June 22, 1864|
Aleksota, Kingdom of Poland
|Died||January 12, 1909
Göttingen, German Empire
|Institutions||University of Göttingen and ETH Zurich|
|Alma mater||Albertina University of Königsberg|
|Doctoral advisor||Ferdinand von Lindemann|
|Doctoral students||Constantin Carathéodory
|Known for||Minkowski space
Hermann Minkowski (June 22, 1864 – January 12, 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).
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. In different sources Minkowski is described variously as German, Lithuanian or Lithuanian-German, or Russian. His parents were Lewin Minkowski, a businessman, and Rachel Taubmann, both of Jewish descent.
Life and work
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 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.
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 (September 21, 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.
- Relativity papers
- Minkowski, Hermann (1907/1915). "Das Relativitätsprinzip". Annalen der Physik 352 (15): 927–938. Bibcode:1915AnP...352..927M. doi:10.1002/andp.19153521505.
- Minkowski, Hermann (1907/8). "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern". Nachrichten von 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 (1908/9). "Raum und Zeit". Jahresbericht der Deutschen Mathematiker-Vereinigung: 75–88.
- Various English translations on Wikisource: Space and Time
- H. A. Lorentz, Albert Einstein, Hermann Minkowski, and Hermann Weyl, 1952. The Principle of Relativity: A Collection of Original Memoirs. Dover.
- Mathematical papers (posthumous)
- Minkowski, Hermann (1910). Geometrie der Zahlen. Leipzig-Berlin: R. G. Teubner. MR 0249269.
- Minkowski, Hermann (1911). Gesammelte Abhandlungen 2 vols. Leipzig-Berlin: R. G. Teubner. Reprinted in one volume New York, Chelsea 1967
- Abraham–Minkowski controversy
- Brunn–Minkowski theorem
- Hasse–Minkowski theorem
- Minkowski addition
- Minkowski–Bouligand dimension
- Minkowski (crater)
- Minkowski diagram
- Minkowski functional
- Minkowski inequality
- Minkowski problem
- Minkowski's question mark function
- Minkowski space
- Minkowski–Steiner formula
- Minkowski's theorem in geometry of numbers
- Separating axis theorem
- Smith–Minkowski–Siegel mass formula
- 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.)
- 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.
- (editors), Katherine Bracher ... [et al.] (2007). The biographical encyclopedia of astronomers ([Online-Ausg.] ed.). New York, NY: Springer. p. 787. ISBN 9780387304007.
- James, Ioan (2009). Driven to innovate : a century of Jewish mathematicians and physicists. Witney: Peter Lang. p. 122. ISBN 9781906165222.
- Yeshua,, Jacob E. Safra,... Ilan (2003). Encyclopaedia Britannica. ([New ed.]. ed.). Chicago, Ill.: Encyclopaedia Britannica. p. 665. ISBN 9780852299616.
- Encyclopedia of earth and physical sciences. New York: Marshall Cavendish. 1998. p. 1203. ISBN 9780761405511.
- "Minkowski Sausage", WolframAlpha
- Dickson, L. E. (1914). "Review: Hermann Minkowski, Geometrie der Zahlen". Bull. Amer. Math. Soc. 21 (3): 131–132.
- Wilson, E. B. (1915). "Review: Gesammelte Abhandlungen von Hermann Minkowski". Bull. Amer. Math. Soc. 21 (8): 409–412.
|Wikisource has original text related to this article:|
|German Wikisource has original text related to this article:|
- O'Connor, John J.; Robertson, Edmund F., "Hermann Minkowski", MacTutor History of Mathematics archive, University of St Andrews.
- Hermann Minkowski at the Mathematics Genealogy Project