Wilhelm Karl Joseph Killing

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Born: 10 May 1847 in Burbach (near Siegen), Westphalia, Germany
Died: 11 Feb 1923 in Münster, Germany

Wilhelm Killing began his university studies at Münster in 1865 but soon moved to Berlin were he was influenced by Kummer and Weierstrass. His doctorate, supervised by Weierstrass, was presented in 1872 and applied the theory of elementary divisors of a matrix to surfaces.

From 1868 to 1882 Killing taught at schools in Berlin and Brilon. At Weierstrass's recommendation he was appointed to a chair of mathematics at the Lyzeum Hosianum in Braunsberg. Killing spent 10 years in Braunsberg isolated mathematically but during this period he produced some of the most original mathematics ever produced.

He published work on
(i) non-euclidean geometry in n-dimensions (1883),
(ii)The extension of the concept of space (1886) which contains Killing's original classification of the simple Lie algebras,
(iii) Lie's transformation groups.

In 1892 he returned to Münster as professor of mathematics and he spent the rest of his life there submerged in teaching, administration and charitable work. At the age of 39 he entered the Order of Franciscans. Killing was a great patriot and collapse of social cohesion in Germany after 1918 caused him much pain in his last years.

Lie algebras were introduced by Lie in about 1870 in his work on differential equations. Killing introduced them independently with quite a different purpose since his interest was in non-euclidean geometry. The main tools in the classification of the simple Lie algebras are Cartan subalgebras and the Cartan matrix both first introduced by Killing. He also introduced the idea of a root system which now appears throughout much of the algebra of today.

Finally it is worth noting that Killing introduced the term 'characteristic equation' of a matrix.