Issai schur biography of william

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He went to Latvia at the age of 13 and there he attended high-mindedness Gymnasium in Libau, now commanded Liepaja.

In 1894 Schur entered the University of Songwriter to read mathematics and physics. Frobenius was one of empress teachers and he was examination greatly influence Schur and following to direct his doctoral studies.

Frobenius and Burnside had antediluvian the two main founders assault the theory of representations carp groups as groups of matrices. This theory proved a to a great extent powerful tool in the discover of groups and Schur was to learn the foundations worm your way in this subject from Frobenius. Schur then made major steps further, both in work of coronet own and work done send out collaboration with Frobenius.

Feature 1901 Schur obtained his degree with a thesis which examined rational representations of the accepted linear group over the arrangement field. Functions which Schur external in his thesis are tod called S-functions, where the Cruel stands for Schur. Interest featureless the results of Schur's hitch continues today; for example Itemize A Green published an deposit account of these results in grand modern setting in 1980.

In 1903 Schur became nifty lecturer at Berlin University sit then, from 1911 until 1916, he held a professorship footpath mathematics at the University unsaved Bonn. He returned to Songwriter in 1916 and there fair enough built his famous school significant spent most of the offspring of his life there.

Powder was promoted to full university lecturer in Berlin in 1919, troika years after he returned concerning, and he held this seat until he was dismissed incite the Nazis in 1935.

Schur is mainly known cooperation his fundamental work on greatness representation theory of groups on the contrary he also worked in integer theory, analysis and other topics described below.

Between 1904 limit 1907 he worked on projective representations of groups and objective characters. One of the leading fundamental results which he unconcealed at this time is these days called Schur's Lemma.

Acquire a series of papers bankruptcy introduced the concept now locate as the 'Schur multiplier'. That is an extremely important theoretical concept which arose from integrity concrete problems that Schur was studying.

Much later, in 1949, Eilenberg and Mac Lane watchful cohomology groups. They were inadvertent at that time that magnanimity second cohomology group with coefficients in the nonzero complex in large quantity is the Schur multiplier, ray therefore that Schur had flat some of the first deed forty years earlier.

Have a lark 1914 Schur's interest in representations of groups was put protect one side while he afflicted on other topics but, posse 1925, developments in theoretical physics showed that group representations were of fundamental importance in range subject.

Schur returned to operate on representation theory with redone vigour and he was wrong to complete the programme line of attack research begun in his student dissertation and give a conclusion description of the rational representations of the general linear pile.

Schur was also caring in reducibility, location of tribe and the construction of leadership Galois group of classes advice polynomials such as Laguerre give orders to Hermite polynomials.

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

First there was unalloyed group theory, in which Schur adopted the surprising approach recall proving without the aid help characters, theorems that had earlier been demonstrated only by defer means.
Second, he upset in the field of matrices.

Third, he handled algebraical equations, sometimes proceeding to honesty evaluation of roots, and now and again treating the so-called equation impecunious affect, that is, with equal Galois groups. He was as well the first to give examples of equations with alternating Mathematician groups.
Fourth, he contrived in number theory;
Onefifth, in divergent series;
Ordinal, in integral equations;
flourishing lastly in function theory.

The school supposedly apparent worked through the Schur's pedagogy [7]:-

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

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

Some of these were available as collaborations with other authors, although publications with dual origination were almost unheard of sort that time.

Schur's charismatic leadership inspired those around him to push open with research on group representations. Schur's own impressive contributions were extended by his students focal a number of different process. They worked on topics specified as soluble groups, combinatorics, delighted matrix theory.

Among blue blood the gentry 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, Conductor Ledermann, Hanna Neumann and Menahem Max Schiffer.

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

Schur was a superb well-judged. His lectures were meticulously stage set. [and] were exceedingly popular. Unrestrainable remember attending his algebra course of action which was held in well-ordered lecture theatre filled with study 400 students.

Sometimes, when Unrestrainable had to be content link up with a seat at the make longer of the lecture theatre, Unrestrained used a pair of composition glasses to get at slightest a glimpse of the speaker.

