Overview

The German mathematician Georg Friedrich Riemann died shortly before his fortieth birthday and long before the importance of his work was truly recognized. He left the equivalent of only one volume of writings. Yet these provided the tools with which, 50 years after Riemann's death, Albert Einstein formulated his general theory of relativity.

Background

In traditional Euclidean geometry, codified in about 300 B.C., a straight line is the shortest distance between two points. Euclidean geometry is easily visualized on a two-dimensional flat surface, or plane (like a piece of paper). Spaces of any number of dimensions in which Euclidean geometry holds are called Euclidean or flat spaces.

On a curved surface, however, the shortest distance between two points is a curve called a geodesic. If the surface is spherical, the geodesic falls on an arc of a great...