Georg Friedrich Bernhard Riemann 1, also proved himself a genius in the study of surfaces. He studied at Berlin and Gottingen, receiving his doctorate at the latter university in 1851. His dissertation 2 has since been recognized as a genuine contribution to the theory of functions. Three years later (1854) he became a Privatdozent in Gottingen and in 1857 became a professor 3 of mathematics in the university. His introduction of the notion of geometric order into the theory of Abelian functions, and his invention of the surfaces which bear his name, led to a great advance in the function theory. He also se forth (1854) a new system of non-Euclidean geometry 4, and wrote on partial differential equations 5, elliptic functions 6, and physics 7.

(Smith, p. 508.)