KLEIN, FELIX

born April 25, 1849, Dsseldorf, Prussia died June 22, 1925, Gttingen, Ger. in full Christian Felix Klein German mathematician whose synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm, profoundly influenced mathematical development. He became professor of mathematics at the University of Erlangen (187275), where his inaugural lecture set forth the views contained in the Erlanger Programm, derived from his admiration for the unifying possibilities of group theory. He collaborated with Sophus Lie of Norway and was first to systematize Lie's contact transformations. Shortly before 1916, new geometries were discovered that do not fit Klein's Programm, but his synthesis is still important and useful for those geometries that do conform. Klein was professor at the universities of Leipzig (188086) and Gttingen (18861913). He was editor of the Mathematische Annalen of Gttingen from 1872 and in 1895 founded the great mathematical Encyklopdie, which he continued to supervise until his death. His works on elementary mathematics, including Elementar mathematik von hheren standpunkte aus (1908; Elementary Mathematics from an Advanced Standpoint), reached a wide public. Of his more technical writings, Vorlesungen ber das Ikosaeder (1884; Lectures on the Icosahedron) and Vorlesungen ber die Theorie der automorphen Functionen, 2 vol. (1897, 1902; Lectures on the Theory of Automorphous Functions) are considered outstanding.