**Wilhelm Specht**'s parents were Benno Mafia Specht and Anna Naegele. Benno Specht, who was an engineering graduate, and his wife Anna both were born in Berlin into families with long traditions. Wilhelm was the eldest of his parents' three children. The family lived in Rastatt until Wilhelm was nine years old when his father Benno Specht got a job as director of a factory making trucks in Berlin so the family moved to that city. It was in Berlin that Wilhelm attended school. In Berlin he spent a happy childhood, free from financial worries despite the difficult times that Germany went through during World War I followed by years of economic hardship caused by hyperinflation. He was an excellent swimmer, whose achievements were reported in the press, he rowed, loved literature and loved music. He was an exceptionally talented pianist and loved to play Bach on the piano. He found mathematics really easy and he was able to tutor students studying in more advanced classes. He completed his school studies at the Fichte Gymnasium in Berlin in 1925.

Specht loved both music and mathematics, and he had a real talent for both. After he graduated from the Fichte Gymnasium he was still undecided which of these he should make his career. He briefly thought that music was right for him but, before the start of the 1925-26 academic year, he had changed his mind and he matriculated at the University of Munich in autumn 1925 beginning his studies of mathematics, physics and philosophy. 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. He was a confident young man who, even at this stage, was certain that he would make his career as a university professor. Not only did he believe in his own abilities but he also knew that, despite the desperate financial times Germany had gone through, his family would be able to support him financially. He spent the two years 1925-27, consisting of four semesters, in Munich where he attended lectures by, among others, Constantin Carathéodory, Oskar Perron and Arnold Sommerfeld.

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. He took physics courses given by Albert Einstein, by Max von Laue, and by Erwin Schrödinger and a chemistry course from Walter Nernst. Specht's main love, however, was mathematics where he was taught by Erhard Schmidt and lssai Schur. He asked whether Schur would be his thesis advisor and Schur was pleased to agree. 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. They discussed mathematics for hours, often continuing at night when they would telephone each other with ideas.

Specht submitted his doctoral thesis *Eine Verallgemeinerung der symmetrischen Gruppe* Ⓣ to the University of Berlin in April 1931. The thesis was examined by Schur, with Erhard Schmidt appointed as the second examiner, on 9 May 1932 and was he awarded his doctorate. He published a paper based on his thesis *Eine Verallgemeinerung der Permutationsgruppen* Ⓣ in 1933. Before this, in November 1931, he had been appointed as a research assistant in mathematics at the university. Also at this time he was an editorial assistant to Georg Feigl who had been managing editor of the reviewing journal *Jahrbuchs über die Fortschritte der Mathematik* Ⓣ since 1925. He continued to undertake these tasks until March 1934 while he sought a permanent university position. 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. This, of course, was a very difficult time in many mathematics departments due to the Nazi government.

On 30 January 1933 Hitler had came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course removing those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. Kurt Reidemeister had held a chair at Königsberg from 1927 but he had been forced to resign in 1933 because he was considered "politically unsound" by the Nazis. In fact he was dismissed even before Jewish colleagues. Nazi students at Königsberg created a protest at the Rector in January 1933 before Hitler came to power. Reidemeister devoted a lecturer to explaining why the students' behaviour was unacceptable and for this he was dismissed. 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. We note that Gabor Szegő, Richard Brauer and Werner Rogosinski, as Jews, had been forced to resign from Königsberg. Although the university atmosphere in Königsberg was difficult, in another way his period there was important to him in a personal way since he met Ursula Dannenberg; they later married.

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. In Breslau, Feigl became a colleague of Johann Radon who had held a chair there since 1928. 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. He had published a number of papers on the representation theory of groups, such as *Die irreduziblen Darstellungen der symmetrischen Gruppe* Ⓣ (1935), *Darstellungstheorie der Hyperoktaedergruppe* Ⓣ (1937), *Zur Darstellungstheorie der symmetrischen Gruppe* Ⓣ (1937), *Darstellungstheorie der affinen Gruppe* Ⓣ (1938), and *Darstellungstheorie der alternierenden Gruppe* Ⓣ (1938). 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. He had also published the papers *Ebene hyperbolische Geometrie * Ⓣ (1935), *Zur Theorie der Matrizen* Ⓣ (1936), and *Zur Theorie der Gruppen linearer Substitutionen* Ⓣ (1937). His first attempt to gain a position as docent was rejected by the Nazi Ministry of Education which considered Specht's political position unsatisfactory. However, he was successful at his second attempt and, in September 1938, he became a docent at the University of Breslau. This allowed him to marry Ursula Dannenberg and the marriage took place in September 1938.

The mathematics department at Breslau, headed by Feigl and Radon, had a pleasant atmosphere unlike that at Königsberg. 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). The whole department enjoyed a good social life in addition to profitable mathematical collaborations. We note that Tautz and Ostmann had both been students at Breslau having Radon as their thesis advisor and awarded their doctorates in 1930 and 1938 respectively. Kanold had also been a student at Breslau with both Feigl and Radon as advisors and was awarded his doctorate in 1941. 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. In fact Specht got to the stage of disliking the telephone since it would ring so frequently with Feigl looking for Specht's assistance. Later in life, he had no telephone in his home.

Specht was much appreciated by both his students and by his younger colleagues. He was always happy to talk to students and to help them with any difficulties that they were encountering. Younger colleagues appreciated him as an imaginative mathematician who showed them open problems and encouraged them to carry out their own research. 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. He continued to publish significant papers such as *Zur Theorie der Gruppen linearer Substitutionen* II Ⓣ (1940), *Wurzelabschätzungen bei algebraischen Gleichungen* Ⓣ (1940), *Zur Theorie der Matrizen* II Ⓣ (1940), *Klassifikation der halblinearen Transformationen* Ⓣ (1940), and *Darstellungstheorie der endlichen Gruppen* Ⓣ (1940).