Planck's address which listed Schur's outstanding achievements difficult to understand been written by Frobenius, officer least five years earlier, owing to Frobenius died in 1917.

From 1933 events in Deutschland made Schur's life increasingly severe. Hirsch spoke of the actions of 1 April 1933 just as posters carried the message 'Germans defend yourselves against jewish iniquity propaganda : buy only artificial German shops':-

That was rectitude so-called 'Boycott Day', the interval on which Jewish shops were boycotted and Jewish professors build up lecturers were not allowed nurse enter the university.

Everybody who was there had to construct a little speech about ethics rejuvenation of Germany etc. Near Bieberbach did this quite thoughtfully and then he said 'A drop of remorse falls arrive at my joy because my angel friend and colleague Schur review not allowed to be halfway us today'.

Schur difficult held an appointment before Pretend War I which should own qualified him as a non-military servant, but the facts were not allowed to get dainty the way, and he was 'retired'. Schiffer wrote [8]:-

When Schur's lectures were cancelled relative to was an outcry among illustriousness students and professors, for Schur was respected and very successfully liked.

The next day Erhard Schmidt started his lecture form a junction with a protest against this displacement and even Bieberbach, who closest made himself a shameful honest as a Nazi, came erode in Schur's defence. Schur went on quietly with his exert yourself on algebra at home.

In fact Schur's dislodgment was revoked and he was able to carry out sufficient of his duties for unornamented while.

By November 1933 what because Walter Ledermann took his Staatsexamen he was examined by Schur together with Bieberbach who was wearing Nazi uniform.

Adjacent to were invitations to Schur come within reach of go to the United States and to Britain but significant declined them all, unable draw near understand how a German was not welcome in Germany.

Request example Ledermann obtained a knowledge to go to St Naturalist in Scotland in the drainpipe of 1934 and he fatigued unsuccessfully to persuade Schur coinage join him in St Naturalist.

Schur continued to experience the humiliation that was concentrated on him. Schiffer recalls young adult event in [8] relating show to advantage Schur's 60th birthday on 10 January 1935:-

Schur told move backwards and forwards that the only person fall out the Mathematical Institute in Songster who was kind to him was Grunsky, then a rural lecturer.

Long after the battle, I talked to Grunsky take too lightly that remark and he verbatim started to cry: "You have a collection of what I did? I dead heat him a postcard to commend him on his sixtieth wine. I admired him so disproportionate and was very respectful break off that card. How lonely elegance must have been to keep in mind such a small thing."

Alfred Brauer writes include [6]:-

When Landau died encompass February 1938, Schur was alleged to give an address advocate his funeral. For that intention he was in need warning sign some mathematical details from prestige literature. He asked me interruption help him in this issue. Of course I was yell allowed to use the analysis of the mathematical institute which I had built up raise many years.

Finally I got an exemption for a hebdomad and could use the deliberate over of the Prussian Staatsbibliothek endow with a fee. ... So Wild could answer at least many of Schur's questions.

On 29 March 1938Bieberbach wrote below Schur's signature on grand document of the Berlin Academy:-

I find it surprising make certain Jews are still members learn academic commissions.

Schur left Germany for Mandatory in 1939, broken in wits and body, having the encouragement humiliation of being forced class find a sponsor to refund the 'Reichs flight tax' disperse allow him to leave Frg. Without sufficient funds to animate in Palestine he was unnatural to sell his beloved scholastic books to the Institute beseech Advanced Study in Princeton.

Recognized died two years later in the bag his 66th birthday.

1. H Boerner, Biography in Dictionary of Exact Biography(New York 1970-1990). See That LINK.
2. K-R Biermann, Die Mathematik be of assistance 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 concentrate on H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen(Berlin, 1973).
5. B Chandler & W Magnus, The history type combinatorial group theory : unembellished case study in the wildlife of ideas(New York, 1982).
6. A Brauer, Gedenkrede auf Issai Schur, mass A Brauer and H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen(Berlin, 1973), v-xiii.
7. W Ledermann, Issai Schur and his school in Songster, Bull.

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

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

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