# Hermann Minkowski

**Hermann Minkowski** (June 22, 1864 - January 12, 1909) was a German mathematician who developed the geometrical theory of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.

Hermann Minkowski was born in Russia, and educated in Germany at the Universities of Berlin and Königsberg, where he achieved his doctorate in 1885. Minkowski taught at the universities of Bonn, Königsberg and Zurich. In Zurich, he was one of Einstein's teachers.

Minkowski explored the arithmetic of quadratic forms, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space of n dimensions. In 1896, he presented his "*geometry of numbers*", a geometrical method that solved problems in number theory.

In 1902, he joined the Mathematics Department of Goettingen and became one of the close colleagues of David Hilbert.

By 1907 Minkowski realised that the special theory of relativity, introducted by Einstein in 1905 and based on previous work of Lorentz and Poincaré, could be best understood in a non-euclidean space, since known as "Minkowski space", in which the time and space are not separated entities but intermingled in a four dimensional space-time, and in which the Lorentz Geometry of special relativity can be nicely represented. This nice representation certainly helped Einstein's quest for general relativity. The beginning part of his address delivered at the 80th *Assembly of German Natural Scientists and Physicians* (September 21, 1908) is now famous:

*The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.*