**Herbert Seifert** was a German mathematician who made important contributions to topology and knot theory.

- Herbert attended the local primary school for boys, in Bautzen.
- Seifert took his Abitur in early 1926 at the age of eighteen and, leaving school, he entered the Technische Hochschule in Dresden to study mathematics and physics..
- 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 Seifert being twenty years younger than his friend and teacher.
- It was common practice for German students to spend time at a number of different universities and Seifert spent part of the session 1928-29 at Göttingen University.
- At this time Göttingen was the leading mathematics centre of the whole world so it was a good choice for Seifert.
- During Seifert's time at Göttingen, Aleksandrov was again a visitor and Seifert's visit only heightened his knowledge of, and passion for, topology.
- Seifert took his examinations to become a school teacher which he passed on 17 July 1930.
- At this stage Seifert was awarded a scholarship by the Technische Hochschule in Dresden to allow him to continue to study for a doctorate of philosophy.
- Although this was the official position, in fact Seifert returned to Dresden every weekend and he worked with Threlfall, so certainly Threlfall was an unofficial supervisor.
- Seifert and Threlfall also spent vacations together working on mathematics but of course it was to Leipzig that Seifert submitted his dissertation Topology of 3-dimensional fibred spaces on 1 February 1932 and he was awarded his doctorate of philosophy after his oral examination on 3 March.
- In this paper Seifert introduced the term "fibre space" for the first time, although its definition was not quite the same as the one used today.
- Much of Seifert and Threlfall's collaboration at this time was working on making a textbook out of Threlfall's lecture notes on topology.
- There is little doubt that Threlfall had honestly described Seifert's enormous contribution but Seifert was far too modest to allow such a preface.
- For his habilitation Seifert submitted his paper Continuous vector fields and by the beginning of 1934 he was ready to become a university teacher.
- Although he did not realise what was happening at first, this worked in a certain way to Seifert's advantage.
- Seifert was offered Liebmann's in November 1935 (again according to Threlfall this is not strictly true as he claims that Seifert was ordered to take the chair).
- Certainly Seifert was no supporter of the Nazis and it was a situation with which he was very unhappy.
- In August 1936 Seifert attended the International Mathematical Congress in Oslo.
- Strangely though, by the time he returned to Heidelberg the chair had been transferred from mathematics to another subject and Seifert spent the war years as an extraordinary professor although he was given the rights of an ordinary professor.
- It is remarkable that Threlfall and Seifert risked their positions by insisting that the epigram remain.
- they won their case, the epigram appeared in the book when published, and Blaschke wrote a letter to Seifert expressing fury that the quote had not been deleted.
- When war broke out Seifert volunteered for war work with the Institut für Gasdynamik which was a research centre attached to the German Air Force.
- Seifert, on leave from Heidelberg University, became Head of a department in the Institut für Gasdynamik.
- Seifert, still able to do mathematical research, worked on differential equations and wrote a series of papers on the topic through the war years.
- Seifert was one of only a very few professors accepted by the Allies and he returned to the university when it reopened in 1946.
- Seifert retired in 1975 and enjoyed gardening and entertaining his former colleagues and students.
- We have already mentioned some of Seifert's work.
- In particular, in 1934 he published results, using surfaces today called Seifert surfaces, which he used to calculate homological knot invariants.
- Another topic which Seifert worked on was the homeomorphism problem for 3-dimensional closed manifolds.

Born 27 May 1907, Bernstadt, Saxony, Germany. Died 1 October 1996, Heidelberg, Germany.

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Origin Germany, Topology

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