Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, ETH Zürich, and the University of Göttingen, described variously as German, 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 Aleksotas, 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 Jewish. 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. 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. and the Minkowski cover of a curve.

In 1902, he joined the Mathematics Department of Göttingen University 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 <math>x^2 + y^2 + z^2 - c^2 t^2</math> (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

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

Mathematical (posthumous)

  • 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

Archival collections

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