Mathematician:Felix Christian Klein

Mathematician
German mathematician best known for his work establishing the connections between geometry and group theory.

Architect of the Erlangen program, which classifies geometries according to their symmetry groups.

Noted for the Klein bottle and the Klein $4$-group.

Not to be confused with.

Nationality
German

History

 * Born: 25 April 1849 in Düsseldorf, Prussia (now Germany)
 * 1875: Married Anne Hegel, the granddaughter of the philosopher
 * Died: 22 June 1925 in Göttingen, Germany

Theorems and Definitions

 * Erlangen Program


 * Klein Bottle
 * Klein $4$-Group
 * Klein Quartic
 * Kleinian Group
 * Klein Geometry
 * Klein Quadric
 * Klein's $j$-Invariant


 * Beltrami-Klein Model (with ) (also known as the Cayley-Klein Model, with, the Klein Model or the Klein Disk Model)

Publications

 * 1868: Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form
 * 1872:
 * 1882: Ueber Riemann's Theorie der Algebraischen Functionen und ihre Integrale
 * 1884: Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5ten Grade (English translation by : Lectures on the Icosahedron; and the Solution of Equations of the Fifth Degree, 1914)
 * 1890, 1892: Vorlesungen über die Theorie der elliptischen Modulfunktionen (2 volumes) (with (2 volumes: 1890 and 1892)
 * 1893: Evanston Colloquium (before the Congress of Mathematics, reported and published by Alexander Ziwet, 1894)
 * 1894: Über die hypergeometrische Funktion
 * 1894: Über lineare Differentialgleichungen der 2. Ordnung
 * 1895: ) (English translation by and : Famous Problems of Elementary Geometry, 1897)
 * 1897 - 1910: Theorie des Kreisels (with )
 * 1897 - 1912: Vorlesungen über die Theorie der automorphen Funktionen (2 volumes: the second volume was published in three parts) (with )
 * 1897: Mathematical Theory of the Top (Princeton address, New York)
 * 1908:
 * 1925:
 * 1939: (translated by  and  from )


 * The Felix Klein Protocols

Notable Quotes

 *  said, "God is a geometer." changed this to, "God is an arithmetician." Then came  and fashioned the memorable expression, "God created the natural numbers, and all the rest is the work of man."
 * -- Quoted as an epigraph to the preface to

Also known as
Felix Christian Klein is also sometimes reported as Christian Felix Klein.

... and while we're about it

 * A mathematician named Klein
 * Thought the Möbius band was divine.
 * He said, "If you glue
 * The edges of two,
 * You get a weird bottle like mine."

(Quoted by in one of his Mathematical Games columns in Scientific American, c. )