Search Results for Minkowski

Biographies

1. Minkowski biography
   
   • Hermann Minkowski .
     
   • Hermann Minkowski's parents were Lewin Minkowski, a businessman, and Rachel Taubmann.
     
   • Hermann was his parents' second son, the eldest being Oskar Minkowski who went on to become a famous pathologist.
     
   • Lewin and Rachel Minkowski were Germans although their son Hermann was born while they were living in Russia.
     
   • When Hermann was eight years old the family returned to Germany and settled in Konigsberg where Lewin Minkowski conducted his business.
     
   • Minkowski first showed his talent for mathematics while studying at the Gymnasium in Konigsberg.
     
   • His became close friends with Hilbert while at Konigsberg, for Hilbert was an undergraduate at the same time as Minkowski.
     
   • The student Minkowski soon became close friends with the newly appointed academic Hurwitz.
     
   • Minkowski became interested in quadratic forms early in his university studies.
     
   • Minkowski, although only eighteen years old at the time, reconstructed Eisenstein's theory of quadratic forms and produced a beautiful solution to the Grand Prix problem.
     
   • The decision was that the prize be shared between Minkowski and Smith but this was a stunning beginning to Minkowski's mathematical career.
     
   • On 2 April 1883 the Academy granted the Grand Prize in Mathematics jointly to the young Minkowski at the start of his career and the elderly Smith at the end of his.
     
   • Minkowski's doctoral thesis, submitted in 1885, was a continuation of this prize winning work involving his natural definition of the genus of a form.
     
   • In 1887, a professorship became vacant at the University of Bonn, and Minkowski applied for that position; according to the regulations of German universities, he had to submit orally to the faculty an original paper, as an Habilitationsschrift.
     
   • Minkowski presented Raumliche Anschauung und Minima positiv definiter quadratischer Formen (Spatial visualization and minima of positive definite quadratic forms) which was not published at the time but in 1991 the lecture was published in [Jahresber.
     
   • This lecture is particularly interesting, for it contains the first example of the method which Minkowski would develop some years later in his famous "geometry of numbers".
     
   • Minkowski taught at Bonn from 1887, being promoted to assistant professor in 1892.
     
   • Minkowski married Auguste Adler in Strasburg in 1897; they had two daughters, Lily born in 1898 and Ruth born in 1902.
     
   • The family left Zurich in the year that their second daughter was born for Minkowski accepted a chair at the University of Gottingen in 1902.
     
   • It was Hilbert who arranged for the chair to be created specially for Minkowski and he held it for the rest of his life.
     
   • Minkowski developed a new view of space and time and laid the mathematical foundation of the theory of relativity.
     
   • By 1907 Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space.
     
   • Minkowski worked out a four-dimensional treatment of electrodynamics.
     
   • In a paper published in 1908 Minkowski reformulated Einstein's 1905 paper by introducing the four-dimensional (space-time) non-Euclidean geometry, a step which Einstein did not think much of at the time.
     
   • But more important is the attitude or philosophy that Minkowski, Hilbert - with whom Minkowski worked for a few years - Felix Klein and Hermann Weyl pursued, namely, that purely mathematical considerations, including harmony and elegance of ideas, should dominate in embracing new physical facts.
     
   • In this view Minkowski followed Poincare whose philosophy was that mathematical physics, as opposed to theoretical physics, can furnish new physical principles.
     
   • In fact Minkowski had a major influence on Einstein as Corry points out in [Endeavor 22 (3) (1998), 95-97.',7)">7]:- .
     
   • A main motive behind this change was the influence of two prominent German mathematicians: David Hilbert and Hermann Minkowski.
     
   • We have mentioned several times in this biography that Minkowski and Hilbert were close friends.
     
   • Less well known is the fact that Minkowski actually suggested to Hilbert what he should take as the theme for his famous 1900 lecture in Paris.
     
   • Minkowski, in a letter to Hilbert written on 5 January 1900, writes:- .
     
   • Time has certainly proved Minkowski correct! .
     
   • Minkowski's original mathematical interests were in pure mathematics and he spent much of his time investigating quadratic forms and continued fractions.
     
   • Minkowski published Diophantische Approximationen: Eine Einfuhrung in die Zahlentheorie in 1907.
     
