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Hermann Minkowski

From Wikipedia, the free encyclopedia
German mathematician and physicist (1864–1909)

Hermann Minkowski
Born(1864-06-22)22 June 1864
Died12 January 1909(1909-01-12) (aged 44)
CitizenshipRussian Empire[1] or Germany
Alma materAlbertina University of Königsberg
Known for
SpouseAuguste Adler
Children2
Scientific career
FieldsMathematics,physics,philosophy
InstitutionsUniversity of Göttingen andETH Zurich
Doctoral advisorFerdinand von Lindemann
Doctoral studentsConstantin Carathéodory
Louis Kollros
Dénes Kőnig
Signature
Special relativity
The world line: a diagrammatic representation of spacetime

Hermann Minkowski (/mɪŋˈkɔːfski,-ˈkɒf-/ming-KAWF-skee, -⁠KOF-;[2]German:[mɪŋˈkɔfski]; 22 June 1864 – 12 January 1909) was amathematician and professor at theUniversity of Königsberg, theUniversity of Zürich, and theUniversity of Göttingen, described variously asGerman,[3][4][5]Polish,[6][7][8]Lithuanian-German,[9] orRussian.[1] He created and developed thegeometry of numbers and elements ofconvex geometry, and usedgeometrical methods to solve problems innumber theory,mathematical physics, and thetheory of relativity.

Minkowski is perhaps best known for his foundational work describing space and time as afour-dimensional space, now known as "Minkowski spacetime", which facilitated geometric interpretations ofAlbert Einstein'sspecial theory of relativity (1905).

Personal life and family

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Hermann Minkowski was born in the town ofAleksota, theSuwałki Governorate, theKingdom of Poland, since 1864 part of theRussian Empire, to Lewin Boruch Minkowski, a merchant who subsidized the building of thechoral synagogue in Kovno,[10][11][12] and Rachel Taubmann, both ofJewish descent.[13] Hermann was a younger brother of themedical researcherOskar (born 1858).[14] In different sources Minkowski's nationality is variously given as German,[3][4][5]Polish,[6][7][8] or Lithuanian-German,[9] or Russian.[1]

To escape Jewishpersecution in the Russian Empire, the family moved to Königsberg in 1872,[15] 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).[16]

Minkowski studied inKönigsberg and taught inBonn (1887–1894), Königsberg (1894–1896) andZürich (1896–1902), and finally inGöttingen from 1902 until his death in 1909. He married Auguste Adler in 1897 with whom he had two daughters; theelectrical engineer and inventorReinhold Rudenberg was his son-in-law.

Minkowski died ofappendicitis in Göttingen on 12 January 1909.Max Born delivered the obituary on behalf of the mathematics students at Göttingen.[17]David Hilbert's obituary of Minkowski illustrates the deep friendship between the two mathematicians:

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. 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.

— Hilbert, 1909

The main-beltasteroid12493 Minkowski andM-matrices are named in Minkowski's honor.[18]

Education and career

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Minkowski in 1883, at the time of being awarded the Mathematics Prize of theFrench Academy of Sciences

Minkowski was educated inEast Prussia at theAlbertina University of Königsberg, where he earned his doctorate in 1885 under the direction ofFerdinand von Lindemann. In 1883, while still a student at Königsberg, he was awarded the Mathematics Prize of theFrench Academy of Sciences for his manuscript on the theory ofquadratic forms. Due to the very young age of 18, which was unheard of in the mathematics community, and his obscurity as a mathematician at the time, his sharing the award with eminent English mathematicianHenry Smith (who was certainly a great deal more famous than Hermann and to whom the prize was awarded posthumously) caused severe unrest among English mathematicians. The prize committee, despite the numerous complaints, never changed their decision. He also became a friend of another renowned mathematician, David Hilbert. His brother,Oskar Minkowski (1858–1931), was a well-known physician and researcher.[15]

Minkowski taught at the universities of Bonn, Königsberg, Zürich, and Göttingen. At theEidgenössische Polytechnikum, today theETH Zurich, he was one of Einstein's teachers.

Minkowski explored the arithmetic ofquadratic forms, especially concerningn variables, and his research into that topic led him to consider certain geometric properties in a space ofndimensions. In 1896, he presented hisgeometry of numbers, a geometrical method that solved problems innumber theory. He is also the creator of theMinkowski Sausage[19] and theMinkowski cover[20] of a curve.

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.

Work on relativity

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Further information:Minkowski space andMinkowski diagram

By 1908 Minkowski realized that the special theory of relativity, introduced by his former studentAlbert Einstein in 1905 and based on the previous work ofLorentz andPoincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in whichtime andspace are not separated entities but intermingled in a four-dimensionalspace–time, and in which theLorentz geometry of special relativity can be effectively represented using the invariant intervalx2+y2+z2c2t2{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}} (seeHistory of special relativity).

