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 theory 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 functions of one complex variable, the function theory, introducing among other things the surfaces which carry his name, the Riemann surfaces, 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 geometry, especially opening the for the non-Euclidean geometries and the http://en.wikipedia.org/wiki/Theory_of_relativitytheory of relativity.

The only work of Riemann on number theory, 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 theorem, assumed by Gauss.  Riemann applies function theory making far-reaching consequences on the distribution of primes.  In this context is born the Riemann hypothesis on the zeroes (http://planetmath.org/ZeroOfAFunction) of Riemann zeta function.