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=√
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) 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.
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 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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49) that the mapping of the real root singularities corresponding to the Stoneley waves onto the d-plane will locate them in the upper half of the d-plane, while the mapping of the complex root singularities corresponding to the leaky waves onto the d-plane will never occur on the top Riemman sheet of the d-plane.
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