Hermann Minkowski

Short description: German mathematician and physicist (1864–1909)

Hermann Minkowski

Born|

Aleksotas, Suwałki Governorate, Kingdom of Poland (now in Kaunas, Lithuania)

Died| 12 January 1909(1909-01-12) (aged 44)

Göttingen, German Empire

Citizenship| Russian Empire[1] or Germany
Alma mater| Albertina University of Königsberg
Known for|

* Geometry of numbers
* Minkowski content
* Minkowski diagram
* Minkowski's question-mark function
* Minkowski space
* Work on the Diophantine approximations

Spouse(s)| Auguste Adler
Children| 2
Scientific career
Fields| Mathematics, physics, philosophy
Institutions| University of Göttingen and ETH Zurich
Doctoral advisor| Ferdinand von Lindemann
Doctoral students| Constantin Carathéodory
Louis Kollros
Dénes Kőnig
Signature

Hermann Minkowski (/mɪŋˈkɔːfski, -ˈkɒf-/;[2] German: [mɪŋˈkɔfski]; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. 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 foundational work describing space and time as a four-dimensional space, now known as "Minkowski spacetime", which facilitated geometric interpretations of Albert Einstein's special theory of relativity (1905).

## Contents

* 1 Personal life and family
* 2 Education and career
* 3 Work on relativity
* 4 Publications
* 5 See also
* 6 Notes and references
* 7 External links
* 7.1 Archival collections

## Personal life and family

Hermann Minkowski was born in the town of Aleksota, the Suwałki Governorate, the Kingdom of Poland, since 1864 part of the Russian Empire, to Lewin Boruch Minkowski, a merchant who subsidized the building of the choral synagogue in Kovno,[3][4][5] and Rachel Taubmann, both of Jewish descent.[6] Hermann was a younger brother of the medical researcher Oskar (born 1858).[7] In different sources Minkowski's nationality is variously given as German,[8][9][10] Poland ,[11][12][13] or Lithuanian-German,[14] or Russian.[1]

To escape Jewish persecution 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 in Königsberg and taught in Bonn (1887–1894), Königsberg (1894–1896) and Zürich (1896–1902), and finally in Göttingen from 1902 until his death in 1909. He married Auguste Adler in 1897 with whom he had two daughters; the electrical engineer and inventor Reinhold Rudenberg was his son-in-law.

Minkowski died suddenly of appendicitis in Göttingen on 12 January 1909. 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.

Max Born delivered the obituary on behalf of the mathematics students at Göttingen.[17]

The main-belt asteroid 12493 Minkowski and M-matrices are named in Minkowski's honor.[18]

## Education and career

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

Minkowski was educated in East Prussia 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. 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 mathematician Henry 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 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. He is also the creator of the Minkowski Sausage[19] and the Minkowski 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

Further information: Physics:Minkowski space and Minkowski diagram

By 1908 Minkowski realized that the special theory of relativity, introduced by his former student 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 using the invariant interval x2+y2+z2−c2t2 (see History of special relativity).

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

Relativity

* Minkowski, Hermann (1915). "Das Relativitätsprinzip". Annalen der Physik 352 (15): 927–938. doi:10.1002/andp.19153521505. Bibcode: 1915AnP...352..927M. https://zenodo.org/record/1447307.
* Minkowski, Hermann (1908). "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern". Nachrichten der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 53–111.
* English translation: "The Fundamental Equations for Electromagnetic Processes in Moving Bodies". In: The Principle of Relativity (1920), Calcutta: University Press, 1–69.
* Minkowski, Hermann (1909). "Raum und Zeit". Jahresbericht der Deutschen Mathematiker-Vereinigung 18: 75–88. Bibcode: 1909JDMaV..18...75M.
* Various English translations on Wikisource: "Space and Time".
* Blumenthal O. (ed): Das Relativitätsprinzip, Leipzig 1913, 1923 (Teubner), Engl tr (W. Perrett & G. B. Jeffrey) The Principle of Relativity London 1923 (Methuen); reprinted New York 1952 (Dover) entitled H. A. Lorentz, Albert Einstein, Hermann Minkowski, and Hermann Weyl, The Principle of Relativity: A Collection of Original Memoirs.
* Space and Time – Minkowski's Papers on Relativity, Minkowski Institute Press, 2012 ISBN 978-0-9879871-3-6 (free ebook).

