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Biography

The parents of Klein are Prussian; his/her father was civil servant in the Prussian Rhineland. Felix is pupil of the college of Düsseldorf, then, in 1865, studies the Mathématiques and the Physique with the Université of Bonn in the intention to become Physicien. At this time, Julius Plücker is named with the pulpit of mathematics and experimental physics in Bonn. Felix becomes its assistant in 1866, at one moment when Plücker is interested of close with the geometry. Under the direction of Plücker, it receives its doctorate in 1868.

Plücker dies the same year, leaving behind him an unfinished book, Neue Geometrie of Raumes , on the projective line geometry (see Coordonnées of Plücker). Klein being the person best placed to supplement the second part, it contacts Alfred Clebsch. In July 1870, it is in Paris. The Franco-German war obliges it to turn over to Germany; it serves a time in the Prussia army before being named reader with Göttingen in 1871.

In 1872, at the 23 years age, Klein becomes professor with Erlangen thanks to the providential assistance of Clebsch, which sees in him one of the futures larger mathematicians of its time. Not enough students being in Erlangen, it obtains with its relief a pulpit with the Technische Hochschule of Munich in 1875. There, he teaches mathematics with Hurwitz, Carl Runge, max Planck, Luigi Bianchi and Gregorio Ricci-Curbastro. It is as into 1875 as Klein marries Anne Hegel, the grand-daughter of the philosopher Hegel.

Five years later, Klein obtains a pulpit of geometry to the Université of Leipzig. These years in Leipzig are remembered by a degradation of its health. From 1883 to 1884, he suffers from depression.

Its career of mathematician being behind him, it accepts a pulpit with the Université of Göttingen in 1886; it will remain there until its retirement in 1913. He teaches various courses, the majority at the border of mathematics and physics, like courses of Mécanique or Théorie of the potential. It wished to restore Göttingen like the first mathematical research world center. What did not occur. However, the research center that Klein establishes was used as model: it introduces the weekly meetings, and creates a library of mathematics.

Under the direction of Klein, Mathematische Annalen becomes one of the most known newspapers of mathematics of the world. Been based by Clebsch, this newspaper competes then exceeds the Journal of Crelle . Klein makes democratic decisions, with assent of a small team of editors whom it chose. The newspaper specializes in the Analyze complexes and the algebraic Géométrie. It also publishes on the real Analyze and the theory incipient from the groups.

Grace partly to the efforts of Klein, the women are allowed in Göttingen starting from 1893. It supervises itself the first thesis in mathematics written in Göttingen by a woman, an English coed of Arthur Cayley.

Starting from 1900, Klein is interested in the training of mathematics in the schools. In 1905, it recommends to teach the rudiments of the Integral calculus and differential as of the secondary. This recommendation is gradually applied in many countries throughout the world. It engaged also in the Didactique mathematics.

Klein is elected member of the Royal Society in 1885. The mathematical Société of London decrees to him the Medal of Morgan in 1893. He is prize winner of the Médaille Copley in 1912. He takes his retirement the year following, because of a bad health, but continuous to give private lessons of mathematics during a few years.

Work

The Program of Erlangen

Sophus Lie presents to Klein the concept of groups, which he also studied at the sides of Camille Jordan. The first important discoveries of Klein go back to 1870. In collaboration with Dregs, he studies the fundamental properties of the asymptotic lines on the Surface of Kummer. They come from there to be interested in invariant curves under a group of projective transformations.

In 1871, then in Göttingen, Klein made of important discovered in geometry. It publishes two articles, of which One the So-called Non-Euclidian Geometry , placing the Euclidean geometries and not euclidennes on the same plan, and putting a term at the controversy around the nonEuclidean Géométrie.

The synthesis of Klein of the geometry like study of the invariants under a group of transformations given, known under the name of Programme of Erlangen (1872) deeply influenced the evolution of the geometry and mathematics as a whole. This program was the inaugural course of Klein as professor with Erlangen. This program proposes a unified vision of the geometry. Klein describes in details how the central properties of a given geometry result in the action of a group of transformations.

Today, this vision became so banal in the spirit of the mathematicians who it is difficult to judge their importance, to appreciate its innovation and to include/understand the opposition to which it had to face.

Analyzes

August 1st

See too

External bond

Biography

Simple: Felix Klein

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