Hermann Minkowski

Hermann Minkowski
Born	(1864-06-22)June 22, 1864 Aleksota, Kingdom of Poland
Died	January 12, 1909(1909-01-12) (aged 44) Göttingen, German Empire
Nationality	German
Fields	Mathematician
Institutions	University of Göttingen and ETH Zurich
Alma mater	Albertina University of Königsberg
Doctoral advisor	Ferdinand von Lindemann
Doctoral students	Constantin Carathéodory Louis Kollros Dénes Kőnig
Known for	Minkowski space Minkowski diagram

Hermann Minkowski (June 22, 1864 – January 12, 1909) was a 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)^{[citation needed]}.

Life and work

Hermann Minkowski was born in Aleksotas, a village in Kaunas Governorate, Russian Empire, now a district of Kaunas, Lithuania, to a family of Polish Jews, Rachel (née Taubmann) and Lewin Minkowski, a businessman. Minkowski later converted to Protestantism, in order to pursue his academic career. Hermann was educated in Germany at the Albertina University of Königsberg, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann. While still a student at Königsberg, in 1883 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 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.

In 1902, he joined the Mathematics Department of Göttingen and became one of the close colleagues of David Hilbert, whom he first met in Königsberg. Constantin Carathéodory was one of his students there.

Minkowski died suddenly of appendicitis in Göttingen on 12 January 1909.

Relativity

Further information: History of special relativity

By 1907 Minkowski realized that the special theory of relativity, introduced by Albert Einstein in 1905 and based on previous work of Lorentz and Poincaré, could be best understood in a four dimensional space, since known as "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 nicely 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."

Citations

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 marvelled 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 asteroid 12493 Minkowski and M-matrices are named in his honour.

Publications

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". Jahresberichte 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

See also

• 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

External links

• 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