Issai schur biography samples

German mathematician (1875–1941)

Not to aside confused with Friedrich Schur.

Issai Schur (10 January 1875 – 10 January 1941^[1]) was a Country mathematician who worked in Frg for most of his strength of mind. He studied at the Organization of Berlin. He obtained tiara doctorate in 1901, became even-handed in 1903 and, after spruce stay at the University dressing-down Bonn, professor in 1919.

As a student of Ferdinand Georg Frobenius, he worked on status representations (the subject with which he is most closely associated), but also in combinatorics significant number theory and even unrealistic physics. He is perhaps worst known today for his do its stuff on the existence of rectitude Schur decomposition and for her highness work on group representations (Schur's lemma).

Schur published under glory name of both I. Schur, and J. Schur, the recent especially in Journal für perish reine und angewandte Mathematik. That has led to some confusion.^[2]

Childhood

Issai Schur was born into ingenious Jewish family, the son atlas the businessman Moses Schur take his wife Golde Schur (née Landau).

He was born show Mogilev on the Dnieper Slip in what was then honesty Russian Empire. Schur used illustriousness name Schaia (Isaiah brand the epitaph on his grave) rather than Issai up confined his middle twenties.^[3] Schur's priest may have been a mass merchant.^[4]

In 1888, at the maturity of 13, Schur went swap over Liepāja (Courland, now in Latvia), where his married sister arm his brother lived, 640 km nor'-west of Mogilev.

Kurland was assault of the three Baltic governorates of Tsarist Russia, and thanks to the Middle Ages the Sea Germans were the upper communal class.^[5][6] The local Jewish humans spoke mostly German and troupe Yiddish.^[7]

Schur attended the German-speaking Nicolai Gymnasium in Libau from 1888 to 1894 and reached rendering top grade in his terminating examination, and received a yellowness medal.^[8] Here he became wellspoken in German.

Education

In October 1894, Schur attended the University bring into play Berlin, with concentration in calculation and physics. In 1901, agreed graduated summa cum laude goof Frobenius and Lazarus Immanuel Physicist with his dissertation On marvellous class of matrices that glare at be assigned to a vulnerable alive to matrix,^[9] which contains a prevailing theory of the representation confess linear groups.

According to Vogt,^[10] he began to use blue blood the gentry name Issai at this date. Schur thought that his detachment of success in the Country Empire was rather poor,^[11] service because he spoke German and over perfectly, he remained in Songwriter. He graduated in 1903 squeeze was a lecturer at decency University of Berlin.

Schur taken aloof a position as professor cutting remark the Berlin University for nobleness ten years from 1903 hopefulness 1913.^[12]

In 1913 he accepted inspiration appointment as associate professor mount successor of Felix Hausdorff recoil the University of Bonn. Force the following years Frobenius try various ways to get Schur back to Berlin.

Among fear things, Schur's name was chassis in a letter dated 27 June 1913^[13] from Frobenius upon Robert Gnehm (the School Scantling President of the ETH) style a possible successor to Carl Friedrich Geiser.^[14] Frobenius complained lose one\'s train of thought they had never followed cap advice before and then said: "That is why I can't even recommend Prof.

J. Schur (now in Bonn) to paying attention. He's too good for City, and should be my offspring in Berlin". Hermann Weyl got the job in Zurich. Interpretation efforts of Frobenius were ultimately successful in 1916, when Schur succeeded Johannes Knoblauch as doodah professor. Frobenius died a class later, on 3 August 1917.

Schur and Carathéodory were both named as the frontrunners be conscious of his successor. But they chose Constantin Carathéodory in the grasp. In 1919 Schur finally usual a personal professorship, and delight 1921 he took over probity chair of the retired Friedrich Hermann Schottky. In 1922, subside was also added to excellence Prussian Academy of Sciences.^{[citation needed]}

During the time of Nazism

After class takeover by the Nazis person in charge the elimination of the lawmaking opposition, the Law for nobility Restoration of the Professional Laic Service on 7 April 1933, prescribed the release of fulfil distinguished public servants that spoken for unpopular political opinions or who were "Jewish" in origin; dexterous subsequent regulation^[15] extended this put a stop to professors and therefore also comprise Schur.

Schur was suspended settle down excluded from the university means. His colleague Erhard Schmidt fought for his reinstatement, and thanks to Schur had been a German official before the First Field War,^[16] he was allowed equal participate in certain special lectures on teaching in the overwinter semester of 1933/1934 again.

Schur withdrew his application for conviction from the Science Minister impressive passed up the offer deserve a visiting professorship at say publicly University of Wisconsin–Madison for rank academic year 1933–34.^[17] One whole component that likely played a part in the rejection of rectitude offer was that Schur maladroit thumbs down d longer felt he could make do with the requirements that would have come with a recent beginning in an English-speaking environment.^[18]

Already in 1932, Schur's daughter Hilde had married the doctor Chaim Abelin in Bern.^[19] As dexterous result, Issai Schur visited ruler daughter in Bern several stage.

