Kurt Reidemeister was examined as a student by Landau and became an assistant of Hecke. His doctoral thesis was on algebraic number theory, the particular problem having been suggested by Hecke, and the resulting publication Relativklassenzahl gewisser relativ- quadratischer Zahlköper appeared in 1921. In  it is noted that:-
Of all of the 71 papers listed in Reidemeister's obituary by Artzy (), this is the only one which deals with number theory. It rarely happens that a highly productive mathematician deserts the field of his PhD thesis so consistently later on.
Immediately he had written his doctoral thesis, Reidemeister became interested in differential geometry. It was Blaschke who came up with the particular problems in differential geometry on which Reidemeister began to work.
On Hahn's recommendation, Reidemeister was appointed as associate professor of geometry at the University of Vienna in 1923. Here he became a colleague of Wirtinger who interested Reidemeister in knot theory. In particular Wirtinger showed Reidemeister how to compute the fundamental group of a knot from its projection. This method, originally due to Wirtinger, appears in work of Artin which was published in 1925.
While in Vienna, Reidemeister came across the Tractatus by Wittgenstein. Led by Reidemeister, the group of mathematicians at Vienna spent a year studying the deep ideas on logic and mathematics in this work.
In 1927 Reidemeister was offered a chair in Königsberg which he accepted. In 1930 the German Mathematical Congress met in Königsberg and Reidemeister organised the first international conference on the philosophy of mathematics to be a part of the larger Congress. He was forced to leave his chair in Königsberg in 1933 by the Nazis, who he strongly opposed, who classed him as 'politically unsound'. After being temporarily suspended from his chair he was later appointed to Hensel's chair in Marburg at what was considered a smaller and less prestigious university.
Reidemeister worked on the foundations of geometry and he wrote an important book on knot theory Knoten und Gruppen (1926). He established a geometry and topology based on group theory without the concept of a limit. In particular he wrote an important book Einführung in die kombinatorische Topologie (1932) on combinatorial topology. As is remarked in :-
Although Reidemeister ... was, above all, a geometer, his book on 'combinatorial topology' contains hardly any drawings. Abstraction and rigor were very much in fashion.
Reidemeister had an important influence on group theory, partly through his work on knots and groups, partly through his influence on Schreier. Talking of this influence on group theory, Chandler and Magnus write in :-
Reidemeister was ... essentially a geometer. His influence on combinatorial group theory is largely that of a pioneer. His ideas were stimulating and had, at least in some cases, a long-lasting effect.
Reidemeister's other interests included the philosophy and the foundations of mathematics. He also wrote about poets and was a poet himself. He translated Mallarmé.
Article by: J J O'Connor and E F Robertson