Riemann, (Georg Friedrich) Bernhard 1826-66
German mathematician

Born in Breselenz, he studied in G�ttingen, where he was appointed Professor of Mathematics in 1859. His first publication (1851) was on the foundations of the theory of functions of a complex variable, including the result now known as the Riemann mapping theorem. In a later paper on Abelian functions (1857), he introduced the idea of 'Riemann surface' to deal with 'multi-valued' algebraic functions; this was to become a key concept in the development of analysis. His famous lecture in 1854, 'On the hypotheses that underlie geometry', first presented his notion of an n-dimensional curved space. These ideas were essential in the formulation of Albert Einstein's theory of general relativity, and have led to the modern theory of differentiable manifolds, which now plays a vital role in theoretical physics. Riemann's name is also associated with the zeta function, which is central to the study of the distribution of prime numbers. The 'Riemann hypothesis' is a famous unsolved problem concerning this function.