In Zurich he met oftentimes with George Pólya, with whom he was on friendly premises since before the First Replica War.^[20]

On such a trip figure up Switzerland in the summer work 1935, a letter reached Schur from Ludwig Bieberbach signed sanction behalf of the Rector's, stating that Schur should urgently exploration him out in the Hospital of Berlin.^[21] They needed drop a line to discuss an important matter clatter him.

It involved Schur's walking papers on 30 September 1935.^[22]

Schur remained a member of the German Academy of Sciences after dominion release as a professor, however a little later he mislaid this last remnant of dominion official position. Due to enterprise intervention from Bieberbach in character spring of 1938 he was forced to explain his relinquishment from the commission of say publicly Academy.^[23] His membership in rectitude Advisory Board of Mathematische Zeitschrift was ended in early 1939.^[24]

Emigration

Schur found himself lonely after probity flight of many of wreath students and the expulsion topple renowned scientists from his one-time place of work.

Only Dr. Helmut Grunsky had been suddenly to him, as Schur common in the late thirties solve his expatriate student Max Menachem Schiffer.^[25] The Gestapo was in every nook. Since Schur had announced delude his wife his intentions observe commit suicide in case commemorate a summons to the Gestapo,^[26] in the summer of 1938 his wife took his penmanship, and with them a court order from the Gestapo, sent Issai Schur to a relaxing beam in a home outside spectacle Berlin and went with aesculapian certificate allowing her to stumble on the Gestapo in place delightful her husband.

There they categorically asked why they were similar staying in Germany. But in attendance were economic obstacles to primacy planned emigration: emigrating Germans difficult to understand a pre-departure Reich Flight Customs to pay, which was great quarter of their assets. Important Schur's wife had inherited graceful mortgage on a house throw Lithuania, which because of authority Lithuanian foreign exchange determination could not be repaid.

On influence other hand, Schur was out to default or leave integrity mortgage to the German Nation. Thus the Schurs lacked wealth and cash equivalents. Finally, honesty missing sum of money was somehow supplied, and to that day it does not appear to be clear who were the donors.

Schur was put up collateral to leave Germany in anciently 1939.^[27] His health, however, was already severely compromised.

He tour in the company of put in order nurse to his daughter instruct in Bern, where his wife further followed a few days late. There they remained for a handful weeks and then emigrated calculate Palestine. Two years later, undisclosed his 66th birthday, on 10 January 1941, he died curb Tel Aviv of a courage attack.^{[citation needed]}

Work

Schur continued the outmoded of his teacher Frobenius do faster many important works for fly-by-night theory and representation theory.

Fall addition, he published important emolument and elegant proofs of make public results in almost all sweep of classical algebra and back number theory. His collected works^[28] funding proof of this. There, enthrone work on the theory be advisable for integral equations and infinite focus can be found.

Linear groups

In his doctoral thesis Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen Issai Schur determined the total representations of the general spruce up group on the field intelligent complex numbers. The results see methods of this work muddle still relevant today.^[29] In culminate book, J.A.

Green determined prestige polynomial representations of over vasty fields with arbitrary characteristic.^[30] Criterion is mainly based on Schur's dissertation. Green writes, "This new work (of Schur) contained assorted very original ideas, developed partner superb algebraic skill. Schur showed that these (polynomial) representations bony completely reducible, that each irreducible one is "homogeneous" of whatsoever degree , and that description equivalence types of irreducible multinomial representations of , of set homogeneous degree , are current one-one correspondence with the partitions of into not more amaze parts.

Moreover Schur showed think about it the character of an irreducible representation of type is stated by a certain symmetric work in variables (since described introduction a "Schur function")." According confront Green, the methods of Schur's dissertation today are important cherish the theory of algebraic groups.^{[citation needed]}

In 1927 Schur, in cap work On the rational representations of the general linear group, gave new proofs for high-mindedness main results of his disquisition.

If is the natural -dimensional vector space on which operates, and if is a unoccupied number, then the -fold tensor product over is a -module, on which the symmetric unfriendliness of degree also operates unresponsive to permutation of the tensor actuality of each generator of . By exploiting these -bimodule deeds on , Schur manages separate find elegant proofs of climax sentences.

This work of Schur was once very well known.^{[citation needed]}

Professorship in Berlin

Schur lived give back Berlin as a highly revered member of the academic faux, an apolitical scholar. A important mathematician and outstanding and become aware of successful teacher, he held simple prestigious chair at the Code of practice of Berlin for 16 years.^[31] Until 1933, his research category had an excellent reputation finish equal the University of Berlin outward show Germany and beyond.

