Oswald Teichmüller

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Paul Julius Oswald Teichmüller (born June 18, 1913 in Nordhausen , † probably September 1943 in the Dnepr region , Soviet Union) was a German mathematician who dealt with function theory and algebra .

Life

Teichmüller was the son of a weaver with his own workshop, who had been away from the First World War for a long time in his childhood. He first grew up in Sankt Andreasberg in the Harz Mountains. The father died in 1925 when Teichmüller was twelve years old. Teichmüller then moved to Nordhausen, where he lived with an aunt and graduated from secondary school in 1931 with the Abitur. Teichmüller studied mathematics at the University of Göttingen from the summer semester of 1931, listening to Richard Courant (analysis), Hermann Weyl , Otto Neugebauer , Gustav Herglotz and Edmund Landau , among others .

At the university he was more of an outsider because of his background from a humble background. He was active there from the beginning with the National Socialist student body. In July 1931 he joined the NSDAP and shortly afterwards the SA . As head of the mathematics section of the National Socialist student body, he was primarily responsible for the boycott of the world-famous Jewish mathematician Edmund Landau , at a time when Jewish professors were being forced out of the universities due to the new laws passed by the National Socialists (exceptions, however, concerned participants in the First World War, for example ). In the summer semester of 1933, Landau had initially given his analysis lectures, which were unpopular with many students because of their high degree of abstraction, to his assistant Weber, but wanted to give them himself again in the winter semester. With his boycott, Teichmüller ensured that his lecture hall remained empty on November 2nd - the students crowded into the vestibule. As spokesman for the boycott, Teichmüller personally explained the reasons to Landau and even gave Landau a written explanation when asked. In it he wrote that he held Landau in high esteem and had nothing against the fact that he held lectures for advanced students, but that, as a Jew, he held lectures in differential and integral calculus for beginners. Landau was deeply affected and submitted his resignation, enclosing Teichmüller's letter (without giving his name). He was then retired the following year. Another goal of Teichmüller and his like-minded fellows was to combat what he called the Courant clique at the University of Göttingen and to set up Nazi-minded successors for mathematicians like Hermann Weyl or Richard Courant who were eventually expelled from Göttingen . 1934 but not a favorite of them candidate has been nominated, but Helmut Hasse , who is a DC circuit as the German Mathematical Association resisted and was classified as a political opponent of Teichmüller.

In addition to his political activities, he devoted himself intensively to mathematics. In 1933/34 he attended lectures given by Courant's pupil Franz Rellich , from which his dissertation, Operators in the Wax Room , emerged, which was accepted by Helmut Hasse (doctorate in June 1935 summa cum laude ). He also got on well with Hasse mathematically, was very active in his seminar on algebra, from which Teichmüller's several research papers emerged, and became Hasse's assistant in Göttingen (as was Ernst Witt , who was also active in the National Socialist). In one of the published essays he introduced the Teichmüller characters named after him today.

For his habilitation, however, Teichmüller turned from algebra to function theory after he had heard lectures on the theory of value distribution by Rolf Nevanlinna with Egon Ullrich in the summer of 1936 and even with Nevanlinna himself, who had come to Göttingen for a year in the winter semester of 1936. In 1937 he moved to Berlin to join Ludwig Bieberbach , the main representative of German mathematics and specialist in function theory. Teichmüller studied the then current work on quasi- conformal mapping by Herbert Grötzsch and Lars Ahlfors and completed his habilitation in March 1938 with the work Investigations on conformal and quasi-conformal mapping at Bieberbach in Berlin. He also published much of his work in the journal Deutsche Mathematik , which was edited by Bieberbach. Initially, however, he did not have a position in Berlin, but was financed by a state scholarship. It was not until the end of 1939, when he had already been drafted as a soldier, that he became an unpaid lecturer, and in 1940 he became a paid lecturer at the Humboldt University in Berlin . Politically, too, he was quite independent of Bieberbach and suffered from the increasingly obvious contrast between the Berliners and the Göttingen mathematicians. For example, he did not follow Bieberbach in his private theories about the division of mathematics itself into "Jewish" (according to Bieberbach, for example, abstract algebra) and "Aryan" areas.

Around the turn of the year 1938/39 he created his work Extremal quasi-conformal images and quadratic differentials , with which he founded the Teichmüller theory, the theory of modular spaces of Riemannian surfaces (so-called Teichmüller spaces ), whereby he made substantial use of the theory of quasi-conformal images. It predominantly had the character of a program script and contained hardly any evidence, which was made up for in some later works. He also did not give up on algebra and published, for example, a work on the axiom of choice in algebra in 1939 . He also continued to work on value distribution theory.

