Bernhard Riemann

The German mathematician Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was born in Breselenz, Hanover, and died in Selasca, Italy.  In spite of his short life, he made important pioneering works in mathematical analysis, differential geometry, analytic number theoryMathworldPlanetmath and mathematical physics.  He is one of the most notable mathematicians.

In his PhD thesis in 1851, supervised by Gauss, Riemann developed the theory of functionsMathworldPlanetmath of one complex variable, the function theory, introducing among other things the surfaces which carry his name, the Riemann surfacesDlmfPlanetmath, and the Riemann sphere.  In his habilitation work Über die Hypothesen welche der Geometrie zu Grunde liegen he created the of the differential geometry, which has profoundly changed the notion of geometryMathworldPlanetmathPlanetmath, especially opening the for the non-Euclidean geometries and the of relativity.

The only work of Riemann on number theoryMathworldPlanetmath, Über die Anzahl der Primzahlen unter einer gegebenen Größe, forms together with some works of Chebyshev and Dirichlet the of analytic number theory.  It was a question of proving and sharpening the prime number theoremMathworldPlanetmath, assumed by Gauss.  Riemann applies function theory making far-reaching consequences on the distribution of primes.  In this context is born the Riemann hypothesisMathworldPlanetmath on the zeroes ( of Riemann zeta functionDlmfDlmfMathworld.

Title Bernhard Riemann
Canonical name BernhardRiemann
Date of creation 2013-03-22 18:34:21
Last modified on 2013-03-22 18:34:21
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Biography
Classification msc 01A70
Classification msc 01A55
Synonym Riemann