Gottfried Maria Hugo Köthe (25 December 1905 – 30 April 1989) was an Austrian mathematician working in abstract algebra and functional analysis.

He started studying chemistry, but switched to mathematics a year later after meeting the philosopher Alfred Kastil.

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.

Köthe's Habilitationsschrift, Schiefkörper unendlichen Ranges über dem Zentrum ("Skew fields of infinite rank over the center"), was accepted in 1931.

In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969).