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Felix Klein

Felix Christian Klein (German: [klaɪn]; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory. His 1872 Erlangen program classified geometries by their basic symmetry groups and was an influential synthesis of much of the mathematics of the time.

This article is about the German mathematician. For the French priest, see Félix Klein.

During his tenure at the University of Göttingen, Klein was able to turn it into a center for mathematical and scientific research through the establishment of new lectures, professorships, and institutes. His seminars covered most areas of mathematics then known as well as their applications. Klein also devoted considerable time to mathematical instruction, and promoted mathematics education reform at all grade levels in Germany and abroad. He became the first president of the International Commission on Mathematical Instruction in 1908 at the Fourth International Congress of Mathematicians in Rome.

The link between certain ideas of and invariant theory,

Riemann

and abstract algebra;

Number theory

;

Group theory

in more than 3 dimensions and differential equations, especially equations he invented, satisfied by elliptic modular functions and automorphic functions.

Geometry

Internet Archive

1886: Über hyperelliptische Sigmafunktionen. Erster Aufsatz, pp. 323–356, Bd. 27,

Mathematische Annalen

1888: Über hyperelliptische Sigmafunktionen. Zweiter Aufsatz, pp. 357–387, Math. Annalen, Bd. 32,

1890: (with ) Vorlesungen über die Theorie der elliptischen Modulfunktionen (2 volumes)[17] and 1892)

Robert Fricke

1894:

Über die hypergeometrische Funktion

1894: Über lineare Differentialgleichungen der 2. Ordnung

1894: Evanston Colloquium (1893) reported and published by Ziwet (New York, 1894)

[18]

Klein, Felix (1894), , New York, London: Macmillan and Co.

Lectures on Mathematics

[19]

1897: (with ) Theorie des Kreisels (later volumes: 1898, 1903, 1910)

Arnold Sommerfeld

Fricke, Robert; Klein, Felix (1897), (in German), Leipzig: B. G. Teubner, ISBN 978-1-4297-0551-6, JFM 28.0334.01[20] Zweiter Band. 1901.[20]

Vorlesungen über die Theorie der automorphen Functionen. Erster Band; Die gruppentheoretischen Grundlagen

1897: (Princeton address, New York)[21]

Mathematical Theory of the Top

1901: [22]

Gauss' wissenschaftliches Tagebuch, 1796—1814. Mit Anmerkungen von Felix Klein

Fricke, Robert; Klein, Felix (1912), (in German), Leipzig: B. G. Teubner., ISBN 978-1-4297-0552-3, JFM 32.0430.01

Vorlesungen über die Theorie der automorphen Functionen. Zweiter Band: Die funktionentheoretischen Ausführungen und die Anwendungen. 1. Lieferung: Engere Theorie der automorphen Funktionen

1908: Elementarmathematik vom höheren Standpunkte aus (Leipzig)

1926: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert (2 Bände), Julius Springer Verlag, Berlin & 1927. S. Felix Klein Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert

[23]

1928: Vorlesungen über nichteuklidische Geometrie, Grundlehren der mathematischen Wissenschaften, Springer Verlag

[24]

1933: Vorlesungen über die hypergeometrische Funktion, Grundlehren der mathematischen Wissenschaften, Springer Verlag

1887. in Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press: 965–71.

"The arithmetizing of mathematics"

1921. "Felix Klein gesammelte mathematische Abhandlungen" R. Fricke and A. Ostrowski (eds.) Berlin, Springer. 3 volumes. (online copy at )

GDZ

1890. ""

Nicht-Euklidische Geometrie

Dianalytic manifold

j-invariant

Line complex

Grünbaum–Rigby configuration

Homomorphism

Ping-pong lemma

Prime form

W-curve

Uniformization theorem

Felix Klein Protocols

List of things named after Felix Klein

Caroline Series, and David Wright Indra's Pearls: The Vision of Felix Klein. Cambridge Univ. Press. 2002.

David Mumford

(with Fritz König) Felix Klein. Teubner Verlag, Leipzig 1981.

Tobies, Renate

"Felix Klein, David Hilbert, and the Göttingen Mathematical Tradition", in Science in Germany: The Intersection of Institutional and Intellectual Issues, Kathryn Olesko, ed., Osiris, 5 (1989), 186–213.

Rowe, David

(1921) L'oeuvre mathematique de Klein in Scientia.

Federigo Enriques

at Project Gutenberg

Works by Felix Klein

at Internet Archive

Works by or about Felix Klein

at the Mathematics Genealogy Project

Felix Klein

(ed.). "Klein, Felix (1849–1925)". ScienceWorld.

Weisstein, Eric Wolfgang

Felix Klein, Klein Protokolle

Felix Klein (Encyclopædia Britannica)

F. Klein, "On the theory of line complexes of first and second order"

F. Klein, "On line geometry and metric geometry"

F. Klein, "On the transformation of the general second-degree equation in line coordinates into canonical coordinates"