Felix Klein
,
in full
Christian Felix Klein
(born
April 25, 1849
, Dusseldorf, Prussia [Germany]?died
June 22, 1925
, Gottingen, Germany), German mathematician whose unified view 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 developments.
As a student at the University of Bonn (Ph.D., 1868), Klein worked closely with the physicist and geometer
Julius Plucker
(1801?68). After Plucker’s death, he worked with the geometer Alfred Clebsch (1833?72), who headed the mathematics department at the
University of Gottingen
. On Clebsch’s recommendation, Klein was appointed professor of mathematics at the University of Erlangen (1872?75), where he set forth the views contained in his
Erlanger Programm
. These ideas reflected his close collaboration with the Norwegian mathematician
Sophus Lie
, whom he met in Berlin in 1869. Before the outbreak of the
Franco-German War
in July 1870, they were together in Paris developing their early ideas on the role of transformation groups in geometry and on the theory of
differential equations
.
Klein later taught at the Institute of Technology in Munich (1875?80) and then at the Universities of Leipzig (1880?86) and Gottingen (1886?1913). From 1874 he was the editor of
Mathematische Annalen
(“Annals of Mathematics”), one of the world’s leading mathematics journals, and from 1895 he supervised the great
Encyklopadie der mathematischen Wissenschaften mit Einschluss iher Anwendungen
(“Encyclopedia of Pure and Applied Mathematics”). His works on elementary mathematics, including
Elementarmathematik vom hoheren Standpunkte aus
(1908; “Elementary Mathematics from an Advanced Standpoint”), reached a wide public. His technical papers were collected in
Gesammelte Mathematische Abhandlungen
, 3 vol., (1921?23; “Collected Mathematical Treatises”).
Beyond his own work Klein made his greatest impact on mathematics as the principal architect of the modern community of mathematicians at Gottingen, which emerged as one of the world’s leading research centres under Klein and
David Hilbert
(1862?1943) during the period from 1900 to 1914. After Klein’s retirement
Richard Courant
(1888?1972) gradually assumed Klein’s role as the organizational leader of this still vibrant community.