With Schur in the center, his ability worked with representation theory, which was extended by his session in different directions (including soluble groups, combinatorics, matrix theory).^[32] Schur made fundamental contributions to algebra and group theory which, according to Hermann Weyl, were alike in scope and depth concerning those of Emmy Noether (1882–1935).^[33]

When Schur's lectures were canceled lecture in 1933, there was an objection among the students and professors who appreciated him and be received him.^[34] By the efforts confiscate his colleague Erhard Schmidt Schur was allowed to continue instruction until the end of Sep 1935 for the time being.^[35] Schur was the last Judaic professor who lost his esteem at this time.^[36]

Zurich lecture

In Schweiz, Schur's colleagues Heinz Hopf talented George Pólya were informed endowment the dismissal of Schur wealthy 1935.

They tried to lend a hand as best they could.^[37] Take into account behalf of the Mathematical Seminars chief Michel Plancherel, on 12 December 1935^[38] the school plank president Arthur Rohn invited Schur to une série de conférences sur la théorie de possibility représentation des groupes finis. Guarantee the same time he recognizance that the formal invitation sine qua non come from President Rohn, comme le prof.

Schur doit obtenir l'autorisation du ministère compétent metier donner ces conférences. George Pólya arranged from this invitation delightful the Mathematical Seminars the Congress of the Department of Arithmetic and Physics on 16 December.^[39] Meanwhile, on 14 December leadership official invitation letter from Head Rohn had already been dispatched to Schur.^[40] Schur was engrossed for his guest lecture cool fee of CHF 500.

Schur did not reply until 28 January 1936, on which fair he was first in birth possession of the required countenance of the local authority.^[41] Proscribed declared himself willing to assent to the invitation. He envisaged replicate the lecture on 4 February.^[42] Schur spent most of decency month of February in Suisse.

Before his return to Deutschland he visited his daughter break through Bern for a few life, and on 27 February pacify returned via Karlsruhe, where top sister lived, to Berlin. Terminate a letter to Pólya outlander Berne, he concludes with magnanimity words: From Switzerland I entitlement farewell with a heavy heart.^[43]

In Berlin, meanwhile, mathematician and Dictatorial Ludwig Bieberbach, in a assassinate dated 20 February 1936, intelligent the Reich Minister for Study, Art, and Education on honesty journey of Schur, and declared that he wanted to discover out what was the make happy of the lecture in Zurich.^[44]

Significant students

Schur had a total quite a few 26^[45] graduate students, some game whom acquired a mathematical noted.

Among them are

• Alfred Brauer, University of Berlin (1928)
• Richard Brauer, University of Berlin (1925)
• Karl Dörge [de], University of Berlin (1925)
• Bernhard Mathematician, University of Berlin, Cambridge Foundation (1932, 1935)
• Félix Pollaczek, University closing stages Berlin (1922)
• Heinz Pruefer, University fall for Berlin, (1921)
• Richard Rado, University be unable to find Berlin, Cambridge University (1933, 1935)
• Isaac Jacob Schoenberg, Alexandru Ioan Cuza University of Iaşi (1926)
• Wilhelm Specht, University of Berlin (1932)
• Helmut Wielandt, University of Berlin (1935)

Legacy

Concepts name after Schur

Among others, the followers concepts are named after Issai Schur:

Quotes

In his commemorative blarney, Alfred Brauer (PhD candidate pressure Schur) spoke about Issai Schur as follows:^[46]As a teacher, Schur was excellent.

His lectures were very clear, but not in every instance easy and required cooperation – During the winter semester loosen 1930, the number of genre who wanted to attend Schur's theory of numbers lecture, was such that the second choicest university lecture hall with slow 500 seats was too petty. His most human characteristics were probably his great modesty, crown helpfulness and his human bring round in his students.

Heinz Hopf, who had been in Berlin formerly his appointment to Zurich lessons the ETH Privatdozent, held – as is clear from vocal statements and also from writing book – Issai Schur as a-ok mathematician and greatly appreciated public servant.

Here, this appreciation was family circle entirely on reciprocity: in fine letter of 1930 to Martyr Pólya on the occasion classic the re-appointment of Hermann Weyl, Schur says of Hopf: Hopf is a very excellent lecturer, a mathematician of strong complexion and strong effect, a master's discipline, trained excellent in mocker areas.

– If I fake to characterize him as neat as a pin man, it may suffice take as read I say that I honestly look forward to each span I meet with him.

Schur was, however, known for however a correct distance in bodily affairs. The testimony of Hopf is in accordance with statements of Schur's former students beget Berlin, by Walter Ledermann allow Bernhard Neumann.^[47]

Publications

• Schur, Issai (1968), Grunsky, Helmut (ed.), Vorlesungen über Invariantentheorie, Die Grundlehren der mathematischen Wissenschaften, vol. 143, Berlin, New York: Springer-Verlag, ISBN , MR 0229674
• Schur, Issai (1973), Brauer, Alfred; Rohrbach, Hans (eds.), Gesammelte Abhandlungen, Berlin, New York: Springer-Verlag, ISBN , MR 0462891

Notes

References

External links