   • At the young age of 44, Minkowski died suddenly from a ruptured appendix.
     
   • Honours awarded to Hermann Minkowski .
     
   • Lunar featuresCrater Minkowski .
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Minkowski.html .
     

2. Born biography
   
   • Back in Breslau he talked to his fellow students Toeplitz and Hellinger who told him of the great teachers of mathematics, Klein, Hilbert and Minkowski, at the University of Gottingen.
     
   • Born was soon in Gottingen attending lectures by Hilbert and Minkowski.
     
   • He became Hilbert's assistant in 1905, continuing to attend lectures by Klein and Runge on elasticity and a seminar by Hilbert and Minkowski on electrodynamics.
     
   • Perhaps the most benefit he derived from his famous teachers was during walks he would make in the woods with Hilbert and Minkowski where all manner of fascinating subjects were discussed in addition to mathematics, such as problems of philosophy, problems of politics, and social problems.
     
   • His work on combining ideas of Einstein and Minkowski led to an invitation to Gottingen in 1909 and he began a collaboration with Minkowski who died only weeks after the collaboration had begun [Biographical Memoirs of Fellows of the Royal Society of London 17 (1971), 17-52.',8)">8]:- .
     

3. Hilbert biography
   
   • One of Hilbert's friends there was Minkowski, who was also a doctoral student at Konigsberg, and they were to strongly influence each others mathematical progress.
     
   • Hilbert turned down the Berlin chair, but only after he had used the offer to bargain with Gottingen and persuade them to set up a new chair to bring his friend Minkowski to Gottingen.
     
   • Insofar as the creation of new ideas is concerned, I would place Minkowski higher, and of the classical great ones, Gauss, Galois, and Riemann.
     

4. Kelly biography
   
   • This paper was published in the Bulletin of the American Mathematical Society, as was his papers On isometries of product sets of 1948 and On Minkowski bodies of constant width of 1949.
     
   • Kelly showed that this theorem went over to entire subsets of Minkowski n-space.
     

5. Hurwitz biography
   
   • Here he taught Hilbert and Minkowski, becoming a life long friend of Hilbert.
     
   • Even after Minkowski left the University of Konigsberg and went to Bonn, he still returned to Konigsberg for every vacation and joined Hurwitz and Hilbert in their almost daily walks [Proc.
     

6. Lewy biography
   
   • Among the first papers he published after emigrating to the United States were A priori limitations for solutions of Monge-Ampere equations (two papers, the first in 1935, the second two years later), and On differential geometry in the large : Minkowski's problem (1938).
     
   • Minkowski's problem is to construct a convex surface in three dimensional space that realises a given curvature as a function of the direction of the normal.
     

7. Golab biography
   
   • He was awarded the degree based on his paper Queques problemes metrique de la geometrie de Minkowski in 1932.
     
   • One can divide them into three almost equal parts; papers on the theory of geometric objects (40), papers on classical differential geometry under weak regularity assumptions (43) and papers belonging to various other domains in geometry (50) mainly connected with some special spaces such as spaces with linear or projective connection, Riemann, Minkowski and Finsler spaces, general metric spaces, etc.
     

8. Wheeler biography
   
   • There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild.
     

9. Wiener Hermann biography
   
   • Wiener was a founder member of the German Mathematical Society, as were Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber who all gave lectures at the Bremen meeting.
     

10. Smith biography
    
    • After his death the Academy awarded two full prizes, one to Smith and one to Minkowski.
      

11. Mahler biography
    
    • Other major themes of his work were rational approximations of algebraic numbers, p-adic numbers, p-adic Diophantine approximation, geometry of numbers (a term coined by Minkowski to describe the mathematics of packings and coverings) and measure on polynomials.
      

12. Sommerfeld biography
    
    • Two slightly older pupils at the same school were Minkowski and Wien.
      

13. Hsiung biography
    
    • The central themes are the Gauss-Bonnet formula and uniqueness theorems for the Minkowski and Christoffel problems.
      

14. Konig Denes biography
    
    • At Gottingen, Konig had been influenced by Minkowski's lectures on the four colour problem.
      

15. Koksma biography
    
    • One then finds a discussion of Minkowski's analysis, his 'Geometry of Numbers' and applications to homogeneous and non-homogeneous linear forms.
      

