**Wilhelm Specht** was a German mathematician who in worked group theory and representation theory.

- It was in Berlin that Wilhelm attended school.
- Specht loved both music and mathematics, and he had a real talent for both.
- One of the reasons that he started his university career in Munich was that his grandparents lived there and Specht was able to board with them.
- As was typical of German students at this time, Specht did not spend his whole university career at a single university.
- In 1927 he returned to Berlin where he continued his studies at the Friedrich-Wilhelm University.
- At this time Berlin had many world-leading mathematicians and physicists on the staff and Specht benefited greatly from these impressive professors.
- Specht's main love, however, was mathematics where he was taught by Erhard Schmidt and lssai Schur.
- Specht then began to mix with the group of mathematicians at Berlin including Alfred Brauer, Richard Brauer, Kurt Hirsch, Bernhard Neumann, Robert Remak, Hans Rohrbach, Hanna von Caemmerer, and John von Neumann.
- Specht's closest friend was Bernhard Neumann, with whom he often played a board game invented by the chess champion Eduard Lasker.
- Specht submitted his doctoral thesis Eine Verallgemeinerung der symmetrischen Gruppe Ⓣ(A generalization of the symmetric group) to the University of Berlin in April 1931.
- With a strong reference for Schur, in April 1934 Specht was appointed as an assistant to Gabor Szegő in the Mathematics and Physics Department of the University of Königsberg.
- A successor had been appointed but the mathematics department in Königsberg was a place where tensions were running high before Specht was appointed.
- Certainly Specht did not improve the situation by making anti-Nazi comments.
- For example, when the picture of Gauss hanging in the departmental library was replaced by a picture of Hitler, Specht said, "Why do we need to?
- He's not a mathematician." When he went to Königsberg Specht had been intending to habilitate there but after Gabor Szegő, Richard Brauer and Werner Rogosinski were forced to leave, he realised that there was no way he could succeed in Königsberg.
- When he had been at Berlin, Specht had assisted Georg Feigl in his editorial duties.
- Feigl had been extraordinary professor at Berlin when Specht left Berlin for Königsberg but Feigl had been appointed to the Chair of Mathematics at the University of Breslau in 1935 where he was head of the Department.
- Feigl and Radon were keen to have Specht join them in Breslau, and he took up a position there in March 1936.
- One year later, in the spring of 1937, Specht habilitated at Breslau.
- It is in the first of these papers, published in 1935, that the representation that today is known as a 'Specht module' appears.
- Over a field of characteristic 0, the Specht modules provide a complete set of irreducible representations of symmetric groups.
- His expertise on the representation theory of groups had been exactly what he needed to solve a problem posed by a physicist and its solution formed the basis for Specht's habilitation thesis.
- There were also a number of more junior colleagues who worked with Specht at Breslau over the following years including Hans-Joachim Kanold, Georg Tautz (1901-1983) and Hans-Heinrich Ostmann (1913-1959).
- Specht would meet with his colleague Tautz at Radon's home for a musical evening where Specht played the piano, Radon played the violin and Tautz sang tenor.
- Feigl appreciated Specht both as a mathematical collaborator and as a table tennis partner.
- Specht got to the stage of disliking the telephone since it would ring so frequently with Feigl looking for Specht's assistance.
- Specht was much appreciated by both his students and by his younger colleagues.
- Specht's home became a popular meeting place where students or colleagues came to discuss mathematics, to chat or just to warm up a little when their own supply of fuel had run out.
- This happy and productive time at Breslau came to an abrupt end in August 1940 when Specht was called up for military service.
- The war, however, saw tragedy for Specht.
- All Specht had left was a small suitcase with scientific papers, which he always carried with him throughout the war.
- For two years Specht worked at an American airfield.
- He spoke to van der Waerden asking if he knew of promising people to appoint and, without hesitation, van der Waerden strongly recommended Specht.
- Haupt and Specht agreed to meet following a meeting of the Bavarian Academy of Sciences in Munich and Haupt was so impressed that he immediately asked him to join the department of mathematics at Erlangen.
- Specht was appointed as an assistant at Erlangen in December 1947 and, after another habilitation, became a docent there in the summer of 1948.
- Specht was very successful in his two roles at Erlangen.
- Also it is clear that Specht was always very willing and able to teach himself any topics that he needed to extend his knowledge.
- We have indicated above that Specht had two positions at Erlangen, one in algebra and the other in applied mathematics.
- His home was an oasis of tranquillity where he lived without a telephone, lovingly cared for by Mrs Specht.
- Specht was an editor of Zentralblatt für Mathematik from 1962.
- However in 1987, two years after Specht's death, Hermann Heineken completed and submitted for publication their joint paper Gruppen mit endlicher Komponentenzahl fastgleicher Untergruppen Ⓣ(Groups with a finite number of components almost equal subgroups).
- In 1977 Specht began to suffer neuralgia which increasingly restricted both his physical and mental capabilities.
- Specht published 50 papers, mostly on group theory or polynomials.

Born 22 September 1907, Rastatt, Baden, Germany. Died 19 February 1985, Herrsching, Bavaria, Germany.

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Group Theory, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive