View source for Hermann Minkowski

{{Short description|German mathematician and physicist (1864–1909)}}
{{Use dmy dates|date=April 2017}}
{{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]], [[Suwałki Governorate]], [[Congress Poland|Kingdom of Poland]] (now in [[Kaunas]], [[Lithuania]])
| death_date = {{death date and age|1909|1|12|1864|6|22|df=y}}
| death_place = [[Göttingen]], [[German Empire]]
| field = [[Mathematics]], [[physics]], [[philosophy]]
| work_institution = [[University of Göttingen]] and [[ETH Zurich]]
| alma_mater = [[Albertina University of Königsberg]]
| doctoral_advisor = [[Ferdinand von Lindemann]]
| doctoral_students = [[Constantin Carathéodory]]<br/>[[Louis Kollros]]<br/>[[Dénes Kőnig]]
| known_for = {{indented plainlist|
* [[Geometry of numbers]]
* [[Minkowski content]]
* [[Minkowski diagram]]
* [[Minkowski's question-mark function]]
* [[Minkowski space]]
* Work on the [[Diophantine approximation]]s
}}
| spouse = Auguste Adler
| children = 2
| prizes = 
| signature = Hermann Minkowski signature.svg
}}
{{Special relativity sidebar}}
'''Hermann Minkowski'''{{efn|{{IPAc-en|m|ɪ|ŋ|ˈ|k|ɔː|f|s|k|i|,_|-|ˈ|k|ɒ|f|-}} {{respell|ming|KAWF|skee|,_|-|KOF|-}};<ref>[https://www.dictionary.com/browse/minkowski"Minkowski"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref> {{IPA|pol|miŋˈkɔfskʲi|lang}}; {{IPA|de|mɪŋˈkɔfski|lang}}}} (22 June 1864 – 12 January 1909) was a [[mathematician]] and professor at the [[University of Königsberg]], [[ETH Zurich|ETH Zürich]], and the [[University of Göttingen]], described variously as [[Germany|German]],<ref name="Encyclopædia Britannica" /><ref name=":1" /><ref name=":2" /> [[Poland|Polish]],<ref name=":3" /><ref name=":4" /><ref name=":5" /> [[Lithuania]]n-German,<ref name=":6" /> or [[Russia]]n.<ref name="Marshall Cavendish">{{cite book |title=Encyclopedia of Earth and Physical Sciences |url=https://archive.org/details/encyclopediaofea02mars |url-access=registration |year=1998 |publisher=Marshall Cavendish |location=New York |isbn=9780761405511 |page=1203}}</ref> He created and developed the [[geometry of numbers]] and elements of [[convex geometry]], and used [[Geometry|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).

==Personal life and family==
Hermann Minkowski was born in the town of [[Aleksota]], the [[Suwałki Governorate]], the [[Congress Poland|Kingdom of Poland]], since 1864 part of the [[Russian Empire]], to Lewin Boruch Minkowski, a merchant who subsidized the building of the [[Kaunas Synagogue|choral synagogue in Kovno]],<ref>{{cite web |author=А. И. Хаеш |url=https://www.berkovich-zametki.com/Nomer16/Chaesh1.htm |title=Коробочное делопроизводство как источник сведений о жизни еврейских обществ и их персональном составе |language=ru |year=1873 |quote=...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}}</ref><ref>{{cite web |archive-url=https://web.archive.org/web/20150108144042/http://www.litvaksig.org/litvaksig-online-journal/box-tax-paperwork-records |archive-date=January 8, 2015 |url=http://www.litvaksig.org/litvaksig-online-journal/box-tax-paperwork-records |title=Box-Tax Paperwork Records |quote=Kovno. In 1873 the merchant ([[:wikt:kupez|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 [[History of Jews in Poland|Jewish]].<ref>{{cite web |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Minkowski.html |title=Minkowski biography }}</ref> Hermann was a younger brother of the [[medical research]]er [[Oskar Minkowski|Oskar]] (born 1858).<ref>[http://www.diabetologia-journal.org/webpages/covers/2005/august.html Oskar Minkowski (1858–1931)]. {{Webarchive|url=https://web.archive.org/web/20131229142542/http://www.diabetologia-journal.org/webpages/covers/2005/august.html |date=29 December 2013 }}. 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 name="Encyclopædia Britannica">{{cite web|url=https://www.britannica.com/biography/Hermann-Minkowski |title=Hermann Minkowski German mathematician|publisher=[[Encyclopædia Britannica]] |access-date=6 January 2021}}</ref><ref name=":1">{{cite book |editor-last=Gregersen |editor-first=Erik |title=The Britannica Guide to Relativity and Quantum Mechanics |year=2010 |publisher=Britannica Educational Pub. Association with Rosen Educational Services |location=New York |isbn=978-1-61530-383-0 |page=201 |edition=1st }}</ref><ref name=":2">{{cite book |editor-last=Bracher |editor-first=Katherine |display-editors=etal |title=Biographical Encyclopedia of Astronomers |url=https://archive.org/details/biographicalency00hock_878 |url-access=limited |year=2007 |publisher=Springer |location=New York |isbn=978-0-387-30400-7 |page=[https://archive.org/details/biographicalency00hock_878/page/n820 787] |edition=Online }}</ref> [[Poland|Polish]],<ref name=":3">{{cite book |first=N. Katherine |last=Hayles |title=The Cosmic Web: Scientific Field Models and Literary Strategies in the Twentieth Century |url=https://archive.org/details/cosmicwebscienti00hayl_0 |url-access=limited |publisher=Cornell University Press |year=1984 |page=[https://archive.org/details/cosmicwebscienti00hayl_0/page/46 46] |isbn=978-0-8014-1742-9 }}</ref><ref name=":4">{{cite book |first=K. J. |last=Falconer |title=Fractals: A Very Short Introduction |publisher=Oxford University Press |year=2013 |page=119 |isbn=978-0-19-967598-2 }}</ref><ref name=":5">{{cite book |first=Adrian |last=Bardon |title=A Brief History of the Philosophy of Time |publisher=Oxford University Press |year=2013 |page=68 |isbn=978-0-19-930108-9 }}</ref> or Lithuanian-German,<ref name=":6">{{cite book |last2=Yeshua |first1=Jacob E. |last1=Safra |first2=Ilan |title=Encyclopædia Britannica |url=https://archive.org/details/newencyclopaedia26chic |url-access=registration |year=2003 |publisher=Encyclopædia Britannica |location=Chicago, Ill. |isbn=978-0-85229-961-6 |page=[https://archive.org/details/newencyclopaedia26chic/page/665 665] |edition=New }}</ref> or Russian.<ref name="Marshall Cavendish"/>

To escape Jewish [[Anti-Jewish pogroms in the Russian Empire|persecution in the Russian Empire]], the family moved to Königsberg in 1872,<ref name=":0">{{cite web |url=https://www.hormones.gr/165/article/article.html |title=Historical note: Oskar Minkowski (1858–1931). An outstanding master of diabetes research |date=2006}}</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 [[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 engineering|electrical engineer]] and inventor [[Reinhold Rudenberg]] was his son-in-law.

Minkowski died of [[appendicitis]] in Göttingen on 12 January 1909. [[Max Born]] delivered the obituary on behalf of the mathematics students at Göttingen.<ref>{{cite book |title=[[The End of the Certain World|The End of the Certain World. The Life and Science of Max Born: The Nobel Physicist Who Ignited the Quantum Revolution]] |first=Nancy Thorndike |last=Greenspan |pages=42–43 |year=2005 |isbn=9780738206936 |publisher=Basic Books }}</ref> [[David Hilbert]]'s obituary of Minkowski illustrates the deep friendship between the two mathematicians:
{{blockquote|author=Hilbert|source=1909|text=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.}}

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 [[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 form]]s. Because of his 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 John Stephen Smith|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.<ref name=":0" />

