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{{Infobox scientist
|name = Hermann Minkowski
|image = De Raum zeit Minkowski Bild (cropped).jpg
|caption =
|birth_date = {{birth date|1864|6|22|df=y}}
|birth_place = [[Aleksotas]], [[Kovno Governorate]], [[Russian Empire]] (now in [[Kaunas]], [[Lithuania]])
|death_date = {{death date and age|1909|1|12|1864|6|22|df=y}}
|death_place = [[Göttingen]], [[German Empire]]
|residence =
|nationality = German
|field = [[Mathematician]]
|work_institution = [[Georg-August University of Göttingen|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 = [[Geometry of numbers]] [[Minkowski content]] [[Minkowski diagram]] [[Minkowski's question mark function]] [[Minkowski space]]
|spouse = Auguste Adler
|children = Lily (1898–1983), Ruth (b. 1902-2000)
|prizes =
|footnotes =
|signature = De Raum zeit Minkowski Bild Signature (cropped).jpg
}}

'''Hermann Minkowski''' ({{IPAc-en|m|ɪ|ŋ|ˈ|k|ɔː|f|s|k|i|,_|-|ˈ|k|ɒ|f|-}};<ref>[http://www.dictionary.com/browse/minkowski"Minkowski"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref> {{IPA-de|mɪŋˈkɔfski|lang}}; 22 June 1864 – 12 January 1909) was a [[mathematician]], 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 work in relativity, in which he showed in 1907 that his former student [[Albert Einstein]]'s [[special theory of relativity]] (1905), could be understood geometrically as a theory of four-dimensional space–time, since known as the "[[Minkowski spacetime]]".

==Personal life and family==
Hermann Minkowski was born in [[Aleksotas]], a village in the [[Kovno Governorate]] of the [[Russian Empire]] (now incorporated into the city of [[Kaunas]], [[Lithuania]]) to Lewin Boruch Minkowski, a merchant who subsidized the building of the [[Kaunas Synagogue|choral synagogue in Kovno]],<ref>[http://www.berkovich-zametki.com/Nomer16/Chaesh1.htm 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...»</ref><ref>{{cite web|url=http://datos.kvb.lt/en/index.php?option=com_laikotarpiai&task=view&id=19&Itemid=65|title=Kaunas: dates and facts. Electronic directory.|publisher=}}</ref><ref>[https://web.archive.org/web/20150108144042/http://www.litvaksig.org/litvaksig-online-journal/box-tax-paperwork-records 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''.</ref> and Rachel Taubmann, both of [[History of the Jews in the Russian Empire|Jewish descent]].<ref>{{cite web|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Minkowski.html|title=Minkowski biography|publisher=}}</ref>
Hermann was a younger brother of the medical researcher, [[Oskar Minkowski|Oskar]] (born 1858).<ref>[http://www.diabetologia-journal.org/webpages/covers/2005/august.html 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.</ref>
In different sources Minkowski's nationality is variously given as German,<ref>{{cite book|last=Gregersen|first=edited by Erik|title=The Britannica guide to relativity and quantum mechanics|year=2010|publisher=Britannica Educational Pub. Association with Rosen Educational Services|location=New york, N.Y.|isbn=1615303839|page=201|edition=1st}};
{{cite book|last=(editors)|first=Katherine Bracher ... [et al.]|title=The biographical encyclopedia of astronomers|year=2007|publisher=Springer|location=New York, NY|isbn=9780387304007|page=787|edition=[Online-Ausg.]}}</ref>
Polish,<ref>
N. Katherine Hayles, ''The Cosmic Web: Scientific Field Models and Literary Strategies in the Twentieth Century'', Cornell University Press, 1986, p. 46.
K. J. Falconer, ''Fractals: A Very Short Introduction'', Oxford University Press, 2013, p. 119.
Adrian Bardon, ''A Brief History of the Philosophy of Time'', Oxford University Press, 2013, p. 68.
</ref>
Lithuanian<ref>{{cite book|last=James|first=Ioan|title=Driven to innovate : a century of Jewish mathematicians and physicists|year=2009|publisher=Peter Lang|location=Witney|isbn=9781906165222|page=122}}</ref> or Lithuanian-German,<ref>{{cite book|last=Yeshua,|first=Jacob E. Safra,... Ilan|title=Encyclopædia Britannica.|year=2003|publisher=Encyclopædia Britannica|location=Chicago, Ill.|isbn=9780852299616|page=665|edition=[New ed.].}}</ref> or Russian.<ref>{{cite book|title=Encyclopedia of earth and physical sciences.|year=1998|publisher=Marshall Cavendish|location=New York|isbn=9780761405511|page=1203}}</ref>

