Felix Klein

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Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.



Klein was born in Düsseldorf, to Prussian parents; his father was a Prussian government official's secretary stationed in the Rhine Province. He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker held Bonn's chair of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest was geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868.

Plücker died in 1868, leaving his book on the foundations of line geometry incomplete. Klein was the obvious person to complete the second part of Plücker's Neue Geometrie des Raumes, and thus became acquainted with Alfred Clebsch, who had moved to Göttingen in 1868. Klein visited Clebsch the following year, along with visits to Berlin and Paris. In July 1870, at the outbreak of the Franco-Prussian War, he was in Paris and had to leave the country. For a short time, he served as a medical orderly in the Prussian army before being appointed lecturer at Göttingen in early 1871.

Erlangen appointed Klein professor in 1872, when he was only 23. In this, he was strongly supported by Clebsch, who regarded him as likely to become the leading mathematician of his day. Klein did not build a school at Erlangen where there were few students, and so he was pleased to be offered a chair at Munich's Technische Hochschule in 1875. There he and Alexander von Brill taught advanced courses to many excellent students, e.g., Adolf Hurwitz, Walther von Dyck, Karl Rohn, Carl Runge, Max Planck, Luigi Bianchi, and Gregorio Ricci-Curbastro.

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