Riemann was born in Breselenz, and educated at the universities of Göttingen and Berlin. His doctoral thesis, "Foundations for a General Theory of Functions of a Complex Variable," submitted in 1851, was an outstanding contribution to function theory. It became a classic of mathematics, and its results were incorporated into Albert Einstein's relativistic theory of gravitation. From 1857 until his death he was professor of mathematics at the University of Göttingen.

Riemann developed the subjects of partial differential equations, complex variable theory, differential geometry, and analytic number theory and laid the foundations for modern topology.

The significance of Riemannian geometry lies in its use and extension of both Euclidean geometry and the geometry of surfaces, leading to a number of generalized differential geometries. Its most important effect was that it made a geometrical application possible for some major abstractions of tensor analysis, leading to the pattern and concepts for general relativity later used by Albert Einstein in developing his theory of relativity. Riemannian geometry is also necessary for treating electricity and magnetism in the framework of general relativity.

His profound conjecture (the Riemann hypothesis) about the behavior of the zeta (or Riemann) function, which he showed determines the distribution of the prime numbers, has resisted proof since its publication in 1857.

Riemann's ideas concerning geometry of space had a profound effect on the development of modern theoretical physics and provided the concepts and methods used later in relativity theory. He was an original thinker and a host of methods, theorems and concepts are named after him.

Back to "Forgotten Pivots" page.