To escape [[Anti-Jewish pogroms in the Russian Empire|persecution in Russia]] the family moved to Königsberg in 1872,<ref>{{cite web|url=http://www.hormones.gr/165/article/article.html|title=Hormones.gr|publisher=}}</ref> 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).<ref>[https://books.google.com/books?id=lVjOAAAAMAAJ&pg=RA1-PA183&lpg=RA1-PA183&dq Report of the Federal Security Agency (p. 183)];
[http://www.antique-toys.dk/default.asp?id=9&lang=uk&pg=4 Tyra lithographed tin toy dog];
[http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/minkowski-rudolph.pdf Rudolph Leo Bernhard Minkowski: A Biographical Memoir]</ref>

Minkowski studied in Königsberg and taught in [[Bonn]] (1887–1894), Königsberg (1894–1896) and [[Zurich]] (1896–1902), and finally in [[Göttingen]] from 1902 until his premature 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.

The main-belt [[asteroid]] [[12493 Minkowski]] and [[M-matrix|M-matrices]] are named in Minkowski's honor.<ref name="springer" />

==Education and career==
[[File:Hermann Minkowski.png|thumb|upright|Minkowski in 1883, at the time of being awarded the Mathematics Prize of the [[French Academy of Sciences]]]]
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 form]]s. 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 [[Federal Polytechnic Institute|''Eidgenössische Polytechnikum'']], today the [[ETH Zurich]], he was one of [[Albert Einstein|Einstein]]'s teachers.

Minkowski explored the arithmetic of [[quadratic form]]s, especially concerning ''n'' variables, and his research into that topic led him to consider certain geometric properties in a space of ''n'' [[dimension]]s. 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 and the Minkowski cover of a curve.<ref>[http://www.wolframalpha.com/input/?i=minkowski+sausage&a=*C.minkowski+sausage-_*MathWorld-&f2=3&f=MinkowskiSausage.n%5Cu005f3 "Minkowski Sausage"], ''[[WolframAlpha]]''</ref>

In 1902, he joined the Mathematics Department of [[University of Göttingen|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|History of special relativity|Minkowski space|Minkowski diagram}}

By 1907 Minkowski realized that the [[special theory of relativity]], introduced by his former student [[Albert Einstein]] in 1905 and based on the previous work of [[Hendrik Lorentz|Lorentz]] and [[Henri Poincaré|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 transformation|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:<blockquote>"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."</blockquote>Notice of Minkowski's death was communicated to the [[Quaternion Society]] in 1910 by its President, [[Alexander Macfarlane]], who had explored [[hyperbolic quaternion]]s as the "Algebra of Space":
:He devoted what proved to be the last years of his life to the scientific statement of fundamental equations of electrodynamics, a work which he accomplished by development of the Algebra of Space, or as he would prefer to call it, the Algebra of Space and Time.<ref>[[Alexander Macfarlane]] (1910) [http://babel.hathitrust.org/cgi/pt?id=pst.000052363498;view=1up;seq=335 Bulletin of the Quaternion Society]</ref>

Einstein 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).<ref>[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.)]</ref>

==Publications==
;Relativity papers
* {{Cite journal
|doi=10.1002/andp.19153521505
|author=Minkowski, Hermann
|origyear=1907|year=1915
|title=[[s:de:Das Relativitätsprinzip (Minkowski)|Das Relativitätsprinzip]]
|journal=Annalen der Physik
|volume=352
|issue=15
|pages=927–938|bibcode = 1915AnP...352..927M }}

* {{Cite journal
|author=Minkowski, Hermann
|year=1908
|title=[[s:de:Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern|Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern]]
|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse
|pages=53–111}}
**English translation: "[[s:Translation:The Fundamental Equations for Electromagnetic Processes in Moving Bodies|The Fundamental Equations for Electromagnetic Processes in Moving Bodies]]." In: The Principle of Relativity (1920), Calcutta: University Press, 1–69
* {{Cite journal
|author=Minkowski, Hermann
|year=1909
|title=[[s:de:Raum und Zeit (Minkowski)|Raum und Zeit]]
|journal=Jahresbericht der Deutschen Mathematiker-Vereinigung
|pages=75–88}}
**Various English translations on Wikisource: "[[s:Space and Time|Space and Time]]"
* [[Hendrik Lorentz|H. A. Lorentz]], [[Albert Einstein]], Hermann Minkowski, and [[Hermann Weyl]], 1952. ''The Principle of Relativity: A Collection of Original Memoirs''. Dover.

