagine Issai Schur as a worthy privy councilor, a somewhat withdrawn, extremely correct and from all sides extremely respected professor.

Fonts (selection)

  • A contribution to Hilbert's theory of complete quadratic forms . In: Mathematical Journal. Volume 12, Number 1 / December 1922, pp. 287-297. Springer Berlin-Heidelberg
  • Some remarks on the above work by Mr. A. Speiser . In: Mathematical Journal. Volume 5, Numbers 1-2 / March 1919, pp. 7-10. Springer Berlin-Heidelberg
  • Elementary proof of a theorem by L. Stickelberger . In: Mathematical Journal. Volume 29, Number 1 / December 1929, pp. 464-465. Springer Berlin-Heidelberg
  • Elementary proof of some asymptotic formulas of additive number theory . In: Mathematical Journal. Volume 24, Number 1 / December 1926, pp. 559-574. Springer Berlin-Heidelberg
  • About the maximum of the absolute amount of a polynomial in a given interval . In: Mathematical Journal. Volume 4, Numbers 3-4 / September 1919, pp. 271-287. Springer Berlin-Heidelberg
  • About the equivalence of the Cesàro and Hölder mean values . In: Mathematical Annals. Volume 74, Number 3 / September 1913, pp. 447-458. Springer Berlin-Heidelberg
  • About the characteristic roots of a linear substitution with an application to the theory of integral equations . In: Mathematical Annals. Volume 67, Number 3 / September, 1909, pp. 488-510. Springer Berlin-Heidelberg
  • On the congruence annual report of the DMV edition 25, pp. 114–117, Teubner Stuttgart 1917.
  • About the distribution of the roots in certain algebraic equations with integer coefficients . In: Mathematical Journal. Volume 1, Number 4 / December 1918, pp. 377-402. Springer Berlin-Heidelberg
  • About a fundamental property of the invariants of a general binary form . In: Mathematical Journal. Volume 15, Number 1 / December 1922, pp. 81-105. Springer Berlin-Heidelberg
  • About an integral theorem used by Mr. L. Lichtenstein . In: Mathematical Journal. Volume 7, Numbers 1-4 / March 1920, pp. 232-234. Springer Berlin-Heidelberg
  • About finite groups and Hermitian forms . In: Mathematical Journal. , Volume 1, Numbers 2-3 / June 1918, pp. 184-207. Springer Berlin-Heidelberg
  • Via groups of linear substitutions with coefficients from an algebraic number field . In: Mathematical Annals. Volume 71, Number 3 / September 1911, pp. 355-367. Springer Berlin-Heidelberg
  • About the arithmetic of power series with integer coefficients . In: Mathematical Journal. Volume 12, Number 1 / December 1922, pp. 95-113. Springer Berlin-Heidelberg
  • On the irreducibility of the equation of division of a circle . Mathematische Zeitschrift, Volume 29, Number 1 / December 1929, p. 463. Springer Berlin-Heidelberg
  • On the theory of Cesàro's and Hölder's mean values . In: Mathematical Journal. Volume 31, Number 1 / December 1930, pp. 391-407. Springer Berlin-Heidelberg
  • To the theory of the linear homogeneous integral equations . In: Mathematical Journal. Volume 67, Number 3 / September, 1909, pp. 306-339. Springer Berlin-Heidelberg


  • Hermann Boerner: Article Schur in Dictionary of Scientific Biography.
  • Konrad Knopp: Comment on the above work by Mr. I. Schur . In: Mathematical Annals. Volume 74, Number 3 / September 1913, pp. 459-461. Springer Berlin-Heidelberg
  • K.-R. Biermann: Mathematics and its lecturers at the Berlin University 1810-1933. Berlin 1988
  • Urs Stammbach: Issai Schur's Zurich lecture on representation theory . ETH Library Zurich, 2004, ISBN 978-3-909386-02-4 , as well as Mathematical-Physical Semester Reports 2004
  • A Century of Mathematics, 1890–1990. Festschrift for the anniversary of the DMV, Vieweg, ISBN 3-528-06326-2
  • A. Brauer and H Rohrbach: Issai Schur. Collected treatises, 3 volumes . Springer, Berlin-Heidelberg 1973, ISBN 978-3-540-05630-0
  • Izrael Gohberg: I. Schur Methods in Operator Theory and Signal Processing . Birkhäuser Verlag AG, 1986, ISBN 978-3-7643-1776-8
  • Walter Ledermann: Issai Schur and his School in Berlin. In: Bulletin London Mathematical Society. Vol. 15, 1983, p. 97
  • Issai Schur in memory . In: Mathematical Journal. Volume 63, Number 1 / December 1955, p. 1. Springer Berlin-Heidelberg, ISSN  0025-5874
  • Bruce M. Landman, Aaron Robertson: Ramsey Theory on the Integers . AMS, Rhode Island, 2004, ISBN 0-8218-3199-2
  • Anthony Joseph, Anna Melnikov, Rudolf Rentschler: Studies in Memory of Issai Schur . Birkhäuser, Boston-Berlin-Basel 2002, ISBN 978-0-8176-4208-2
  • B. Chandler & W. Magnus: The history of combinatorial group theory: a case study in the history of ideas. New York, 1982.
  • Issai Schur, Helmut Grunsky: Lectures on invariant theory . Springer, Berlin 1968, special cover
  • Annette Vogt : Issai Schur - expelled as a scientist . 1999 in: Julius H. Schoeps (Ed.), Menora. Yearbook for German-Jewish History, 1999. pp. 217–235
  • Jürgen Batt:  Schur, Issai. In: New German Biography (NDB). Volume 23, Duncker & Humblot, Berlin 2007, ISBN 978-3-428-11204-3 , p. 760 ( digitized version ).
  • Reinhard Siegmund-Schultze Landau and Schur - documents of a friendship until death in inhuman times , messages DMV, Volume 19, 2011, pp. 164–173

