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 analysis complex 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=−1 (see number ).
..... Click the link for more information. ) 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 Gauss, Carl Friedrich (kärl frē`drĭkh gous)
..... Click the link for more information. 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).

Riemann, (Georg Friedrich) Bernhard

(born Sept. 17, 1826, Breselenz, Hanover—died July 20, 1866, Selasca, Italy) German mathematician. He studied at the Universities of Berlin and Göttingen and later taught principally at Göttingen. His dissertation (1851) was on function theory. He became convinced that mathematical theory could link magnetism, light, gravitation, and electricity and suggested field theories, in which the space surrounding electrical charges may be mathematically described. While continuing to develop unifying mathematical themes in the laws of physics, he created Riemannian geometry (or elliptic geometry), which proved essential to Albert Einstein's model of space-time in relativity theory. Riemann surfaces, Riemann integrals, and Riemann curvature, among other concepts, contributed to the understanding of curves and surfaces, as well as of calculus. With Carl Friedrich Gauss, Riemann helped establish Göttingen's reputation as a world leader in mathematical research. His work widely influenced geometry and analysis.