16. Landau biography
    
    • In 1909 he was appointed to an ordinary professorship at Gottingen as successor to Minkowski.
      

17. Helly biography
    
    • At Gottingen Helly studied under Hilbert, Klein, Minkowski and Runge in 1907-8.
      

18. Bliss biography
    
    • He left Minnesota in 1902 to spend a year in Gottingen where he interacted with Klein, Hilbert, Minkowski, Zermelo, Schmidt, Max Abraham and Caratheodory.
      

19. Wiltheiss biography
    
    • Wiltheiss was a founder member of the German Mathematical Society along with his colleague at Halle Hermann Wiener, as were Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber who all gave lectures at the Bremen meeting.
      

20. Noether Emmy biography
    
    • During 1903-04 she attended lectures by Blumenthal, Hilbert, Klein and Minkowski.
      

21. Janiszewski biography
    
    • Having chosen excellent centres of mathematical research at which to study he was taught by many outstanding mathematicians including Burkhardt, Hilbert, Minkowski, and Zermelo .
      

22. Fischer biography
    
    • He spent 1899 at the University of Berlin, then studied at Zurich and Gottingen with Minkowski.
      

23. Finsler biography
    
    • A Finsler space is a generalisation of a Riemannian space where the length function is defined differently and Minkowski's geometry holds locally.
      

24. Ehrenfest biography
    
    • Klein, Hilbert, Minkowski and Caratheodory were all working in Gottingen at this time and it was an important period for Ehrenfest's research.
      

25. Beckenbach biography
    
    • The book begins with a study of axiomatics, then examines several classical inequalities of analysis such as the relationship between the arithmetic mean and geometric mean, the Cauchy, Holder, and Minkowski inequalities, and the triangle inequality.
      

26. Weierstrass biography
    
    • We name a few who are mentioned elsewhere in our archive: Bachmann, Bolza, Cantor, Engel, Frobenius, Gegenbauer, Hensel, Holder, Hurwitz, Killing, Klein, Kneser, Konigsberger, Lerch, Lie, Luroth, Mertens, Minkowski, Mittag-Leffler, Netto, Schottky, Schwarz and Stolz.
      

27. Courant biography
    
    • At Gottingen Courant began by attending courses by Hilbert and Minkowski and he was also allowed to attend the joint seminar of the two mathematicians on mathematical physics.
      

28. Jarnik biography
    
    • During the decade 1939-49 he wrote a series of papers dealing with the geometry of numbers, in particular dealing with Minkowski's inequality for convex bodies.
      

29. Szekeres biography
    
    • He continued to publish on relativity with work such as Kinematic geometry: An axiomatic system for Minkowski space-time (1968).
      

30. Schwarzschild biography
    
    • In Gottingen he collaborated with Klein, Hilbert and Minkowski.
      

31. Christoffel biography
    
    • This second group, which may partly overlap with the former, would include such illustrious names as Mobius, von Staudt, Plucker, Heine, Du Bois-Reymond, Carl Neumann, Lipschitz, Fuchs, Schwarz, Hurwitz and Minkowski.
      

32. Caratheodory biography
    
    • He received his doctorate in 1904 from Gottingen University for his thesis Uber die diskontinuierlichen Losungen in der Variationsrechnung which he submitted to Hermann Minkowski.
      

33. Voronoy biography
    
    • There he met Minkowski and they discovered that they were each working on similar topics.
      

34. Stackel biography
    
    • Stackel's stay in Halle lasted until 1895 when he was called to take up the post of associate professor at the University of Konigsberg as a successor to Minkowski, who had himself recommended Stackel for the post, having been impressed by his work at Halle.
      

History Topics

1. 20th century time
   
   • On 21 September 1908 Minkowski began his famous lecture at the University of Cologne with these words:- .
     
   • Weyl quickly understood the new notion that Minkowski put forward.
     
   • Before we move on from special relativity, we must consider one aspect which seems particularly difficult in Minkowski's 4-dimensional space-time, and indeed in any version of relativity.
     

2. Special relativity
   
   • Also in 1908 Minkowski published an important paper on relativity, presenting the Maxwell-Lorentz equations in tensor form.
     Go directly to this paragraph
     

Famous Curves

Societies etc

1. German Mathematical Society
   
   • Few societies can have come into existence at a meeting at which so many leading mathematicians spoke, for at this meeting Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber all gave lectures.
     

