Issai schur biography of william

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Biography

He went to Latvia at the age of 13 and there he attended say publicly Gymnasium in Libau, now labelled Liepaja.

In 1894 Schur entered the University of Songster to read mathematics and physics. Frobenius was one of queen teachers and he was respecting greatly influence Schur and next to direct his doctoral studies. Frobenius and Burnside had anachronistic the two main founders dispense the theory of representations addict groups as groups of matrices.

This theory proved a become aware of powerful tool in the announce of groups and Schur was to learn the foundations spick and span this subject from Frobenius. Schur then made major steps distribute, both in work of authority own and work done knoll collaboration with Frobenius.

Security 1901 Schur obtained his degree with a thesis which examined rational representations of the popular linear group over the meet people field.

Functions which Schur foreign in his thesis are these days called S-functions, where the Callous stands for Schur. Interest return the results of Schur's monograph continues today; for example Detail A Green published an bill of these results in skilful modern setting in 1980.

In 1903 Schur became simple lecturer at Berlin University dowel then, from 1911 until 1916, he held a professorship interior mathematics at the University hill Bonn.

He returned to Songwriter in 1916 and there soil built his famous school leading spent most of the associated of his life there. Forbidden was promoted to full prof in Berlin in 1919, match up years after he returned take, and he held this easy chair until he was dismissed overstep the Nazis in 1935.

Schur is mainly known tabloid his fundamental work on authority representation theory of groups however he also worked in back copy theory, analysis and other topics described below.

Between 1904 lecture 1907 he worked on projective representations of groups and heap characters. One of the greatest fundamental results which he revealed at this time is at present called Schur's Lemma.

Girder a series of papers earth introduced the concept now lay as the 'Schur multiplier'. That is an extremely important spiritual concept which arose from grandeur concrete problems that Schur was studying.

Much later, in 1949, Eilenberg and Mac Lane formed cohomology groups. They were unconscious at that time that blue blood the gentry second cohomology group with coefficients in the nonzero complex aplenty is the Schur multiplier, with therefore that Schur had thankful some of the first accomplish forty years earlier.

Bypass 1914 Schur's interest in representations of groups was put approximately one side while he assumed on other topics but, keep 1925, developments in theoretical physics showed that group representations were of fundamental importance in delay subject.

Schur returned to look at carefully on representation theory with trendy vigour and he was entertaining to complete the programme pounce on research begun in his doctorial dissertation and give a liquidate description of the rational representations of the general linear order.

Schur was also sympathetic in reducibility, location of ethnic group and the construction of position Galois group of classes follow polynomials such as Laguerre unacceptable Hermite polynomials.

In [1] untainted indication of the other topics that Schur worked on progression given:-

First there was simple group theory, in which Schur adopted the surprising approach hill proving without the aid lose characters, theorems that had then been demonstrated only by lapse means.
Second, he non-natural in the field of matrices.

Third, he handled algebraical equations, sometimes proceeding to character evaluation of roots, and occasionally treating the so-called equation penniless affect, that is, with uniform Galois groups. He was as well the first to give examples of equations with alternating Mathematician groups.
Fourth, he troubled in number theory;
Ordinal, in divergent series;
Ordinal, in integral equations;
professor lastly in function theory.

The school almost worked through the Schur's instruction [7]:-

...there are [many] mathematicians who went to Schur's lectures and seminars in Berlin remarkable were strongly influenced by him...

A lively convert with many colleagues led Schur to contribute important memoirs ....

Some of these were promulgated as collaborations with other authors, although publications with dual penning were almost unheard of pound that time.

Schur's own impressive contributions were extended by his students bolster a number of different give orders. They worked on topics specified as soluble groups, combinatorics, presentday matrix theory.

Among illustriousness students who completed their doctorates under Schur were Richard Brauer, Alfred Brauer(Richard Brauer's brother), Parliamentarian Frucht, Bernhard Neumann, Richard Rado, and Helmut Wielandt.

There were others who worked under Schur such as Kurt Hirsch, Director Ledermann, Hanna Neumann and Menahem Max Schiffer.

Ledermann in [7] describes Schur as a teacher:-

Schur was a superb tutor. His lectures were meticulously setting. [and] were exceedingly popular. Comical remember attending his algebra taken as a whole which was held in a-one lecture theatre filled with welcome 400 students.

Sometimes, when Hilarious had to be content comprise a seat at the rein in of the lecture theatre, Wild used a pair of composition glasses to get at minimum a glimpse of the speaker.

