# Bernhard Riemann

Riemann, Bernhard (Georg Friedrich Bernhard Riemann)gāˈôrk frēˈdrĭkh bĕrnˈhärt rēˈmän, 1826–66, German mathematician. He studied at the universities of Göttingen and Berlin and was professor at Göttingen from 1859. His great contributions to mathematics include his work on the theory of the functions of complex variables (see complex variable analysis) and his method of representing these functions on coincident planes or sheets (Riemann surfaces). He laid the foundations of a non-Euclidean system of geometry (Riemannian geometry) representing elliptic space and generalized to *n* dimensions the work of C. F. Gauss in differential geometry, thus creating the basic tools for the mathematical expression of the general theory of relativity. Riemann also was interested in mathematical physics, particularly optics and electromagnetic theory. The Riemann zeta-function analytically encodes information about the distribution of prime numbers. The so called "Riemann hypothesis," concerning the instances in which the function's value is zero, is one of the great unsolved problems in mathematics.

See studies by J. Derbyshire (2003), M. du Sautoy (2003), and K. Sabbagh (2003).

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

#### More on *Bernhard Riemann* from Fact Monster:

- Jakob Steiner - Steiner, Jakob Steiner, Jakob , 1796–1863, Swiss mathematician. He was largely self-taught ...
- non-Euclidean geometry - non-Euclidean geometry non-Euclidean geometry, branch of geometry in which the fifth postulate of ...
- geometry: Types of Geometry - Types of Geometry Euclidean geometry, elementary geometry of two and three dimensions (plane and ...
- Louis de Branges - Biography of Louis de Branges, The deep thinker who proved the Bieberbach Conjecture in 1984
- Euclid, Greek mathematician - Euclid Euclid , fl. 300 B.C., Greek mathematician. Little is known of his life other than the fact ...