Minkowski taught at the universities of Bonn, Königsberg, Zürich, and Göttingen. At the [[Federal Polytechnic Institute|''Eidgenössisches Polytechnikum'']], today the [[ETH Zurich]], he was one of 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]]<ref>{{MathWorld|id=MinkowskiSausage|title=Minkowski Sausage|access-date=16 January 2023}}</ref> and the [[Minkowski cover]]<ref>{{MathWorld|id=MinkowskiCover|title=Minkowski Cover|access-date=16 January 2023}}</ref> 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|Minkowski space|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 [[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 using the invariant interval <math>x^2 + y^2 + z^2 - c^2 t^2</math> (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 (mathematician)|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:{{blockquote|text=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===
* {{Cite journal
|doi=10.1002/andp.19153521505
|author=Minkowski, Hermann
|orig-year=1907|year=1915
|title=Das Relativitätsprinzip
|journal=Annalen der Physik
|volume=352
|issue=15
|pages=927–938|bibcode = 1915AnP...352..927M
|url=https://zenodo.org/record/1447307
}}
* {{Cite journal
|author=Minkowski, Hermann
|year=1908
|title=Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern
|journal=Nachrichten der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse
|pages=53–111|title-link=s:de:Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern
}}
** 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=Raum und Zeit
|journal=Jahresbericht der Deutschen Mathematiker-Vereinigung
|pages=75–88|title-link=s:de:Raum und Zeit (Minkowski)
|volume=18
|bibcode=1909JDMaV..18...75M
}}
** Various English translations on Wikisource: "[[s:Space and Time|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 [[Hendrik Lorentz|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===
* {{cite book | author=Minkowski, Hermann | author-link=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 | access-date=2016-02-28}}<ref>{{cite journal|author=Dickson, L. E.|author-link=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=https://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|doi-access=free}}</ref>

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

==See also==
{{cols|colwidth=16em}}
* [[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]]
{{colend}}

==Notes==
{{notelist}}

==References==
{{Reflist
|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
  |isbn       = 978-3-540-00238-3
  |doi       = 10.1007/978-3-540-29925-7_8614 |chapter       = (12493) Minkowski }}</ref>

}}

==External links==
{{wikisource|works=or|Hermann Minkowski}}
{{Wikisource|de|Hermann Minkowski}}
{{Wikiquote}}
{{Commons category}}
* {{MathGenealogy |id=29675}}

'''Archival collections'''
* [https://libserv.aip.org/ipac20/ipac.jsp?session=168116Y30L533.282104&profile=rev-icos&source=~!horizon&view=subscriptionsummary&uri=full=3100006~!3971~!2&ri=9&aspect=power&menu=search&ipp=20&spp=20&staffonly=&term=MINKOWSKI&index=.AW&uindex=&aspect=power&menu=search&ri=9&limitbox_1=LO01+=+icos Hermann Minkowski notebooks, 1882-1906, Niels Bohr Library & Archives]

{{Authority control}}

{{DEFAULTSORT:Minkowski, Hermann}}
[[Category:Hermann Minkowski| ]]
[[Category:1864 births]]
[[Category:1909 deaths]]
[[Category:Scientists from Kaunas]]
[[Category:People from Suwałki Governorate]]
[[Category:Lithuanian Jews]]
[[Category:Emigrants from the Russian Empire to the German Empire]]
[[Category:German people of Lithuanian-Jewish descent]]
[[Category:German people of Polish-Jewish descent]]
[[Category:19th-century German mathematicians]]
[[Category:20th-century German mathematicians]]
[[Category:German geometers]]
[[Category:German number theorists]]
[[Category:German relativity theorists]]
[[Category:University of Königsberg alumni]]
[[Category:Academic staff of the University of Königsberg]]
[[Category:Academic staff of ETH Zurich]]
[[Category:Academic staff of the University of Bonn]]
[[Category:Academic staff of the University of Göttingen]]
[[Category:Deaths from appendicitis]]