2. BMC 1964
   
   • Rogers, C AThe Brunn-Minkowski theorem and related inequalities .
     

3. Young Mathematician prize
   
   • for works on the geometry of Minkowski spaces.
     

4. Lunar features
   

5. Lunar features
   
   • (W) (L) Minkowski .
     

6. Lunar features
   
   • Minkowski .
     

7. International Congress Speakers
   
   • Louis Joel Mordell, Minkowski's Theorems and Hypotheses on Linear Forms.
     

8. BMC 1953
   
   • Rankin, R AThe Minkowski-Hajos theorem on linear forms and the factorisation of abelian groups .
     

References

1. References for Minkowski
   
   • References for Hermann Minkowski .
     
   • H Hancock, Development of the Minkowski Geometry of Numbers (New York, 1939).
     
   • F W Lanchester, Relativity : an elementary explanation of the space-time relations as established by Minkowski, and a discusson of gravitational theory based thereon (London, 1935).
     
   • W Benz, Lorentz-Minkowski geometry, De Sitter's world and Einstein's cylinder universe, in Charlemagne and his heritage.
     
   • L Corry, Hermann Minkowski and the postulate of relativity, Arch.
     
   • L Corry, The influence of David Hilbert and Hermann Minkowski on Einstein's views over the interrelation between physics and mathematics, Endeavor 22 (3) (1998), 95-97.
     
   • L Pyenson, Hermann Minkowski and Einstein's Special Theory of Relativity : With an appendix of Minkowski's 'Funktiontheorie' manuscript, Arch.
     
   • M F Ranada, David Hilbert, Hermann Minkowski, the axiomatization of physics and the Sixth Problem (Spanish), Gac.
     
   • Zur Habilitation von Hermann Minkowski 1887 in Bonn, Jahresber.
     
   • J-P Serre, Smith, Minkowski et l'Academie des Sciences, Gaz.
     
   • T M Tonietti, Arithmetic and Arithmetisierung : Felix Klein and Hermann Minkowski (Italian), in Epistemology of mathematics.
     
   • H J Zassenhaus, On the Minkowski- Hilbert dialogue on mathematization, Canad.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Minkowski.html .
     

2. References for Smith
   
   • J-P Serre, Smith, Minkowski et l'Academie des Sciences, Gaz.
     

3. References for Rogers James
   
   • L Maligranda, Equivalence of the Holder-Rogers and Minkowski inequalities, Math.
     

Additional material

1. Born Inaugural
   
   • At that time Felix Klein was the leading figure in a group of outstanding mathematicians at Gottingen, amongst them Hilbert and Minkowski.
     
   • Minkowski has shown that it is possible to get a description of the connection of all events which is independent of the observer, or invariant, as the mathematicians say, by considering them as points in a four-dimensional continuum with a quasi-Euclidean geometry.
     
   • In the case of space and time these are the laws of the four-dimensional geometry of Minkowski.
     

2. David Hilbert: 'Mathematical Problems
   
   • As an example of an arithmetical theory operating rigorously with geometrical ideas and signs, I may mention Minkowski's work, Die Geometrie der Zahlen.
     

3. EMS 1913 Colloquium 6.html.html
   
   • Without it to bring us back to the obvious world of apparent realities we should have been floundering hopelessly in the Absolute or in Minkowski's Welt.
     

4. G H Hardy addresses the British Association in 1922
   
   • The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real.
     

5. EMS 1913 Colloquium
   
   • Without it to bring us back to the obvious world of apparent realities we should have been floundering hopelessly in the Absolute or in Minkowski's Welt.
     

6. Einstein: 'Ether and Relativity
   
   • In Minkowski's idiom this is expressed as follows:- Not every extended conformation in the four-dimensional world can be regarded as composed of world-threads.
     

7. G H Hardy addresses the British Association in 1922, Part 1
   
   • The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real.
     

Quotations

1. Quotations by Minkowski
   
   • Quotations by Hermann Minkowski .
     
   • http://www-history.mcs.st-andrews.ac.uk/Quotations/Minkowski.html .
     

2. Quotations by Einstein
   
   • This has been done elegantly by Minkowski; but chalk is cheaper than grey matter, and we will do it as it comes.
     

Chronology