Hermann Minkowski

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Hermann Minkowski
De Raum zeit Minkowski Bild.jpg
Born (1864-06-22)22 June 1864
Aleksota, Kingdom of Poland, Russian Empire (now Kaunas, Lithuania)
Died 12 January 1909(1909-01-12) (aged 44)
Göttingen, German Empire
Nationality German
Fields Mathematician
Institutions University of Göttingen and ETH Zurich
Alma mater Albertina University of Königsberg
Doctoral advisor Ferdinand von Lindemann
Doctoral students Constantin Carathéodory
Louis Kollros
Dénes Kőnig
Known for Minkowski space
Minkowski diagram

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

Minkowski is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein's special theory of relativity (1905), presented algebraically by Einstein, could also be understood geometrically as a theory of four-dimensional space-time. Einstein himself at first viewed Minkowski's treatment as a mere mathematical trick, before eventually realizing that a geometrical view of space-time would be necessary in order to complete his own later work in general relativity (1915).[1]


Hermann Minkowski was born in Aleksotas, a village in Kaunas Governorate - the Russian Empire had partitioned territory of the former Grand Duchy of Lithuania, which had been part of the Polish-Lithuanian Commonwealth. His older brother Oskar (1858) and younger brother Tuvia (1868) were both born in Aleksotas.[2][3] In different sources Minkowski is described variously as German,[4][5] Lithuanian[6] or Lithuanian-German,[7] or Russian.[8] His parents were Lewin Boruch Minkowski, a merchant who subsidized the building of The Choral synagogue in Kovno,[9][10][11] and Rachel Taubmann, both of Jewish descent.[12] In 1872 to escape persecution in Russia the family moved to Königsberg,[13] where the father became involved in rag export and later in manufacture of mechanical clockwork tin toys (he operated his firm Lewin Minkowski & Son with his eldest son Max).[14][15][16]

Life and work[edit]

Minkowski was educated in Germany at the Albertina University of Königsberg, where he earned his doctorate in 1885 under the direction of Ferdinand von Lindemann. In 1883, while still a student at Königsberg, 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 renowned mathematician, David Hilbert. His brother, Oskar Minkowski (1858–1931), was a well-known physician and researcher.

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 a close colleague of David Hilbert, whom he first met at university in Königsberg. Constantin Carathéodory was one of his students there.

He is also the creator of the Minkowski Sausage and the Minkowski cover of a curve.[17]

Minkowski died suddenly of appendicitis in Göttingen on 12 January 1909. He had married in 1897 and was the father of two daughters; the electrical engineer and inventor Reinhold Rudenberg was his son-in-law.


By 1907 Minkowski realized that the special theory of relativity, introduced by Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four dimensional space, since known as the "Minkowski spacetime", in which 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 effectively represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 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 of Minkowski illustrates the deep friendship between the two mathematicians (translated):

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 marveled 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 continues to be active in us.

The asteroid 12493 Minkowski and M-matrices are named in Minkowski's honor.


Relativity papers
  • Minkowski, Hermann (1908/9). "Raum und Zeit". Jahresbericht der Deutschen Mathematiker-Vereinigung: 75–88. 
Mathematical papers (posthumous)
  • Minkowski, Hermann (1910). Geometrie der Zahlen. Leipzig-Berlin: R. G. Teubner. MR 0249269. [18]
  • Minkowski, Hermann (1911). Gesammelte Abhandlungen 2 vols. Leipzig-Berlin: R. G. Teubner. [19] Reprinted in one volume New York, Chelsea 1967

See also[edit]


  1. ^ http://www.fisica.net/relatividade/the_non_euclidean_style_of_minkowskian_relativity_by_scott_walter.pdf (Einstein also had need of a third theory and technique, elaborated by his former mathematics professor, Hermann Minkowski (1864–1909), although he did not recognize this for several years.)
  2. ^ Oskar Minkowski (1858–1931)
  3. ^ The Jewish genealogy site JewishGen.org (Lithuania database, registration required) contains the birth record in the Kovno rabbinical books of Herman's younger brother Tuvia in 1868 to Boruch Yakovlevich Minkovsky and his wife Rakhil Isaakovna Taubman.
  4. ^ Gregersen, edited by Erik (2010). The Britannica guide to relativity and quantum mechanics (1st ed. ed.). New york, N.Y.: Britannica Educational Pub. Association with Rosen Educational Services. p. 201. ISBN 1615303839. 
  5. ^ (editors), Katherine Bracher ... [et al.] (2007). The biographical encyclopedia of astronomers ([Online-Ausg.] ed.). New York, NY: Springer. p. 787. ISBN 9780387304007. 
  6. ^ James, Ioan (2009). Driven to innovate : a century of Jewish mathematicians and physicists. Witney: Peter Lang. p. 122. ISBN 9781906165222. 
  7. ^ Yeshua,, Jacob E. Safra,... Ilan (2003). Encyclopaedia Britannica. ([New ed.]. ed.). Chicago, Ill.: Encyclopaedia Britannica. p. 665. ISBN 9780852299616. 
  8. ^ Encyclopedia of earth and physical sciences. New York: Marshall Cavendish. 1998. p. 1203. ISBN 9780761405511. 
  9. ^ А. И. Хаеш «Коробочное делопроизводство как источник сведений о жизни еврейских обществ и их персональном составе»: 1873 г. «...купец Левин Минковский подарил молитвенному обществу при Ковенском казённом еврейском училище начатую им... постройкой молитвенную школу вместе с плацем, с тем, чтобы общество это озаботилась окончанием таковой постройки. Общество, располагая средствами добровольных пожертвований, возвело уже это здание под крышу, но затем средства сии истощились...»
  10. ^ Kaunas: Dates and Facts (1872)
  11. ^ Box-Tax Paperwork Records: Kovno. In 1873 the merchant kupez, Levin Minkovsky, gave (as a gift) to the prayer association of the Kovno state Jewish school a lot with an ongoing construction of a prayer school that (the construction) he had started so that the association would take care of completing the construction. The association, having some funds from voluntary contributions, had built the structure up to the roof, but then, ran out of money.
  12. ^ [1]
  13. ^ Oskar Minkowski (1858-1931), nn outstanding master of diabetes research
  14. ^ Report of the Federal Security Agency (p. 183)
  15. ^ Tyra lithographed tin toy dog
  16. ^ Rudolph Leo Bernhard Minkowski: A Biographical Memoir
  17. ^ "Minkowski Sausage", WolframAlpha
  18. ^ Dickson, L. E. (1914). "Review: Hermann Minkowski, Geometrie der Zahlen". Bull. Amer. Math. Soc. 21 (3): 131–132. 
  19. ^ Wilson, E. B. (1915). "Review: Gesammelte Abhandlungen von Hermann Minkowski". Bull. Amer. Math. Soc. 21 (8): 409–412. 

External links[edit]