**Gottfried Maria Hugo Köthe** was an Austrian mathematician who worked in abstract algebra, functional analysis and topological vector spaces.

- Gottfried attended the Volksschule in Graz before moving to the Realgymnasium where his favourite subjects were philosophy and chemistry.
- Since Köthe became an outstanding mathematician one would assume that he studied mathematics at university but this was certainly not the subject he intended to study.
- After the award of his doctorate, Köthe went to Zürich where he spent the winter term of 1927-28 working with Paul Finsler, who had just been appointed to the university, as well as with Rudolf Fueter and Andreas Speiser.
- After spending the year in Zürich, Köthe was awarded a fellowship by the German Research Foundation which funded a visit to the University of Göttingen.
- This visit proved a major influence on Köthe since, after attending courses by Emmy Noether on Non-Commutative Algebra and by Bartel van der Waerden on Algebraic Numbers, his interests turned to algebra.
- While on this visit to Göttingen, Köthe attended the International Congress of Mathematicians held in Bologna in September 1928 as did Emmy Noether.
- Köthe gave a lecture at the Congress describing the results he had obtained in the structure theory of rings.
- Emmy Noether wrote a letter of recommendation for Köthe to Otto Toeplitz who appointed him as his assistant at Bonn for the year 1929-30.
- Köthe had now turned to research in ring theory and, in 1930, published papers such as: Über maximale nilpotente Unterringe und Nilringe Ⓣ(About maximum nilpotent subrings and nil rings); Abstrakte Theorie nichtkommutativer Ringe mit einer Anwendung auf die Darstellungstheorie kontinuierlicher Gruppen Ⓣ(Abstract theory of noncommutative rings with an application to the representation theory of continuous groups); and Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollständig reduzibel ist Ⓣ(The structure of rings whose residue class ring is completely reducible to the radical).
- The year that Köthe spent as Toeplitz's assistant proved important since it produced another change in the direction of Köthe's research and led him to the area for which he is best known today, namely topological vector spaces.
- Although Köthe only spent a year in Bonn with Toeplitz, they continued joint work.
- After spending the year in Bonn, Köthe went to Münster in 1930 as an assistant to Heinrich Behnke and Lugwig Neder at the Westfälische Wilhelms University of Münster.
- Although Köthe was moving more towards research in functional analysis, he still produced an habilitation thesis which was purely algebraic entitled Schiefkörper unendlichen Ranges über dem Zentrum Ⓣ(Skew fields of infinite rank over the centre) and published in Mathematische Annalen.
- Köthe's research now had become almost exclusively in functional analysis.
- On 1 October 1957 Köthe left Mainz to take up the Chair of Applied Mathematics at the University of Heidelberg and, at the same time, he became Director of the newly established Institute for Applied Mathematics.
- On 1 May 1965 Köthe left Heidelberg to fill the Chair of Applied Mathematics at the Johann Wolfgang Goethe-Universität at Frankfurt.
- The second volume of the treatise still had not appeared and Köthe was keen to find the time to produce it so he decided to retire on 31 March 1971 although he could have remained in post.
- Let us hope that Professor Köthe will find some spare time from his duties as the Rector of the University of Heidelberg in order to finish in a reasonably finite length of time the treatise on topological vector spaces, which he has so successfully begun.
- In addition to the honours mentioned above, Köthe became Commandeur dans l'Ordre des Palmes Académiques in 1961, was awarded the Gauss Medal by the Brunswick Academy of Sciences in 1963, and was elected to the German Academy of Scientists Leopoldina at Halle in 1968.

Born 25 December 1905, Graz, Austria. Died 30 April 1989, Frankfurt, Germany.

View full biography at MacTutor

Origin Austria, Topology

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