Wilhelm Killing
| Wilhelm Karl Joseph Killing | |
|---|---|
 |
|
| Born | 10 May 1847 Burbach near Siegen, Siegen district, Arnsberg, Province of Westphalia |
| Died |
11 February 1923 (aged 75) Münster, Münster, Province of Westphalia |
| Residence | Germany |
| Citizenship | German |
| Fields | Mathematics |
| Doctoral advisor |
Karl Weierstrass Ernst Kummer |
| Known for |
Lie algebras, Lie groups, and non-Euclidean geometry |
| Notable awards | Lobachevsky Prize (1900) |
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
Killing studied at the University of Münster and later wrote his dissertation under Karl Weierstrass and Ernst Kummer at Berlin in 1872. He taught in gymnasia (secondary schools) from 1868 to 1872. He became a professor at the seminary college Collegium Hosianum in Braunsberg (now Braniewo). He took holy orders in order to take his teaching position. He became rector of the college and chair of the town council. As a professor and administrator Killing was widely liked and respected. Finally, in 1892 he became professor at the University of Münster. Killing and his spouse had entered the Third Order of Franciscans in 1886.
In 1878 Killing wrote on space forms in Crelle's Journal 86:72–83. Two years later he wrote on computations in hyperbolic geometry in the same journal. Recounting lectures of Weierstrass, he there introduced the hyperboloid model described by Weierstrass coordinates.
Killing invented Lie algebras independently of Sophus Lie around 1880. Killing's university library did not contain the Scandinavian journal in which Lie's article appeared. (Lie later was scornful of Killing, perhaps out of competitive spirit and claimed that all that was valid had already been proven by Lie and all that was invalid was added by Killing.) In fact Killing's work was less rigorous logically than Lie's, but Killing had much grander goals in terms of classification of groups, and made a number of unproven conjectures that turned out to be true. Because Killing's goals were so high, he was excessively modest about his own achievement.
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