Hermann minkowski biography of williams

Alexotas, Russia [now Lithuanian S. His older brother Oskar became a famous pathologist.

Hermann minkowski biography of williams: Hermann Minkowski (22 June

Except for three semesters at the University of Berlin, he received his higher education at KOuml;nigsberg, where he became a lifelong friend of both Hilbert, who was a fellow student, and the slightly older Hurwitz, who was beginning his professorial career. The Academy was unaware that in H. Smith had published an outline of such a proof, and Smith now sent a detailed memoir developing his methods.

He was led to it by the theory of ternary quadratic forms. Not only can this argument be at once extended to spaces of arbitrary finite dimension, but Minkowski had a second highly original idea: He observed that in the preceding geometric argument, ellipses could be replaced by arbitrary convex symmetric curves and, in higher-dimensional spaces, by symmetric convex bodies.

By varying the nature of these convex bodies with extreme ingenuity polyhedrons, cylindershe immediately obtained far-reaching discoveries in many domains of number theory. If one makes a linear transformation of the space transforming the ellipsoid in a sphere, L is transformed into another lattice consisting of linear combinations with integral coefficients of three vectors.

Minkowski began the study of that difficult problem which extends to any n-dimensional space and of corresponding problems when spheres are replaced by some other type of convex set particularly polyhedrons ; they have been the subject of fruitful research ever since. He was the first to understand the importance of the notion of hyperplane of support both geometrically and analyticallyand he proved the existence of such hyperplanes at each point of the boundary of a convex body.

When the volume of this new convex body is computed, it is seen to be a homogeneous polynomial in t 1t 2t 3 and the mixed volume V K 1K 2K 3 is the coefficient of t 1 t 2 t 3 in that polynomial. Minkowski discovered remarkable relations between these new quantities and more classical notions: if K 1 is a sphere of radius 1, then V K 1KK is one third of the area of the convex surface bounding K ; and V K 1K 1K is one third of the mean value of the mean curvature of that surface.

As a beautiful application of his concepts of hyperplane of support and of mixed volumes, Minkowski showed that a convex polyhedron having a given number m of faces is determined entirely by the areas and directions of the faces, a theorem that he generalized to convex surfaces by a passage to the limit. He also determined all convex bodies having constant width.

Minkowski was always interested in mathematical physics but did not work in that field until the last years of his life, when he participated in the movement of ideas that led to the theory of relativity. Hilbert, ed. Leipzig-Berlin, Among his books are Geometrie der Zahlen Leipzig, ; 2nd ed. New York Lanehester, Relativity. Work on relativity [ edit ].

Further information: Minkowski space and Minkowski diagram. Publications [ edit ]. Relativity [ edit ].

Hermann minkowski biography of williams: Hermann Minkowski, a German mathematician, was

Diophantine approximations [ edit ]. Mathematical posthumous [ edit ]. See also [ edit ]. Notes and references [ edit ]. New York: Marshall Cavendish. ISBN Random House Webster's Unabridged Dictionary. Retrieved 6 January New York: Britannica Educational Pub. Association with Rosen Educational Services. Biographical Encyclopedia of Astronomers Online ed.

New York: Springer. Katherine Cornell University Press. Fractals: A Very Short Introduction.

Hermann minkowski biography of williams: Minkowski's original mathematical interests

Oxford University Press. A Brief History of the Philosophy of Time. Chicago, Ill. He spent three semesters at the University of Berlin, for example spending the winter semester of the academic year - 83 there. The student Minkowski soon became close friends with the newly appointed academic Hurwitz. In the Academy of Sciences Paris announced that the Grand Prix for mathematical science to be awarded in would be for a solution to the problem of the number of representations of an integer as the sum of five squares.

Eisenstein had given a formula for the number of such representations inbut he had not given a proof of the result. In fact the Academy had set a problem for the Grand Prix which had already been solved, for Henry Smith had published an outline of a proof in However the Academy were unaware of Smith 's contributions when the prize topic was set.

Eisenstein had been studying quadratic forms in n n n variables with integer coefficients at the time he published his unproved formula in but as he was already ill by this time details were never published. 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.

Smith reworked his earlier proof, adding detail and submitted that to the Academy. 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 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 inwas a continuation of this prize winning work involving his natural definition of the genus of a form. Ina 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 taught at Bonn frombeing promoted to assistant professor in Einstein was a student in several of the courses he gave and the two would later become interested in similar problems in relativity theory. Minkowski married Auguste Adler in Strasbourg in ; they had two daughters, Lily born in and Ruth born in Herman, Oskar. Herman, NicolauS.

Herman, Michelle Hermann Staudinger. Hermann von Helmholtz. Hermann von Reichenau. Hermann Walther Nernst. Hermann, Carl Heinrich. Hermann, Hans. Hermann, Imre Hermann, Iselin C. Hermann, Jakob. Hermann, Judith —. Hermann, Leo. Hermann, Roland.