Hermann Minkowski

Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, 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).

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, 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 Jewish persecution in the Russian Empire, 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 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 of appendicitis in Göttingen on 12 January 1909. Max Born delivered the obituary on behalf of the mathematics students at Göttingen. David Hilbert's obituary of Minkowski illustrates the deep friendship between the two mathematicians:

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

Education and career

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.

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 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 Königsberg. Constantin Carathéodory was one of his students there.

Work on relativity

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 $x^2 + y^2 + z^2 - c^2 t^2$ (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:

Publications

Relativity

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** English translation: " The Fundamental Equations for Electromagnetic Processes in Moving Bodies". In: The Principle of Relativity (1920), Calcutta: University Press, 1–69.
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** 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 (free ebook).

Diophantine approximations

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Mathematical (posthumous)

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* 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

References

External links

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Archival collections

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

{{DEFAULTSORT:Minkowski, Hermann

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