Felix Klein

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Klein, Felix


Born Apr. 25, 1849, in Düsseldorf; died June 22, 1925, in Göttingen. German mathematician. Corresponding member of the German Academy of Sciences in Berlin (1913).

In 1865, Klein enrolled in the University of Bonn, where he studied under J. Plücker. In 1868 he received a Ph.D. degree from the University of Bonn. From 1872 he was a professor of mathematics at Erlangen, from 1875 at the Munich Technische Hochschule, and from 1880 at the University of Leipzig. In 1886 he moved to Göttingen, where he remained for the rest of his life.

Klein’s principal works were devoted to non-Euclidean geometry, the theory of continuous groups, the theory of algebraic equations, the theory of elliptic functions, and the theory of automorphic functions. He expounded his ideas in the work A Comparative Review of Recent Researches in Geometry (Vergleichende Betrachtungen über neuere geometrische Forschungen; 1872), known as the Erlangen program. He strove to discover intrinsic links between the separate branches of mathematics and between mathematics on the one hand and physics and technology on the other. Klein, together with the German scientist A. Sommerfeld, wrote a four-volume work entitled Theory of the Gyroscope (1910–23). Klein was founder and co-editor of the Encyclopedia of the Mathematical Sciences (Encyklopädie der mathematischen Wissenschaften). For almost 40 years (from 1876) he was editor in chief of the journal Math-ematische Annalen. He was very much occupied with problems of mathematical education: before World War I he organized an international commission on the reorganization of the teaching of mathematics.


Gesammelte mathematische Abhandlungen, vols. 1–3. Berlin, 1921–23.
In Russian translation:
Vysshaia geometriia. Moscow-Leningrad, 1939.
Elementarnaia matematika s tochki zreniia vysshei, vol. 1, 3rd ed., vol. 2, 2nd ed. Moscow-Leningrad, 1934–35.
Neevklidova geometriia. Moscow-Leningrad, 1936.
Lektsii o razvitii matematiki v 19 stoletii, part 1. Moscow-Leningrad, 1937.