Hermann Minkowski

Hermann Minkowski ( born June 22, 1864 in Aleksotas, then Russia (now Kaunas, Lithuania), † 12 January 1909 in Göttingen ) was a German mathematician and physicist.

Minkowski was the second son of a Polish- Jewish merchant family from Lithuania who had immigrated to Germany. His older brother was the physician Oscar Minkowski, astrophysicist Rudolph Minkowski is his nephew.

Life and work

Even as a schoolboy he read Gauss, Dirichlet and Dedekind and caught the attention of the Königsberg professor Heinrich Weber.

Minkowski left the school Kaunas with a matriculation certificate as a five- year-old. Then he studied from 1880 for five semesters at the University of Konigsberg, principally by Heinrich Weber and Woldemar Voigt. Another three semesters studied Minkowski in Berlin where he attended lectures by Ernst Eduard Kummer, Leopold Kronecker, Karl Weierstrass, Hermann von Helmholtz and Gustav Robert Kirchhoff. On July 30, 1885 Minkowski received his doctorate with the thesis " Studies on quadratic forms determine the number of different forms, which contains a given genus " of the faculty of philosophy in Königsberg. His doctor father was Ferdinand von Lindemann.

As a student, he participated in 1881 in the contest of the Paris Academy in part ( it was about the proof of a formula of Eisenstein about the number of representations of a number by five squares) and received in 1883 the price ( with a special praise from Hermite ) along with Henry Smith. The latter had in 1867 given a proof, due to the relative isolation of the English mathematics at the end of the 19th century this was the mathematicians but escaped on the continent. Minkowski's dissertation continued his work rate.

In Konigsberg Minkowski friends with the faculty Adolf Hurwitz and David Hilbert, then a fellow student. The friendship with Hilbert lasted a lifetime and led to a close cooperation later in Göttingen. In 1887 Minkowski taught at the University of Bonn, where he became assistant professor in 1892, 1894 in Königsberg, and from 1896 at the Polytechnic in Zurich, where he was the colleague of his friend Hurwitz and among other things also counted Albert Einstein to his pupils. In 1897 he married Auguste Adler, with whom he had two daughters.

In 1890 he extended his geometry of numbers, which he had begun in its price work and where he pioneered. His major work, the geometry of numbers also appeared in 1896 and completely 1910th He developed and used methods of the theory of convex bodies and lattice and applied them in number theory. A key role was played by Minkowski's lattice point theorem, which he proved important theorems of algebraic number theory as Dirichlet's unit theorem and the finiteness of the class number. In 1907 he released his second large number theoretical work Diophantine approximations, in which he gave his applications geometry of numbers. By 1895, David Hilbert and Minkowski of the German Mathematical Society (DMV) were asked to write reports on number theory in a series of review articles for the annual report to the DMV, where Minkowski part of elementary number theory ( Quadratic forms, continued fractions, geometry of numbers ) should take over. Appeared then only Hilbert number report.

In 1902 he became professor in Göttingen, where he remained until his death. In Göttingen he became interested in mathematical physics and dealt with the then-current theory of the ( newly discovered ) electrons and with problems of electrodynamics.

Around 1907 Minkowski realized that the work of Hendrik Antoon Lorentz (1904 ) and Albert Einstein ( 1905) can be understood the theory of relativity in a non- Euclidean space. He suspected that space and time are connected in a four dimensional space -time continuum with each other and wrote treatises on a four-dimensional electrodynamics. Minkowski held about the 1908 sensational lecture space and time at the meeting of the German Society of Naturalists and Physicians. His ideas for the space-time continuum used Einstein, the four-dimensional approach of Minkowski faced hostile at the beginning, later in his general theory of relativity. The first, the relationship between the Lorentz transformation and a four-dimensional space with the time coordinate ict - ie the speed of light as a constant - realized was Henri Poincaré in 1905 Poincaré thereby succeeded in the basic formulation of four-vectors, but not subsequently, he pursued this line of thought. further. (See → History of special relativity )

At the age of 44 years Minkowski suffered a ruptured appendix. At this time, surgical procedures to cure the disease is not common, and his death were foreseeable. In the last hours he was still trying to complete numerous manuscripts. He has an honorary grave of the city of Berlin in the Dept. 3-A - 30 on the military road cemetery.

In Hilbert's obituary is expressed, which close friendship the two mathematicians:

The Minkowski space and the Minkowski inequality are named after him, as is the asteroid ( 12493 ) Minkowski, a moon crater and the M- matrices. At his longtime residence in Göttingen (1902-1909) in today's Planck road number 15, a memorial tablet.

Publications

• Collected Essays (Editor David Hilbert, with the assistance of Andreas Speiser and Hermann Weyl ), 2 volumes, Teubner 1911, Chelsea 1967
• H. Minkowski: geometry of numbers, first delivery, Leipzig 1896; 2 delivery, Leipzig 1910

• Letters to David Hilbert (Editor Hans Zassenhaus, L. Rüdenberg ), Springer 1973
• Minkowski, Hermann: The principle of relativity. In: Annals of Physics. 352, No. 15, 1907/1915, pp. 927-938.

• Minkowski, Hermann: The basic equations for the electromagnetic processes in moving bodies. In: News from the Society of Sciences in Göttingen, Mathematics and Physical class. 1908, pp. 53-111.

• Minkowski, Hermann: space and time, 80th Assembly of German Natural Scientists (Cologne, 1908). In: Physical review. 10, 1909, pp. 104-111.

• H. Minkowski: Diophantine approximations. An Introduction to Number Theory. Leipzig 1907, reprint: Physica -Verlag Würzburg 1961

• H. Minkowski: Selected works on number theory and geometry. With D. Hilbert's memorial speech on H. Minkowski, Göttingen 1909. ( Teubner Archive for Mathematics, Volume 12 ) Ekkehard Krätzel, Bernulf Weissbach (Eds. ), Leipzig, 1989, ISBN 3322007162nd