;Diophantine approximations
* {{cite book | author=Minkowski, Hermann | authorlink=Hermann Minkowski | title=Diophantische Approximationen: Eine Einführung in die Zahlentheorie | location=Leipzig-Berlin | publisher=R. G. Teubner | year=1907 | url=http://catalog.hathitrust.org/Record/000424095 | accessdate=2016-02-28}}<ref>{{cite journal|author=Dickson, L. E.|authorlink=Leonard Eugene Dickson|title=Review: ''Diophantische Approximationen. Eine Einführung in die Zahlentheorie'' von Hermann Minkowski|journal=Bull. Amer. Math. Soc.|year=1909|volume=15|issue=5|pages=251–252|url=http://www.ams.org/journals/bull/1909-15-05/S0002-9904-1909-01753-7/S0002-9904-1909-01753-7.pdf|doi=10.1090/s0002-9904-1909-01753-7}}</ref>

;Mathematical papers (posthumous)
*{{Cite journal | last1=Minkowski | first1=Hermann | author1-link=Hermann Minkowski | title=Geometrie der Zahlen | url=https://archive.org/details/geometriederzahl00minkrich | publisher=R. G. Teubner | location=Leipzig-Berlin | mr=0249269 | year=1910 | accessdate=2016-02-28 }}<ref>{{cite journal|author=Dickson, L. E.|title=Review: ''Geometrie der Zahlen'' von Hermann Minkowski|journal=Bull. Amer. Math. Soc.|year=1914|volume=21|issue=3|pages=131–132|url=http://www.ams.org/journals/bull/1914-21-03/S0002-9904-1914-02597-2/|doi=10.1090/s0002-9904-1914-02597-2}}</ref>
* {{cite book | author=Minkowski, Hermann | authorlink=Hermann Minkowski | title = Gesammelte Abhandlungen 2 vols| location = Leipzig-Berlin | publisher = R. G. Teubner | year = 1911 | url=http://catalog.hathitrust.org/Record/000169187 | accessdate=2016-02-28}}<ref>{{cite journal|author=Wilson, E. B.|authorlink=Edwin Bidwell Wilson|title=Review: ''Gesammelte Abhandlungen von Hermann Minkowski''|journal=Bull. Amer. Math. Soc.|year=1915|volume=21|issue=8|pages=409–412|url=http://www.ams.org/journals/bull/1915-21-08/S0002-9904-1915-02658-3/|doi=10.1090/s0002-9904-1915-02658-3}}</ref> Reprinted in one volume New York, Chelsea 1967

==See also==
{{div col|colwidth=25em}}
* [[Abraham–Minkowski controversy]]
* [[Brunn–Minkowski theorem]]
* [[Hasse–Minkowski theorem]]
* [[Minkowski addition]]
* [[Minkowski content]]
* [[Minkowski (crater)]]
* [[Minkowski diagram]]
* [[Minkowski functional]]
* [[Minkowski inequality]]
* [[Minkowski problem]]
* [[Minkowski space]]
* [[Minkowski's bound]]
* [[Minkowski's question mark function]]
* [[Minkowski's theorem]] in [[geometry of numbers]]
* [[Minkowski–Bouligand dimension]]
* [[Minkowski–Hlawka theorem]]
* [[Minkowski–Steiner formula]]
* [[Separating axis theorem]]
* [[Smith–Minkowski–Siegel mass formula]]
{{div col end}}

==Notes==
{{reflist|30em
|refs=

<ref name="springer">{{cite book
|title = Dictionary of Minor Planet Names – (12493) Minkowski
|last = Schmadel | first = Lutz D.
|publisher = Springer Berlin Heidelberg
|page = 783
|date = 2007
|url = http://link.springer.com/referenceworkentry/10.1007/978-3-540-29925-7_8614
|isbn = 978-3-540-00238-3
|accessdate = 1 June 2016}}</ref>

}} 

==External links==
{{Wikisource|Author:Hermann Minkowski}}
{{Wikisourcelang|de|Hermann Minkowski}}
* {{Wikiquote inline}}
* {{Commons cat inline}}
* {{MathGenealogy |id=29675}}

{{Authority control}}

{{Use dmy dates|date=April 2017}}

{{DEFAULTSORT:Minkowski, Hermann}}
[[Category:Hermann Minkowski| ]]
[[Category:1864 births]]
[[Category:1909 deaths]]
[[Category:People from Kaunas]]
[[Category:People from Kovno Governorate]]
[[Category:Lithuanian Jews]]
[[Category:Imperial Russian emigrants to Germany]]
[[Category:German people of Lithuanian-Jewish descent]]
[[Category:19th-century German mathematicians]]
[[Category:20th-century mathematicians]]
[[Category:Geometers]]
[[Category:German mathematicians]]
[[Category:Number theorists]]
[[Category:Relativity theorists]]
[[Category:University of Königsberg alumni]]
[[Category:University of Königsberg faculty]]
[[Category:ETH Zurich faculty]]
[[Category:University of Bonn faculty]]
[[Category:University of Göttingen faculty]]

Hermann Minkowski - Revision history

NickPercival: 1 revision imported