Karl Rudolf Fueter (30 June 1880 – 9 August 1950) was a Swiss mathematician, known for his work on number theory.

After a year of graduate study of mathematics in Basel, Fueter began study in 1899 at the University of Göttingen and completed his Promotion in 1903 with dissertation Der Klassenkörper der quadratischen Körper und die komplexe Multiplikation under David Hilbert.

He was called to positions as professor ordinarius in 1908 at Basel, in 1913 at the Technische Hochschule Karlsruhe, and in 1916 at the University of Zurich.

He gave plenary lectures at the International Congress of Mathematicians in 1932 at Zurich (Idealtheorie und Funktionentheorie) and in 1936 at Oslo (Die Theorie der regulären Funktionen einer Quaternionenvariablen).

During WWII he was a colonel of artillery in the Swiss army, an outspoken opponent of German National Socialism, and an advocate for freedom of the press.