**Oswald Teichmüller**'s main contribution was in the area of geometric function theory.

- Although Oswald was born in Nordhausen im Harz, his parent's home was in the small village of Sankt Andreasberg, famed as a winter sports resort, about 25 km north of Nordhausen.
- At some stage during the war Paul Teichmüller was wounded but he did not return to Sankt Andreasberg until the war ended in 1918.
- After one semester studying at Göttingen, Teichmüller joined the NSDAP (Nationalsozialistiche Deutsche Arbeiter Partei) commonly called the Nazi Party.
- It is rather difficult to see whether Teichmüller joined the Nazis because he already shared the far right views of the Party, or whether he rapidly became indoctrinated after joining.
- On 2 November 1933 Teichmüller led the student boycott of Edmund Landau's lectures.
- Teichmüller, as the leader of the boycott, went to Landau's office and discussed what had happened.
- Landau requested that Teichmüller put his views in writing and he did so.
- We note that Teichmüller had some success in converting others to the Nazi beliefs.
- However, despite Hasse being in a very different area of mathematics from Teichmüller, it was Hasse who Teichmüller chose as his thesis supervisor.
- It would have made more sense from a mathematical perspective for Teichmüller to have asked Gustav Herglotz to be his supervisor but Herglotz had no specific connection with the Nazi Party while Hasse did.
- Teichmüller submitted his thesis on 10 June 1935 and he was examined by Hasse, Herglotz and the physicist Robert Pohl on 26 June 1935.
- After his doctoral examination in June 1935, Hasse requested that the university authorities appoint Teichmüller as an assistant in the Department.
- A call for him to come here is in the offing; we cannot approve of it." His views remained the same over the years that he worked in the Göttingen department headed by Hasse, yet Teichmüller chose him as his supervisor and was influenced mathematically by him to work on algebraic problems (considered by some Nazis to be Jewish mathematics).
- In October 1936 Teichmüller began to work towards habilitating in Berlin with Ludwig Bieberbach (also an outstanding mathematician and staunch Nazi sympathiser).
- Teichmüller's habilitation thesis Untersuchungen über konforme und quasikonforme Abbildungen Ⓣ(Studies of conformal and quasiconformal mappings) was not influenced by Hasse, but rather was sparked by lectures that he had attended by Rolf Nevanlinna on complex analysis.
- It is interesting to note that in his report on Teichmüller's thesis Bieberbach chose to put in a critical comment about his earlier algebraic papers influenced by Hasse.
- In Berlin, Teichmüller had someone in Bieberbach who shared his extreme Nazi views.
- The two, however, were also exceptional mathematicians and Teichmüller's two years in Berlin were golden years in terms of his research.
- Teichmüller's main contribution is in the area of geometric function theory.
- Teichmüller's Habilitationsschrift: "Untersuchungen über konforme und quasikonforme Abbildungen" Ⓣ(Studies of conformal and quasiconformal mappings), which appeared in 1938, and the next paper: "Ungleichungen zwischen den Koeffizienten schlichter Funktionen" Ⓣ(Inequalities between the coefficients of simple functions) can be considered as the beginning of his great contributions to function theory, which culminated in his masterpiece: "Extremale quasikonforme Abbildungen und quadratische Differentiale" Ⓣ(Extremal quasiconformal mappings and quadratic differentials), 1939.
- In this paper and its complement: "Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen" Ⓣ(Determination of extremal quasiconformal mappings with closed oriented Riemann surfaces) (1943), Teichmüller laid the basis of what is now known as the theory of Teichmüller spaces.
- Teichmüller was drafted on 18 July 1939 as Germany prepared for World War II.
- Bieberbach requested that Teichmüller be released from military duties to lecture at the university and indeed Teichmüller was able to teach at the university beginning at the start of session 1942-43 while continuing his cryptographic work.
- Teichmüller answered this call and, giving up his cryptographic position in Berlin, joined the forces attempting to recover from the Stalingrad defeat.
- Teichmüller's unit took part in the offensive which began on 5 July 1943.
- Teichmüller was given leave of absence to return home.
- Most of Teichmüller's unit was wiped out but in early September he tried to rejoin them.

Born 18 June 1913, Nordhausen im Harz, Germany. Died 11 September 1943, Dnieper region, USSR.

View full biography at MacTutor

Origin Germany

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