Web links

References and comments

  1. Urs Stammbach: The Zurich lecture by Issai Schur on representation theory. Page i-xxxii, ETH Library 2004.
  2. ^ W. Ledermann: Issai Schur and his school in Berlin . In: Bull. London Math. Soc. . 15, No. 2, 1983, pp. 97-106. doi : 10.1112 / blms / 15.2.97 .
  3. Vogt, Annette. Issai Schur: expelled as a scientist. In Schoeps, Grozinger & Mattenklott [401, pp. 217-235 (1999)]
  4. ^ The Kopelman Foundation. Mogilev. JewishGen Belarus SIG, on The Jewish Encyclopedia Web site conceived, created, and funded by The Kopelman Foundation, accessed December 28, 2003.
  5. Blaushild, Immanuel. Libau. In Snyder [423, §1 (c. 1995)]
  6. Snyder, Stephen, project coordinator. A Town Named Libau (Liepaja, Latvia) . JewishGen Web site accessed December 27, 2003 (Translation of the 36-page booklet: A Town Named Libau in English, German and Hebrew and additional material about Libau , Editor and Publisher of booklet unknown, believed to have been published in Israel, 1985.)
  7. Beare, Arlene, ed. History of Latvia and Courland Web site accessed March 1, 2004: (This history is derived from a few sources including [38] but mainly edited from the presentation made by Ruvin Ferber at the 21st International Conference of Jewish Genealogy held in London in July 2001.)
  8. cf. Vogt, Anne
  9. ^ Shur, Issai. About a class of matrices that can be assigned to a given matrix. Doctoral dissertation, University of Berlin, 1901; reprinted in Brauer k Rohrbach [71, Volume I, pp. 1-72 (1973)]
  10. cf. Vogt, Anne
  11. Chandler, Bruce; Magnus, Wilhelm. The History of Combinatorial Group Theory: A Case Study in the History of Ideas. Studies in the History of Mathematics and Physical Sciences 9. Springer-Verlag, New York, 1982.
  12. cf. Biography of Leopoldino Carolina
  13. Hermann Weyl: Estate. Manuscripts and bequests, ETH Library, 1006: 1.
  14. Carl Friedrich Geiser (1843–1934), who did his doctorate with Ludwig Schläfli in Bern, was a full professor at the Swiss Federal Polytechnic in Zurich from 1873 to 1913.
  15. 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. 220.
  16. ^ Member entry by Issai Schur at the German Academy of Natural Scientists Leopoldina , accessed on June 20, 2016.
  17. ^ Foreign members of the Russian Academy of Sciences since 1724. Issai Schur. Russian Academy of Sciences, accessed November 11, 2015 .
  18. 3. Ordinance on the Implementation of the Professional Civil Servants Act. 6 May 1933, RGBl.I pp.245f.
  19. These so-called “old officials” were initially exempt from dismissal because of their Jewish descent, 1. Ordinance on the implementation of the Law on Civil Servants. 11 April 1933, RGBl.I p.195.
  20. ^ Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. Studies in Memory of Issai Schur , Birkhäuser 2003. Letter from the Ministry of September 11, 1933, letter from Schur of September 15, 1933
  21. This is the view of Alfred Brauer in his memorial speech
  22. Schur was married to the doctor Regina Frumkin in 1906. The marriage produced two children, Georg and Hilde. Georg, who was a little older than Hilde, studied physics and later worked as an actuary in Israel.
  23. ^ George Pólya (1887–1985) completed his habilitation at the ETH after studying in Budapest in 1914 and after stays in Göttingen and Paris. In 1928 he was appointed full professor. From 1940 he worked in the USA, most recently at Stanford University. - His acquaintance with Schur goes back to the time before the First World War: There are numerous letters from Schur to Pólya from the years 1913/14, which are kept in the Stanford University Libraries
  24. ^ Message from Mrs. Susanne Abelin, the granddaughter of Issai Schur, summer 2001. The letter of August 20, 1935 is in Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and Other Documents. In Anthony Joseph et al. Studies in Memory of Issai Schur , Birkhäuser 2003. Page lxxii