Diophantine approximations

* Minkowski, Hermann (1907). Diophantische Approximationen: Eine Einführung in die Zahlentheorie. Leipzig-Berlin: R. G. Teubner. http://catalog.hathitrust.org/Record/000424095. Retrieved 2016-02-28. [21]

Mathematical (posthumous)

* Minkowski, Hermann (1910). Geometrie der Zahlen. Leipzig-Berlin: B. G. Teubner Verlag. https://archive.org/details/geometriederzahl00minkrich. Retrieved 2016-02-28. [22]
* Minkowski, Hermann (1911). Gesammelte Abhandlungen 2 vols. Leipzig-Berlin: R. G. Teubner. http://catalog.hathitrust.org/Record/000169187. Retrieved 2016-02-28. [23] Reprinted in one volume New York, Chelsea 1967.

## See also

* List of things named after Hermann Minkowski
* Abraham–Minkowski controversy
* Brunn–Minkowski theorem
* Hasse–Minkowski theorem
* Hermite–Minkowski theorem
* Minkowski addition
* Minkowski (crater)
* Minkowski distance
* Minkowski functional
* Minkowski inequality
* Minkowski model
* Minkowski plane
* Minkowski problem
* Minkowski problem for polytopes
* Minkowski's second theorem
* Minkowski space
* Minkowski's bound
* Minkowski's theorem in geometry of numbers
* Minkowski–Hlawka theorem
* Minkowski–Steiner formula
* Smith–Minkowski–Siegel mass formula
* Proper time
* Separating axis theorem
* Taxicab geometry
* World line

## Notes and references

1. ↑ 1.0 1.1 Encyclopedia of Earth and Physical Sciences. New York: Marshall Cavendish. 1998. p. 1203. ISBN 9780761405511. https://archive.org/details/encyclopediaofea02mars.
2. ↑ "Minkowski". Random House Webster's Unabridged Dictionary.
3. ↑ А. И. Хаеш (1873). "Коробочное делопроизводство как источник сведений о жизни еврейских обществ и их персональном составе" (in ru). http://www.berkovich-zametki.com/Nomer16/Chaesh1.htm. "...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..."
4. ↑ "Kaunas: dates and facts. Electronic directory". http://datos.kvb.lt/en/index.php?option=com_laikotarpiai&task=view&id=19&Itemid=65.
5. ↑ "Box-Tax Paperwork Records". http://www.litvaksig.org/litvaksig-online-journal/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"
6. ↑ "Minkowski biography". http://www-history.mcs.st-andrews.ac.uk/Biographies/Minkowski.html.
7. ↑ Oskar Minkowski (1858–1931). . 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.
8. ↑ "Hermann Minkowski German mathematician". Encyclopædia Britannica. https://www.britannica.com/biography/Hermann-Minkowski.
9. ↑ Gregersen, 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.
10. ↑ Bracher, Katherine, ed (2007). Biographical Encyclopedia of Astronomers (Online ed.). New York: Springer. p. 787. ISBN 978-0-387-30400-7. https://archive.org/details/biographicalency00hock_878.
11. ↑ Hayles, 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. https://archive.org/details/cosmicwebscienti00hayl_0.
12. ↑ Falconer, K. J. (2013). Fractals: A Very Short Introduction. Oxford University Press. p. 119. ISBN 978-0-19-967598-2.
13. ↑ Bardon, Adrian (2013). A Brief History of the Philosophy of Time. Oxford University Press. p. 68. ISBN 978-0-19-930108-9.
14. ↑ Safra, Jacob E.; Yeshua, Ilan (2003). Encyclopædia Britannica (New ed.). Chicago, Ill.: Encyclopædia Britannica. p. 665. ISBN 978-0-85229-961-6. https://archive.org/details/newencyclopaedia26chic.
15. ↑ 15.0 15.1 "Historical note: Oskar Minkowski (1858–1931). An outstanding master of diabetes research". 2006. http://www.hormones.gr/165/article/article.html.
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". http://mathworld.wolfram.com/MinkowskiSausage.html.
20. ↑ Weisstein, Eric W.. "Minkowski Cover". http://mathworld.wolfram.com/MinkowskiCover.html.
21. ↑ Dickson, L. E. (1909). "Review: Diophantische Approximationen. Eine Einführung in die Zahlentheorie von Hermann Minkowski". Bull. Amer. Math. Soc. 15 (5): 251–252. doi:10.1090/s0002-9904-1909-01753-7. https://www.ams.org/journals/bull/1909-15-05/S0002-9904-1909-01753-7/S0002-9904-1909-01753-7.pdf.
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

* Hermann Minkowski at the Mathematics Genealogy Project

### Archival collections

* Hermann Minkowski notebooks, 1882-1906, Niels Bohr Library & Archives

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