Hermann Minkowski (/mɪŋˈkɔːfski, -ˈkɒf-/; 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 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
1 Personal life and family
2 Education and career
3 Work on relativity
5 See also
7 External links
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 choral synagogue in Kovno, and
Rachel Taubmann, both of Jewish descent. Hermann was a younger
brother of the medical researcher, Oskar (born 1858). In different
sources Minkowski's nationality is variously given as German,
Polish, or Lithuanian-German, or Russian.
To escape persecution in Russia the family moved to Königsberg in
1872, 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).
Minkowski studied in Königsberg and taught in
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-matrices are named in
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. 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 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 and the Minkowski cover 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
Constantin Carathéodory was one of his students there.
Work on relativity
Further information: History of special relativity, Minkowski space,
and 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 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 (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."
Notice of Minkowski's death was communicated to the Quaternion Society
in 1910 by its President, Alexander Macfarlane, who had explored
hyperbolic quaternions 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.
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).
Minkowski, Hermann (1915) . "Das Relativitätsprinzip". Annalen
der Physik. 352 (15): 927–938. Bibcode:1915AnP...352..927M.
Minkowski, Hermann (1908). "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 (1909). "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.
Minkowski, Hermann (1907). Diophantische Approximationen: Eine
Einführung in die Zahlentheorie. Leipzig-Berlin: R. G. Teubner.
Retrieved 2016-02-28. 
Mathematical papers (posthumous)
Minkowski, Hermann (1910). "Geometrie der Zahlen". Leipzig-Berlin: R.
G. Teubner. MR 0249269. Retrieved 2016-02-28. 
Minkowski, Hermann (1911). Gesammelte Abhandlungen 2 vols.
Leipzig-Berlin: R. G. Teubner. Retrieved 2016-02-28. 
Reprinted in one volume New York, Chelsea 1967
Minkowski's question mark function
Minkowski's theorem in geometry of numbers
Separating axis theorem
Smith–Minkowski–Siegel mass formula
^ "Minkowski". Random House Webster's Unabridged Dictionary.
^ 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
пожертвований, возвело уже это здание
под крышу, но затем средства сии
^ "Kaunas: dates and facts. Electronic directory".
^ "Box-Tax Paperwork Records". Archived from the original on January
8, 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
^ "Minkowski biography".
Oskar Minkowski (1858–1931). The Jewish genealogy site
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.
^ Gregersen, Erik, ed. (2010). The Britannica Guide to Relativity and
Quantum Mechanics (1st ed.). New York, N.Y.: Britannica Educational
Pub. Association with Rosen Educational Services. p. 201.
^ Bracher, Katherine; et al., eds. (2007). Biographical Encyclopedia
of Astronomers (Online ed.). New York, NY: Springer. p. 787.
ISBN 978-0-387-30400-7. CS1 maint: Explicit use of et al.
^ Hayles, N. Katherine (1984). The Cosmic Web: Scientific Field Models
and Literary Strategies in the Twentieth Century. Cornell University
Press. p. 46. ISBN 0-8014-1742-2.
^ Falconer, K. J. (2013). Fractals: A Very Short Introduction. Oxford
University Press. p. 119. ISBN 0-19-967598-8.
^ Bardon, Adrian (2013). A Brief History of the Philosophy of Time.
Oxford University Press. p. 68.
^ Safra, Jacob E.; Yeshua, Ilan (2003). Encyclopædia Britannica (New
ed.). Chicago, Ill.: Encyclopædia Britannica. p. 665.
^ Encyclopedia of Earth and Physical Sciences. New York: Marshall
Cavendish. 1998. p. 1203. ISBN 9780761405511.
^ Report of the Federal Security Agency (p. 183); Tyra lithographed
tin toy dog; Rudolph Leo Bernhard Minkowski: A Biographical Memoir
^ Schmadel, Lutz D. (2007). Dictionary of Minor Planet Names –
(12493) Minkowski. Springer Berlin Heidelberg. p. 783.
ISBN 978-3-540-00238-3. Retrieved 1 June 2016.
^ "Minkowski Sausage", WolframAlpha
Alexander Macfarlane (1910) Bulletin of the Quaternion Society
^ (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.)
^ Dickson, L. E. (1909). "Review: Diophantische Approximationen. Eine
Einführung in die Zahlentheorie von Hermann Minkowski" (PDF). Bull.
Amer. Math. Soc. 15 (5): 251–252.
^ Dickson, L. E. (1914). "Review: Geometrie der Zahlen von Hermann
Minkowski". 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.
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