# Bernhard Riemann

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## Riemann, Bernhard

(Georg Friedrich Bernhard Riemann) (gā`ôrk frē`drĭkh bĕrn`härt rē`män), 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 analysiscomplex variable analysis,
branch of mathematics that deals with the calculus of functions of a complex variable, i.e., a variable of the form z=x+iy, where x and y are real and i=√
) 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. GaussGauss, Carl Friedrich
, born Johann Friederich Carl Gauss, 1777–1855, German mathematician, physicist, and astronomer. Gauss was educated at the Caroline College, Brunswick, and the Univ.
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.

### Bibliography

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

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En su corta vida, Bernhard Riemann (1826-1866) hizo contribuciones importantisimas al analisis matematico, inaugurando el enfoque topologico de sus problemas, ampliado y profundizado luego por Poincare; pero su aporte mas conocido y reconocido es el concepto de variedad diferenciable, introducido en su leccion inaugural de 1854, "Sobre las hipotesis en que se funda la geometria", con el proposito de ofrecer a la fisica una nocion de espacio mas general y mas flexible que la pitagorico-euclidiana que utilizaba hasta entonces.
In 1854 a German mathematician, Georg Friedrich Bernhard Riemann (1826-1866), developed another kind of non-Euclidean geometry, one in which it was impossible for any two lines to be parallel, and all lines intersected.
The Riemann hypothesis, first formulated by Bernhard Riemann in 1859, remains one of the more important open problems of contemporary mathematics.
However, Rockmore focuses most intently on Bernhard Riemann, the mathematician whose hypothesis, proposed 150 years ago, continues to puzzle and fascinate mathematicians today.
John Derbyshire Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics.

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