Klein was born in
Düsseldorf, to
Prussian parents; his father was a Prussian government official stationed in the
Rhine Province. He attended the
Gymnasium in Düsseldorf, then studied mathematics and physics at the
University of Bonn, 1865-1866, intending to become a physicist. At that time,
Julius Plücker held Bonn's chair of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest was geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868,
Plücker died in 1868, leaving his book on the foundations of
line geometry incomplete. Klein was the obvious person to complete the second part of Plücker's
Neue Geometrie des Raumes, and thus became acquainted with
Alfred Clebsch, who had moved to Göttingen in 1868. Klein visited Clebsch the following year, along with visits to
Berlin and
Paris. In July 1870, at the outbreak of the
Franco-Prussian War, he was in Paris and had to leave the country. For a short time, he served as a medical orderly in the
Prussian army before being appointed lecturer at Göttingen in early 1871.
Erlangen appointed Klein professor in 1872, when he was only 23. In this, he was strongly supported by Clebsch, who regarded him as likely to become the leading mathematician of his day. Klein did not build a school at Erlangen where there were few students, and so he was pleased to be offered a chair at
Munich's Technische Hochschule in 1875. There he and Brill taught advanced courses to many excellent students, e.g.,
Adolf Hurwitz, Walther von Dyck, Karl Rohn, Carl Runge, Max Planck, Luigi Bianchi, and
Gregorio Ricci-Curbastro.
In 1875 Klein married Anne Hegel, the granddaughter of the philosopher
Georg Wilhelm Friedrich Hegel.
After five years at the Technische Hochschule, Klein was appointed to a chair of
geometry at
Leipzig. There his colleagues included
Walther von Dyck, Rohn,
Eduard Study and
Friedrich Engel. Klein's years at Leipzig, 1880 to 1886, fundamentally changed his life. In 1882, his health collapsed; in 1883-1884, he was plagued by depression.
Klein's career as a research mathematician essentially over, Klein accepted a chair at the
University of Göttingen in 1886. From then until his 1913 retirement, he sought to re-establish Göttingen as the world's leading mathematics research center. Yet he never managed to transfer from Leipzig to Göttingen his own role as the leader of a school of
geometry. At Göttingen, he taught a variety of courses, mainly on the interface between mathematics and physics, such as
mechanics and
potential theory.
The research center Klein established at Göttingen served as a model for the best such centers throughout the world. He introduced weekly discussion meetings, and created a mathematical reading room and library. In 1895, Klein hired
David Hilbert away from
Königsberg; this appointment proved fateful, because Hilbert continued Göttingen's glory until his own retirement in 1932.
Under Klein's editorship,
Mathematische Annalen became one of the very best mathematics journals in the world. Founded by Clebsch, only under Klein's management did it first rival then surpass
Crelle's Journal based out of the
University of Berlin. Klein set up a small team of editors who met regularly, making democratic decisions. The journal specialized in
complex analysis, algebraic geometry, and
invariant theory (at least until Hilbert killed the subject). It also provided an important outlet for
real analysis and the new
group theory.
Thanks in part to Klein's efforts, Göttingen began admitting women in 1893. He supervised the first Ph.D. thesis in mathematics written at Göttingen by a woman; she was an English student of
Arthur Cayley's, whom Klein admired.
Around 1900, Klein began to take an interest in mathematical instruction in schools. In 1905, he played a decisive role in formulating a plan recommending that the rudiments of differential and integral calculus and the function concept be taught in secondary schools. This recommendation was gradually implemented in many countries around the world. In 1908, Klein was elected chairman of the International Commission on Mathematical Instruction at the Rome International Mathematical Congress. Under his guidance, the German branch of the Commission published many volumes on the teaching of mathematics at all levels in Germany.
The
London Mathematical Society awarded Klein its
De Morgan Medal in 1893. He was elected a member of the
Royal Society in 1885, and was awarded its
Copley medal in 1912. He retired the following year due to ill health, but continued to teach mathematics at his home for some years more.
Klein died in Göttingen in 1925.
