Hermann Minkowski.

Hermann Minkowski (June 22, 1864 – January 12, 1909 in Göttingen) was a German mathematician who developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. Download high resolution version (801x948, 47 KB) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Download high resolution version (801x948, 47 KB) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... June 22 is the 173rd day of the year (174th in leap years) in the Gregorian Calendar, with 192 days remaining. ... 1864 (MDCCCLXIV) was a leap year starting on Friday (see link for calendar) of the Gregorian calendar or a leap year starting on Sunday of the 12-day-slower Julian calendar. ... January 12 is the 12th day of the year in the Gregorian calendar. ... 1909 (MCMIX) was a common year starting on Friday (see link for calendar). ... Göttingen ( ) is a city in Lower Saxony, Germany. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n-dimensional space. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ... Two-dimensional analogy of space-time distortion described in General Relativity. ...

Early life and education

Hermann Minkowski was born in Aleksotas (a suburb of Kaunas, Lithuania) to a family of German, Polish, and Jewish descent. He was educated in Germany at the Universities of Berlin and 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. Aleksotas is a neighbourhood in the southern section of the city of Kaunas, Lithuania, on the left bank of the Neman River (Lithuanian: Nemunas). ... Location Ethnographic region AukÅ¡taitija County Kaunas County Municipality Kaunas city municipality Elderate Number of elderates 11 Coordinates General information Capital of Kaunas County Kaunas city municipality Kaunas district municipality Population (rank) 361,274 in 2005 (2nd) First mentioned 1361 Granted city rights 1408 Kaunas ( (help· info), approximate English transcription... The word Jew ( Hebrew: יהודי) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination... Berlin is the capital city and one of the sixteen states of the Federal Republic of Germany. ... Government Russia District Subdivision Russia Northwestern Federal District Kaliningrad Oblast Mayor Yuri Savenko (2005) Geographical characteristics Area  - City 215. ... 1885 (MDCCCLXXXV) is a common year starting on Thursday of the Gregorian calendar (or a common year starting on Saturday of the 12-day slower Julian calendar). ... Carl Louis Ferdinand von Lindemann (April 12, 1852 - March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i. ... Louis XIV visiting the Académie in 1671 The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. ...

Work and research

Minkowski taught at the universities of Bonn, Göttingen, Königsberg and Zurich. He was gay, real gay. He liked it up the butt At the Federal Polytechnic Institute, today the ETH Zurich, he was one of Einstein's teachers. The ETH Zurich, often called Swiss Federal Institute of Technology, is a science and technology university in the city of Zurich, Switzerland. ... The ETH Zurich, often called Swiss Federal Institute of Technology, is a science and technology university in the city of Zurich, Switzerland. ... Einstein redirects here. ...

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 mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. ... :For other senses of this word, see dimension (disambiguation). ... 1896 (MDCCCXCVI) was a leap year starting on Wednesday (see link for calendar). ... In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n-dimensional space. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...

In 1902, he joined the Mathematics Department of Göttingen and became one of the close colleagues of David Hilbert, whom he first met in Koenigsberg. Constantin Carathéodory was one of his students there. 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... David Hilbert (January 23, 1862, Wehlau, East Prussia – February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... This article or section does not cite its references or sources. ...

Relativity

By 1907 Minkowski realised that the special theory of relativity, introduced by 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 space", in which the 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. This nice representation certainly helped Einstein's quest for general relativity. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (September 21, 1908) is now famous: 1907 (MCMVII) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 13-day-slower Julian calendar). ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... Painting of Hendrik Lorentz by Arnhemensis Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist and the winner of the 1902 Nobel Prize in Physics for his work on electromagnetic radiation. ... Jules Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [][1]), was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... A pocket watch, a device used to measure time Two distinct views exist on the meaning of time. ... Space has been an interest for philosophers and scientists for much of human history. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... September 21 is the 264th day of the year (265th in leap years). ... 1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ...

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.

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Death and honours

Minkowski died suddenly of appendicitis in Göttingen. He was the brother of Oskar Minkowski (1858-1931), a well-known physician and researcher. Appendicitis, or epityphlitis, is a condition characterised by inflammation of the appendix. ... Göttingen ( ) is a city in Lower Saxony, Germany. ... Oskar Minkowski (January 13, 1858, Kaunas, Lithuania - July 18, 1931, Mecklenburg, Germany) was a famous Jewish doctor of Polish origin. ...

The asteroid 12493 Minkowski was named in his honour. 253 Mathilde, a C-type asteroid. ...

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's question mark function
• Minkowski space
• Minkowski-Steiner formula
• Minkowski's theorem

The Abraham-Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media. ... In mathematics, the Brunn-Minowski theorem (or Brunn-Minkowski inequality) is a inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. ... In mathematics, the Hasse-Minkowski theorem states that a quadratic form is isotropic globally if and only if it is everywhere isotropic locally; it is the classic local-global principle. ... Minkowski sum A + B B A In geometry, the Minkowski sum of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i. ... In fractal geometry, the Minkowski-Bouligand dimension or Minkowski dimension is a way of determining the fractal dimension of a set S in a Euclidean space , or more generally of a metric space (X,d). ... Minkowski is a lunar crater on the far side of the Moon, in the lower latitudes of the southern hemisphere. ... The Minkowski diagram is a graphical tool used in special relativity to visualize spacetime with regard to an inertial reference frame. ... Let X be a normed space, and let K be a convex subset of X, such that 0 is in the interior of K. The Minkowski functional p of K is defined on X by the mapping , . In particular, when K is the unit sphere on X, . It can be... In mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. ... Minkowski question mark function In mathematics, the Minkowski question mark function, sometimes called the slippery devils staircase, is a function, denoted ?(x), possessing various unusual fractal properties. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In mathematics, the Minkowski-Steiner formula is a formula relating the surface area and volume of compact subsets of Euclidean space. ... In mathematics, Minkowskis theorem in the geometry of numbers applies to convex symmetric sets and lattices; it relates the number of contained lattice points to the volume of such a set. ...

References

• Minkowski, H. (1896). Geometrie der Zahlen. Leipzig: Teubner.

External links

• O'Connor, John J., and Edmund F. Robertson. "Hermann Minkowski". MacTutor History of Mathematics archive.
• Hermann Minkowski at the Mathematics Genealogy Project