**William Threlfall** was a German mathematician who worked on algebraic topology. With Herbert Seifert he wrote a standard work on topology.

- William was brought up in Dresden and he attended the Humanistischen Königlichen Gymnasium in Dresden-Neustadt, graduating with his Abitur in 1907.
- After graduating from the high school, Threlfall entered the University of Jena where his main interest was in chemistry but he also studied mathematics courses.
- In 1927 Threlfall submitted his habilitation thesis to the Technische Hochschule in Dresden and began lecturing there as a Privatdocent, particularly on his research topic of topology.
- Not only did Threlfall turn Seifert into an enthusiastic student of topology, but far more than that, they became firm friends and mathematical collaborators.
- We should note in passing the considerable age difference between the two with Threlfall being twenty years older than his friend and student.
- Threlfall's topology course, attended by Seifert as a student, became the basis of their famous book Lehrbuch der Topologie Ⓣ(Textbook of Topology) (1934).
- Threlfall was appointed as an assistant in the Institute of Engineering Mechanics of the Technical University of Dresden in 1929.
- Frankfurt had been severely affected by the anti-Jewish legislation brought in by the Nazis (this was one of the reasons that Siegel left) and when Threlfall arrived there were several leading mathematicians, such as Paul Epstein, Ernst Hellinger and Max Dehn, who were still in Frankfurt but not allowed to teach.
- Let us now look at some of Threlfall's publications.
- Much of Threlfall's best-known work was done in collaboration with Herbert Seifert.
- In 1938 Seifert and Threlfall published the book Variationsrechnung im grossen (Morsesche Theorie) Ⓣ(The calculus of variations in the large (Morse theory)).
- Threlfall continued to collaborate with Seifert by correspondence and they spent holidays together working on mathematics.
- It is remarkable that Threlfall and Seifert risked their positions by insisting that the epigram remain.
- During the war, both Seifert and Threlfall worked at the Institut für Gasdynamik in Braunschweig, a research centre attached to the German Air Force.
- While Threlfall undertook war work there, he was given leave of absence from Frankfurt where Wolfgang Franz took over his lecturing duties.
- Certainly Threlfall had his problems during these years.
- Threlfall and Seifert had made efforts to obtain jobs at the same university from the time that they were separated in 1935.
- Except for the time they spent at the Institut für Gasdynamik, they did not achieve this until 1946 when Threlfall, supported by Seifert, was appointed to a professorship at the University of Heidelberg on 4 May.
- Mathematicians from military establishments were sent there, including Threlfall and Seifert.
- Threlfall was at Mathematics Research Centre at Oberwolfach when he died and he was buried at Oberwolfach.
- However, in 1980 Seifert had Threlfall's body exhumed and transferred to Heidelberg.
- Threlfall's body is now buried in the Bergfriedhof in Heidelberg next to the graves of Seifert and his wife.
- Finally, let us mention some of Threlfall's last publications.
- After Threlfall's death, another joint paper with Seifert entitled Old and new results on knots (1950) was published.

Born 25 June 1888, Dresden, Germany. Died 4 April 1949, Oberwolfach, Schwarzwald, Germany.

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Origin Germany, Topology

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