Intuitive and original, Georg Friedrich Bernhard Riemann had a gift for understanding connections among apparently heterogeneous phenomena. Almost all his works proved to be the beginning of new, productive research. He anticipated the work of James Clerk Maxwell in electrodynamics, and introduced the novel concept of curvature in a two-dimensional direction, providing the non- Euclidean geometry of space necessary for Albert Einstein's theory of general relativity.

Riemann worked for many years in failing health in a university system where abject poverty was the lot of those without independent means. When he died of tuberculosis at age 40, however, he had known, worked with, and influenced the great mathematicians and physicists of his day. Riemann was shy and self-effacing and recognition for his work came slowly during his lifetime; awareness of his truly striking achievements was to come later as his work was validated and as it stimulated the...