The mathematical basis of Minkowski space can also be found in thehyperboloid model ofhyperbolic space already known in the 19th century, because isometries (or motions) in hyperbolic space can be related toLorentz transformations, which included contributions ofWilhelm Killing (1880, 1885),Henri Poincaré (1881),Homersham Cox (1881),Alexander Macfarlane (1894) and others (seeHistory of Lorentz transformations).

The beginning part of his address called "Space and Time" 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.

Publications

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Relativity

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Diophantine approximations

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Mathematical (posthumous)

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See also

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Notes and references

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  1. ^abcEncyclopedia of Earth and Physical Sciences. New York: Marshall Cavendish. 1998. p. 1203.ISBN 9780761405511.
  2. ^"Minkowski".Random House Webster's Unabridged Dictionary.
  3. ^ab"Hermann Minkowski German mathematician".Encyclopædia Britannica. Retrieved6 January 2021.
  4. ^abGregersen, Erik, ed. (2010).The Britannica Guide to Relativity and Quantum Mechanics (1st ed.). New York: Britannica Educational Pub. Association with Rosen Educational Services. p. 201.ISBN 978-1-61530-383-0.
  5. ^abBracher, Katherine; et al., eds. (2007).Biographical Encyclopedia of Astronomers (Online ed.). New York: Springer. p. 787.ISBN 978-0-387-30400-7.
  6. ^abHayles, N. Katherine (1984).The Cosmic Web: Scientific Field Models and Literary Strategies in the Twentieth Century. Cornell University Press. p. 46.ISBN 978-0-8014-1742-9.
  7. ^abFalconer, K. J. (2013).Fractals: A Very Short Introduction. Oxford University Press. p. 119.ISBN 978-0-19-967598-2.
  8. ^abBardon, Adrian (2013).A Brief History of the Philosophy of Time. Oxford University Press. p. 68.ISBN 978-0-19-930108-9.
  9. ^abSafra, Jacob E.; Yeshua, Ilan (2003).Encyclopædia Britannica (New ed.). Chicago, Ill.: Encyclopædia Britannica. p. 665.ISBN 978-0-85229-961-6.
  10. ^А. И. Хаеш (1873)."Коробочное делопроизводство как источник сведений о жизни еврейских обществ и их персональном составе" (in Russian)....купецЛевин 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...
  11. ^"Kaunas: dates and facts. Electronic directory".
  12. ^"Box-Tax Paperwork Records". Archived fromthe original on 8 January 2015.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
  13. ^"Minkowski biography".
  14. ^Oskar Minkowski (1858–1931).Archived 29 December 2013 at theWayback Machine. The Jewish genealogy site JewishGen.org (Lithuania database, registration required) contains the birth record in the Kovno rabbinical books of Hermann's younger brother Tuvia in 1868 to Boruch Yakovlevich Minkovsky and his wife Rakhil Isaakovna Taubman.
  15. ^ab"Historical note: Oskar Minkowski (1858–1931). An outstanding master of diabetes research". 2006.
  16. ^Report of the Federal Security Agency (p. 183);Tyra lithographed tin toy dog;Rudolph Leo Bernhard Minkowski: A Biographical Memoir.
  17. ^Greenspan, Nancy Thorndike (2005).The End of the Certain World. The Life and Science of Max Born: The Nobel Physicist Who Ignited the Quantum Revolution. Basic Books. pp. 42–43.ISBN 9780738206936.
  18. ^Schmadel, Lutz D. (2007). "(12493) Minkowski".Dictionary of Minor Planet Names – (12493) Minkowski. Springer Berlin Heidelberg. p. 783.doi:10.1007/978-3-540-29925-7_8614.ISBN 978-3-540-00238-3.
  19. ^Weisstein, Eric W."Minkowski Sausage".MathWorld. Retrieved16 January 2023.
  20. ^Weisstein, Eric W."Minkowski Cover".MathWorld. Retrieved16 January 2023.
  21. ^Dickson, L. E. (1909)."Review:Diophantische Approximationen. Eine Einführung in die Zahlentheorie von Hermann Minkowski"(PDF).Bull. Amer. Math. Soc.15 (5):251–252.doi:10.1090/s0002-9904-1909-01753-7.
  22. ^Dickson, L. E. (1914)."Review:Geometrie der Zahlen von Hermann Minkowski".Bull. Amer. Math. Soc.21 (3):131–132.doi:10.1090/s0002-9904-1914-02597-2.
  23. ^Wilson, E. B. (1915)."Review:Gesammelte Abhandlungen von Hermann Minkowski".Bull. Amer. Math. Soc.21 (8):409–412.doi:10.1090/s0002-9904-1915-02658-3.

External links

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