**Herbert Seifert**'s father was a middle ranking official at court. He moved with his family from Bernstadt, where Herbert was born, to Bautzen which is another town in Saxony. Herbert attended the Knabenbürgerschule, the local primary school, in Bautzen. He then attended secondary school, the Oberrealschule, in Bautzen but there was little evidence of the brilliant mathematical career that he would achieve. that is not to say that he performed badly at school, just that he appeared simply to be a good pupil close to the top of the class.

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.. it was in 1927 that his whole life took a new turn when he attended a topology course by William Threlfall who was a Privatdozent at the technical university. 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. More than this, however, as well as world leaders in mathematics such as Hilbert, it had some of the leading topologists in the world. Hopf was a Privatdozent at Göttingen and he had just returned from an exciting year at Princeton with Aleksandrov. During Seifert's time at Göttingen, Aleksandrov was again a visitor and Seifert's visit only heightened his knowledge of, and passion for, topology. He returned to Dresden for the summer term of 1929 and his friendship with Threlfall was now so close that he lived in Threlfall's very fine house in Dresden. Seifert took his examinations to become a school teacher which he passed on 17 July 1930. He had already written a thesis on 3-dimensional closed manifolds and having submitted this he was awarded a doctorate a month later.

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. He chose to use the scholarship to allow him to go to Leipzig University where he was supervised by van der Waerden. 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. The book *Lectures on topology* was published in 1934. Threlfall wrote a preface which reads (see for example [1]):-

This textbook arose from a course which one of us gave to the other at the Technische Hochschule in Dresden. But soon the student contributed new ideas to such an extent and changed the presentation so fundamentally that it would be more justifiable to omit on the title page the name of the original author than his.

There is little doubt that Threlfall had honestly described Seifert's enormous contribution but Seifert was far too modest to allow such a preface. After some discussion, the two friends settled on the following compromise which appears in the preface of the published work:-

The first step towards writing this textbook was a course which one of us(Threlfall)taught at the Technische Hochschule in Dresden. But only part of the course was included in the book. The main part of its contents originated later from daily discussions between the two authors.

Puppe describes the merits of the text in [1]:-

The book gives an excellent account of what was known in topology at that time. It was superior in contents and in ways of presentation to other books in the field not only when it appeared but for a long time to come. it was translated into several languages, and generation of topologists in all countries of the world studied it. Even now, more than60years later, it is worth reading because of its lucid style and because, for some special problems, it is still the best source of information ...

For his habilitation Seifert submitted his paper *Continuous vector fields* and by the beginning of 1934 he was ready to become a university teacher. Turning down an offer of a post from the University of Greifswald, he became an extraordinary professor at the Technische Hochschule in Dresden before the end of 1934. This was of course a difficult time in German universities.

On 30 January 1933 Hitler 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 also to remove 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. Although he did not realise what was happening at first, this worked in a certain way to Seifert's advantage. The two professors of mathematics, Heinrich Liebmann and Artur Rosenthal, at Heidelberg University were both Jewish and were dismissed under the Nazi laws. This, although effectively correct, is not strictly true since Liebmann chose to take ill-health retirement, knowing what was coming.

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 fact the authorities, knowing that he was not supporting the cause in the way they wanted, delayed confirming his appointment even though he was in Heidelberg carrying out the job. In August 1936 Seifert attended the International Mathematical Congress in Oslo. While there he contracted poliomyelitis and was taken to hospital in Oslo. While in hospital he received the formal offer of his Heidelberg chair. 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.

From the time that Seifert took up his duties in Heidelberg until the start of World War II in 1939, he continued his collaboration was Threlfall. they exchanged letters and, as in previous years, spent holidays together working on mathematics. they published their second joint book in 1938 which was the monograph *Variational calculus in the large* which was a text on Morse theory. The book was accepted by Blaschke for the Hamburg monograph series but the two authors ran into problems with a Latin epigraph which they wished to put at the beginning. It was a quote from Kepler which reads in translation:-

Today it is very hard to write mathematical books.

Blaschke, who went along with the Nazi ideas, objected on the grounds that it looked like a political statement, and of course so it was meant to be. 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. This was a clever move which meant that he avoided what would almost certainly been far worse and he was able to continue with research into mathematics throughout the war. Seifert, on leave from Heidelberg University, became Head of a department in the Institut für Gasdynamik. He was successful in getting Threlfall appointed in his department.

Seifert, still able to do mathematical research, worked on differential equations and wrote a series of papers on the topic through the war years. At the end of the war the University of Heidelberg was closed down while the Allies ensured that the Nazis were removed from the staff. Seifert was one of only a very few professors accepted by the Allies and he returned to the university when it reopened in 1946. He now tried to continue his collaboration with Threlfall by pressing for him to be appointed to Heidelberg. Indeed he achieved his aim and after accepting an invitation from Marston Morse to spend the winter term of 1948-49 at Princeton he intended to return to Heidelberg and continue his collaboration with Threlfall. Sadly Threlfall died at age 60 before they could restart their joint work.

Not long after he returned to Heidelberg in 1949, Seifert married Katharina Korn. For three years he was the only ordinary professor of mathematics at Heidelberg but from 1952 the department rapidly expanded. Seifert retired in 1975 and enjoyed gardening and entertaining his former colleagues and students.

We have already mentioned some of Seifert's work. other important work related to knot invariants. 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. In a paper on this problem which he published in 1932, the results of which also appear in his 1934 book with Threlfall, he writes:-

... instead of investigating a complete system of topological invariants of3-dimensional manifolds, we search for a system of invariants for fibre preserving maps of fibred3-manifolds. This problem is completely solved in this paper.

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

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