This happy and productive time at Breslau came to an abrupt end in August 1940 when Specht was called up for military service. After a year's service in the Air Force, he did war work as a meteorologist in the Weather Service. Here he applied mathematics to weather problems and, for the rest of his teaching career, he would use examples from this experience. The war, however, saw tragedy for Specht. His younger brother, who was training to become a teacher of sport and biology, was killed in 1944. Specht's wife, who had served as a Red Cross nurse, was taken prisoner by the Russians and suffered unspeakable hardships before she was eventually able to return to her husband in 1954. When the war ended in 1945, the university in Breslau had been destroyed, his home had been destroyed, all his books were lost and his friends were scattered in different parts of the world. All Specht had left was a small suitcase with scientific papers, which he always carried with him throughout the war. Taken prisoner by the Americans, he was held in captivity in Bad Kreuznach until June 1945 when he was released and able to go to Herrsching, where his parents owned a small holiday home.

For two years Specht worked at an American airfield. Although he had no academic position, this job gave him ample free time to pursue his own research and, although he was not able to publish anything, he did collect together material which he was able to publish in the 1950s. Otto Haupt was head of mathematics at Erlangen and he was looking to built up his department. 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. He was, at the same time, given a temporary appointment as head of the newly established Department of Applied Mathematics. In March 1950 this temporary appointment was made permanent and he became an ordinary professor.

Specht was very successful in his two roles at Erlangen. For many years he was the only algebraist and the only applied mathematician. Of course his training had been very much as an algebraist but his wartime experiences had given him a practical basis in applied mathematics to add to the theoretical work from his undergraduate years. Also it is clear that Specht was always very willing and able to teach himself any topics that he needed to extend his knowledge. The research he had carried out before the war on matrices also gave him a basis for new ideas in applied mathematics. In particular he lectured on numerical methods and was keen to be at the forefront of using electronic computers.

At Erlangen, Specht supervised the doctoral studies of 19 students and you can see their names and thesis titles at THIS LINK.

In the 1950s, he published three books: *Gruppentheorie* Ⓣ (1956); *Elementare Beweise der Primzahlsätze* Ⓣ (1956); and *Algebraische Gleichungen mit reellen oder komplexen Koeffizienten* Ⓣ (1958). For extracts from reviews of the first and third of these see THIS LINK.

We have indicated above that Specht had two positions at Erlangen, one in algebra and the other in applied mathematics. This, together with staff shortages, led to him having an extremely high workload. In some semesters the courses he offered meant that he was teaching 22 hours per week. However, he took on duties in addition to his research, teaching and administration within mathematics. For example, he was Dean, vice-Dean and for five years Financial Officer of the faculty. He also played a large role in the design of the new building of the Mathematical Institute and he also pressed for the construction of the Computer Centre of the University of Erlangen.

The authors of [3] write:-

Specht was an editor ofWith an elegant ease he managed his extensive responsibilities, often mastering critical situations with his excellent Berliner humour. Always cheerful, he came to the institute not too early in the morning. Everything about him was elegant: his clothes, his writing, his reasoning, his car(always a little common Coupé). He remained, however, basically a humble person. Having to show superiority was for him downright embarrassing. Staff and students he met with paternal goodness, making necessary criticism at best with a fine humorous remark. Even students with excellent performances could learn from him much kindness and human warmth. ... His home was an oasis of tranquillity where he lived without a telephone, lovingly cared for by Mrs Specht. It was here that he undertook research. He worked as a hobby and never saw it as a workload, although he regularly sat at his desk until late into the night or even into the early hours of the morning.

*Zentralblatt für Mathematik*from 1962. He retired from his positions at Erlangen in the summer semester of 1972. He did not come to the Mathematics Institute after he retired and he spent most of his retirement back in his home town of Berlin. Here he did further work on his manuscripts, but apparently he had no intention of publishing anything further. In fact, because of his heavy teaching and administrative commitments, he published nothing after 1963. 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*Ⓣ. This paper looks at pairs of subgroups that are commensurable, that is the intersection of the two subgroups has intersection has finite index in both of them.

In 1977 Specht began to suffer neuralgia which increasingly restricted both his physical and mental capabilities. His physical problems eventually led to a fall in February 1985 from which he died. He was buried in Herrsching, surrounded by his relatives and closest friends. A Colloquium was held in the Mathematical Institute of the University of Erlangen-Nuremberg on 4 June 1985 in his memory.

Specht published 50 papers, mostly on group theory or polynomials. However, he did publish two papers on radiation which were the result of questions he was asked during the two years following the war when he did not have a university position. These papers were (with H A Bomke) *Der Einfluss von endlicher Präparat- und Ionisationskammergrösse auf die Dosismessung in unmittelbarer Nähe von Radiumpräparaten* Ⓣ (1950) and *Eine mathematische Frage zur Strahlentherapie* Ⓣ (1953). However, it was a consequence of his nature that he did not publish more. Following his death a variety of manuscripts were found among his papers of different degrees of completeness. He demanded perfection of his papers so often he would continue to revise them, perfecting the language, the terminology and the symbolism, for many years, even decades, before he submitted them for publication. Taking this approach, particularly when he was working on ideas in many different areas of algebra, number theory and analysis of polynomials, naturally meant that many of his ideas were never published. Papers found after his death show that, as well as topics already mentioned, he worked on non-euclidean geometry, optimal airplane landing strategies, theory of planning, biological balance and many others.

**Article by:** *J J O'Connor* and *E F Robertson*

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