From July 1939 he was a soldier, including during the invasion of Norway in 1940 . In the military, where he only made it to private, he continued to work intensively in mathematics in his free time. In 1941 he was back in Berlin, where he worked as a cryptanalyst in the encryption department of the Wehrmacht High Command . He also gave lectures at the university in 1942/43. After the Battle of Stalingrad , he volunteered for the Eastern Front and in May 1943 joined the 355th Infantry Division (led by Lieutenant General Dietrich Kraiss ), which took part in the last major German offensive near Kursk . In June / July 1943 he attended a non-commissioned officer course in the Crimea and was then briefly on home leave in August. His unit had since been encircled and worn out in the fighting for Kharkov . In September Teichmüller tried to join the remnants of his division in the Poltava area and has been missing since then - most likely he had died at the front shortly after his return. His division was disbanded in November due to the heavy losses.

Another pioneering work by him appeared posthumously in 1944, in which he introduced not only real analytical, but also complex analytical structures in Teichmüller rooms, which, like his work from 1939, was only sketchy (Changeable Riemann surfaces) .

The theory of the modular spaces of Riemann surfaces goes back to Bernhard Riemann , who found that compact Riemann surfaces are parameterized by 3g-3 complex parameters. The problem was to prove the real or complex analytical structure of this parameter space (module space). Teichmüller used an assignment of extremal quasi-conformal images to holomorphic quadratic differentials defined on the Riemann surfaces, a construction with a differential geometric background. After the war, his theory was strictly justified by Lars Ahlfors and Lipman Bers in particular . From the 1980s onwards, the theory gained great importance in string theory .

Quote

"[...] the ingenious, but fanatical Nazi with actions against Landau and Courant ingloriously emerged Oswald Teichmüller"

- Friedrich Ludwig Bauer : Deciphered secrets

Fonts

literature

  • Erhard Scholz : Teichmüller, Paul Julius Oswald in the Dictionary of Scientific Biography (English; online version from 2008)
  • William Abikoff: Oswald Teichmüller , The Mathematical Intelligencer 8 No. 3, September 1986, pp. 8-17 (English)
  • Norbert Schappacher , Erhard Scholz (ed.): Oswald Teichmüller - Leben und Werk , DMV 94 annual report, February 19, 1992, pp. 1–39 ( online ; with picture)
  • Munibur Rahman Chowdhury: Landau and Teichmüller , The Mathematical Intelligencer 17 No. 2, June 1995, pp. 12-14 (English; Years ago column by Jeremy Gray )
  • Norbert Schappacher, Erhard Scholz: How to write about Teichmüller , The Mathematical Intelligencer 18 No. 1, March 1996, pp. 5–6 (English; in Letters to the editor ; response to criticism of Schappacher, Scholz (ed.): Oswald Teichmüller - Life and Work , 1992)
  • Thomas Huckle: Jewish mathematicians in the "Third Reich" ( PDF file, 270 kB)

Web links

Individual evidence

  1. ↑ Printed in the appendix by Schappacher, Scholz (Ed.): Oswald Teichmüller - Leben und Werk , 1992, pp. 28–30. In a letter from 1948, Teichmüller's mother said that she would have been appalled by the naivety of her son who thereby jeopardized his career, see Schappacher, Scholz (ed.): Oswald Teichmüller - Leben und Werk , 1992, p. 5 .
  2. ↑ cf. Schappacher, Scholz (Ed.): Oswald Teichmüller - Leben und Werk , 1992, p. 9
  3. ^ Oswald Teichmüller: Extremal quasi-conformal images and quadratic differentials , treatises of the Prussian Academy of Sciences: Mathematisch-Naturwissenschaftliche Klasse, 22, 1939, pp. 1–197
  4. ↑ in particular determination of the extremal quasi-conformal images in closed, oriented Riemann surfaces , treatises of the Prussian Academy of Sciences: Mathematisch-Naturwissenschaftliche Klasse, 4, 1943 (42 pages)
  5. ↑ Oswald Teichmüller: Does the algebraist need the axiom of choice? , Deutsche Mathematik 4, 1939, pp. 567-577
  6. ↑ Oswald Teichmüller: Assumptions and theorems about the value distribution of fractional functions of finite order , Deutsche Mathematik 4, 1939, pp. 161–190, as well as simple examples for the theory of value distribution , Deutsche Mathematik 7, 1944, pp. 360–368
  7. ^ Grenadier Regiment 867th This was disbanded on August 28th and set up again on September 9th. The division was reorganized in May 1943 and initially belonged to the 8th Army of Army Group South, the remainder were attached to the 1st Panzer Army from October. On November 2, the division was disbanded.
  8. ↑ According to a later letter from his mother, he was supposed to report to the rest of his unit on September 11th
  9. ↑ Oswald Teichmüller: Veränderliche Riemannsche surfaces , Deutsche Mathematik 7, 1944, pp. 344–359
personal data
SURNAME Teichmüller, Oswald
ALTERNATIVE NAMES Teichmüller, Paul Julius Oswald (full name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH June 18, 1913
PLACE OF BIRTH Nordhausen
DATE OF DEATH September 1943
Place of death Dnepr region , Soviet Union