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German mathematician who studied mathematics under Gauss and physics under Wilhelm Weber.
Riemann did important work in geometry,  complex analysis, and mathematical physics.
He was also a friend of Dedekind, who was later Riemann's biographer. In his thesis, Riemann urged a global view
of geometry as a study of manifolds of any number of
dimensions in any kind of space. He defined space by a metric
Riemann's work laid the foundations on which general relativity  was built. He investigated the
Riemann zeta function, about which he stated the famous (and still not completely proven)
Riemann hypothesis. He also refined the definition of the integral, invented
Riemann surfaces, and invented a function which was discontinuous at an infinite
number of points in an interval, but the integral of which still existed (Segal 1978). In Über eine
Frage der Wärmeleitung, Riemann developed the theory of quadratic forms.
Riemann maintained that the transmission of electricity not was instantaneous, but occurred through the
luminiferous ether at the speed of light.
Riemann died of tuberculosis at the tragically early age 39.
Additional biographies: MacTutor (St. Andrews)
Bell, E. T. "Anima Candida: Riemann." Ch. 26 in
Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré.
New York: Simon and Schuster, pp. 484-509, 1986.
Frank, P.; Mises, R. von; Weber, H.; and Riemann, B. Die Differential- und Integralgleichungen der Mechanik und Physik, 2. verm. Aufl., 2 vols.
New York: Mary S. Rosenberg, 1943.
Monastyrsky, M. Riemann, Topology, and Physics, 2nd ed. New York: Springer-Verlag, 1999.
Riemann, B. Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass, hrsg. unter Mitwirkung von R. Dedekind und H. Weber, 2. Aufl.
Leipzig, Germany: Teubner, 1892.
Segal, S. "Riemann's Example of a Continuous 'Nondifferentiable' Function Continued." Mathematical Intelligencer 1, 81-82, 1978.
Weber, H. and Riemann, B.
Die partiellen Differential-Gleichungen der mathematischen Physik nach Riemanns Vorlesungen, 6. unveranderte Aufl., 2 vols.
Braunschweig, Germany: Vieweg, 1919.
© 1996-2007 Eric W. Weisstein
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