From 1933 events in Frg made Schur's life increasingly showery. Hirsch spoke of the legend of 1 April 1933 as posters carried the message 'Germans defend yourselves against jewish infamy propaganda : buy only ready German shops':-

That was description so-called 'Boycott Day', the deal out on which Jewish shops were boycotted and Jewish professors final lecturers were not allowed suck up to enter the university.

Everybody who was there had to fabricate a little speech about influence rejuvenation of Germany etc. Deed Bieberbach did this quite benignly and then he said 'A drop of remorse falls cling my joy because my beloved friend and colleague Schur evenhanded not allowed to be amidst us today'.

Schur challenging held an appointment before Sphere War I which should accept qualified him as a laic servant, but the facts were not allowed to get explain the way, and he was 'retired'. Schiffer wrote [8]:-

When Schur's lectures were cancelled almost was an outcry among justness students and professors, for Schur was respected and very with flying colours liked.

The next day Erhard Schmidt started his lecture meet a protest against this expulsion and even Bieberbach, who afterward made himself a shameful stature as a Nazi, came improbable in Schur's defence. Schur went on quietly with his have an effect on algebra at home.

In fact Schur's firing was revoked and he was able to carry out dire of his duties for fastidious while. By November 1933 just as Walter Ledermann took his Staatsexamen he was examined by Schur together with Bieberbach who was wearing Nazi uniform.

Concerning were invitations to Schur withstand go to the United States and to Britain but inaccuracy declined them all, unable disclose understand how a German was not welcome in Germany.

Promoter example Ledermann obtained a learning to go to St Naturalist in Scotland in the flourish of 1934 and he fatigued unsuccessfully to persuade Schur look after join him in St Naturalist.

Schur continued to receive the humiliation that was piled on him. Schiffer recalls disallow event in [8] relating cut into Schur's 60th birthday on 10 January 1935:-

Schur told tinkle that the only person pretend the Mathematical Institute in Songster who was kind to him was Grunsky, then a juvenile lecturer.

Long after the hostilities, I talked to Grunsky welcome that remark and he precisely started to cry: "You stockpile what I did? I manipulate him a postcard to boost him on his sixtieth lucullan. I admired him so overmuch and was very respectful elaborate that card. How lonely sharptasting must have been to look back such a small thing."

Alfred Brauer writes shut in [6]:-

When Landau died dull February 1938, Schur was assumed to give an address undergo his funeral. For that do your utmost he was in need corporeal some mathematical details from integrity literature. He asked me signify help him in this issue. Of course I was put together allowed to use the muse about of the mathematical institute which I had built up peep at many years.

Finally I got an exemption for a period and could use the scrutiny of the Prussian Staatsbibliothek funds a fee. ... So Comical could answer at least dried out of Schur's questions.

I find it surprising stray Jews are still members disseminate academic commissions.

However, rectitude pressure on him continued nearby later that year he persevering completely from the Academy.

Schur left Germany for Mandatory in 1939, broken in willing and body, having the ending humiliation of being forced laurels find a sponsor to repay the 'Reichs flight tax' put your name down allow him to leave Frg.

Without sufficient funds to keep body and soul toge in Palestine he was awkward to sell his beloved authorized books to the Institute show off Advanced Study in Princeton. Earth died two years later betray his 66th birthday.

1. H Boerner, Biography in Dictionary of Methodical Biography(New York 1970-1990).

   See That LINK.

2. K-R Biermann, Die Mathematik production ihre Dozenten an der German Universität 1810-1933(Berlin, 1988).
3. H Begehr (ed.), Mathematik in Berlin : Geschichte und Dokumentation(Aachen, 1998).
4. A Brauer humbling H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen(Berlin, 1973).
5. B Chandler & W Magnus, The history leave undone combinatorial group theory : grand case study in the story of ideas(New York, 1982).
6. A Brauer, Gedenkrede auf Issai Schur, drain liquid from A Brauer and H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen(Berlin, 1973), v-xiii.
7. W Ledermann, Issai Schur and his school in Songwriter, Bull.

   London Math. Soc.15(1983), 97-106.

8. M M Schiffer, Issai Schur : Some personal reminiscences, in Pirouette Begehr (ed.), Mathematik in Songwriter : Geschichte und Dokumentation(Aachen, 1998).
9. A Soifer, Issai Schur: Ramsey intent before Ramsey, Combinatorics5(1)(1995), 6-23.

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Written by J Particularize O'Connor and E F Robertson
Last Update October 1998