Hermann Minkowski

[ming-kawf-skee, -kof-]

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

Early life and education

Hermann Minkowski was born in Aleksotas (at the time a suburb of Kaunas, Lithuania, Russian Empire) to a family of Jewish and Polish descent. He was educated in Germany at the Albertina University of Königsberg, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences for his manuscript on the theory of quadratic forms.

Work and research

Minkowski taught at the universities of Bonn, Göttingen, Königsberg and Zürich. At the Eidgenössische Polytechnikum, today the ETH 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 Göttingen and became one of the close colleagues of David Hilbert, whom he first met in Königsberg. Constantin Carathéodory was one of his students there.


By 1907 Minkowski realized that the special theory of relativity, introduced by Einstein in 1905 and based on previous work of Lorentz and Poincaré, could be best understood in a four dimensional space, since known as "Minkowski spacetime", 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. 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.

Death and honours

Minkowski died suddenly of appendicitis in Göttingen. He was the brother of Oskar Minkowski (1858–1931), a well-known physician and researcher.


David Hilbert's obituary illustrates the deep friendship between the two mathematicians:

Seit meiner Studienzeit war mir Minkowski der beste und zuverlässigste Freund, der an mir hing mit der ganzen ihm eigenen Tiefe und Treue. Unsere Wissenschaft, die uns das liebste war, hatte uns zusammengeführt; sie erschien uns wie ein blühender Garten. Gern suchten wir dort auch verborgene Pfade auf und entdeckten manche neue, uns schön dünkende Aussicht, und wenn der eine dem andern sie zeigte und wir sie gemeinsam bewunderten, war unsere Freude vollkommen. Er war mir ein Geschenk des Himmels, wie es nur selten jemand zuteil wird, und ich muss dankbar sein, dass ich es so lange besaß. Jäh hat ihn der Tod von unserer Seite gerissen. Was uns aber der Tod nicht nehmen kann, das ist sein edles Bild in unserem Herzen und das Bewusstsein, dass sein Geist in uns fortwirkt.


Since my student time Minkowski was the best and most reliable friend who stuck to me with all the fidelity and deepness of his character. Our science that had brought us together and that was at our hearts appeared us like a flourishing garden. We loved to detect concealed trails and discovered many prospects which seemed us beautiful. When one of us showed it to the other and when we admired it jointly our enjoyment was complete. He was a present from heaven to me, as it happens to come only rarely and I can be thankful that I was able to own it for such a long time. Suddenly, death has taken him away from our side. But what death can not take is his noble image in our hearts and the awareness that his spirit is acting in us.

The asteroid 12493 Minkowski and M-matrices are named in his honour.

See also


References in popular culture


External links

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