  25. The signed by Hitler and Goering Entpflichtungsurkunde dated September 28, 1935. See Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and Other Documents. In Anthony Joseph et al. Studies in Memory of Issai Schur , Birkhäuser 2003. Page lxxiv. According to the Reich Citizenship Act, the dismissal would have been ordered by December 31, 1935 at the latest
  26. The process is described in the book by Reinhard Siegmund-Schultze: Mathematicians on the run from Hitler. Documents for the History of Mathematics, Volume 10. German Mathematicians Association, Vieweg, 1998. Page 69/70; the resignation is dated April 6, 1938. The book also contains other interesting information about Schur's situation in the 1930s
  27. See Volker R. Remmert: Mathematical Publishing in the Third Reich. Math. Intelligencer 22 (3) 2000, pp. 22-30
  28. ^ "Long after the war, I talked to Grunsky about that remark and he literally started to cry: You know what I did? I sent him a postcard to contratulate him on his sixtieth birthday. I admired him so much and was very respectful in that card. How lonely he must have been to remember such a small thing ", Schiffer, Menachem Max; Issai Shur. Some Personal Reminiscences (1986); 1998 in: Begehr, H. (Ed.), Mathematik in Berlin. History and documentation, 1998 Aachen.
  29. See on this and for the following: Alfred Brauer's memorial speech
  30. Compare the letter from the Reich Minister for Science, Education and Public Education to Issai Schur of February 24, 1939. Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and Other Documents. In Anthony Joseph et al. Studies in Memory of Issai Schur , Birkhäuser 2003. Page lxxxi
  31. published by Alfred Brauer and Hans Rohrbach
  32. s. Festschrift of the DMV page 549
  33. Polynomial representations of ISBN 978-0-387-10258-0
  34. cf. Chandler, Bruce; Magnus, Wilhelm.
  35. Briining, Jochen; Ferus, Dirk; Siegmund-Schultze; Reinhard. Terror and Exile: Persecution and Expulsion of Mathematicians from Berlin between 1933 and 1945. An Exhibition on the Occasion of the International Congress of Mathematicians, Technische Universitat Berlin, August 19 to 27, 1998, Deutsche Mathematiker-Vereinigung, Berlin, 1998.
  36. Pinl, Max; Furtmiiller, Lux. Mathematicians under Hitler. Page 178
  37. cf. Briining, Jochen page 27
  38. Pinl, Max; Furtmiiller, Lux. Mathematicians under Hitler. Page 178
  39. Soifer, Alexander. Issai Schur: Ramsey theory before Ramsey. Geombinatorics, 5: 6-23 (1995)
  40. Urs Stammbach Issai Schur's Zurich lecture on representation theory, page xiii, ETH Library 2004
  41. School council archive of the ETH Zurich. Files 1935/36, ETH Library.
  42. ^ Secretary of Department IX, Mathematics and Physics. Minutes of the conferences of Dept. IX, Hs 1079: 3, manuscripts and bequests, ETH Library Zurich
  43. School council archive of the ETH Zurich. Missiven 1935, 3119, ETH Library
  44. School council archive of the ETH Zurich. Files 1935/36, ETH Library
  45. According to a résumé written later - see Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. Studies in Memory of Issai Schur. Page lxxvii, Birkhäuser 2003. - the lectures took place between February 4th and 18th
  46. ^ See Department of Special Collections and University Archives, Stanford University Libraries, February 26, 1936.
  47. The process is described in Charles Curtis: Pioneers of representation theory. History of Mathematics vol. 15, Amer. Math. Soc./London Math. Soc. 1999, page 131
  48. See Mathematics Genealogy Project, North Dakota State University [1]
  49. ^ Commemorative speech of November 8, 1960 on the occasion of the Schur memorial service as part of the 150th anniversary of the University of Berlin. See Issai Schur: Collected Treatises, pp. V-xiv. Alfred Brauer received his doctorate from Schur in 1928.
  50. See Interview with Bernhard Neumann , Newsletter of the European Mathematical Society, 39, March 2001, 9-11; Walter Ledermann: Issai Schur and his school in Berlin , Bull. London Math. Soc. 1983, 15: 97-106. Bernhard Neumann received his doctorate in 1932, Walter Ledermann passed the examination for teacher training candidates in 1933