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Hermann Minkowski (June 22, 1864 ‚Äď January 12, 1909) was a German mathematician of Polish Jewish 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.

Life and work

Hermann Minkowski was born in Aleksotasmarker, a suburb of Kaunasmarker, Lithuaniamarker, which was then part of the Russian Empiremarker, to a family of Lithuanian Jew and Polish Jewish 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. He also became a friend of another German mathematician, David Hilbert.

Minkowski taught at the universities of Bonnmarker, G√∂ttingenmarker, K√∂nigsbergmarker and Z√ľrichmarker. At the Eidgen√∂ssische Polytechnikummarker, today the ETH Zurichmarker, 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 Göttingenmarker and became one of the close colleagues of David Hilbert, whom he first met in Königsberg. Constantin Carathéodory was one of his students there.

Minkowski died suddenly of appendicitis in G√∂ttingenmarker. His brother, Oskar Minkowski (1858‚Äď1931), was a well-known physician and researcher.


By 1907 Minkowski realized that the special theory of relativity, introduced by Albert 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.


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

Seit meiner Studienzeit war mir Minkowski der beste und zuverl√§ssigste Freund, der an mir hing mit der ganzen ihm eigenen Tiefe und Treue. Unsere Wissenschaft, die uns das liebste war, hatte uns zusammengef√ľhrt; sie erschien uns wie ein bl√ľhender Garten. Gern suchten wir dort auch verborgene Pfade auf und entdeckten manche neue, uns sch√∂n d√ľnkende 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 besa√ü. J√§h 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 years Minkowski was my best, most dependable friend who supported me with all the depth and loyalty that was so characteristic of him. Our science, which we loved above all else, brought us together; it seemed to us a garden full of flowers. In it, we enjoyed looking for hidden pathways and discovered many a new perspective that appealed to our sense of beauty, and when one of us showed it to the other and we marvelled over it together, our joy was complete. He was for me a rare gift from heaven and I must be grateful to have possessed that gift for so long. Now death has suddenly torn him from our midst. However , what death cannot take away is his noble image in our hearts and the knowledge that his spirit in us continue to be active.

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

References in popular culture


Relativity papers

Mathematical papers

See also


  1. Jewish Mathematicians at

External links

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