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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.