In 1923 Köthe enrolled in the
University of Graz. He started studying
chemistry, but switched to mathematics a year later after meeting the
philosopher Alfred Kastil. In 1927 he submitted his thesis
Beiträge zu Finslers Grundlegung der Mengenlehre ("Contributions to Finsler's foundations of set theory") and was awarded a doctorate. After spending a year in
Zürich working with
Paul Finsler, Köthe received a fellowship to visit the
University of Göttingen, where he attended the lectures of
Emmy Noether and
Bartel van der Waerden on the emerging subject of abstract algebra. He began working in
ring theory and in 1930 published the
Köthe conjecture stating that a sum of two left
nil ideals in an arbitrary
ring is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of
Otto Toeplitz in
Bonn University in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward. Köthe's
Habilitationsschrift,
Schiefkörper unendlichen Ranges über dem Zentrum ("Skew fields of infinite rank over the center"), was accepted in 1931. He became Privatdozent at
University of Münster under
Heinrich Behnke. During
World War II he was involved in coding work. In 1946 he was appointed the director of the Mathematics Institute at the
University of Mainz and he served as a dean (1948–1950) and a rector of the university (1954–1956). In 1957 he became the founding director of the Institute for Applied Mathematics at the
University of Heidelberg and served as a rector of the university (1960–1961). Köthe's best known work has been in the theory of
topological vector spaces. In 1960, volume 1 of his seminal monograph
Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of
lattices. == Awards and honors ==