Riemann's housekeeper threw away some of his unpublished mathematics
Bernhard Riemann, a shy pastor's son who died at 39, laid the geometric groundwork for Einstein's relativity and posed the most famous unsolved problem in mathematics. He refused to publish anything unfinished, and after his death his housekeeper discarded papers from his office. Nobody knows what insights went with them.
Riemann was born in 1826 in Breselenz, in the Kingdom of Hanover, the second of six children of a poor Lutheran minister who had fought in the Napoleonic Wars. He was frail, timid and afraid of public speaking, but astonishingly quick at calculation; at school in Lüneburg his teachers found he often outpaced them. In 1846 his father sent him to Göttingen to study theology. Once there he attended lectures by Carl Friedrich Gauss, who urged him to switch to mathematics, and with his father's blessing he did, spending two years in Berlin among teachers such as Jacobi and Dirichlet.
In 1853 Gauss asked him to prepare a qualifying lecture on the foundations of geometry. Delivered at Göttingen on 10 June 1854, it extended the geometry of curved surfaces into any number of dimensions, introducing what are now called the Riemannian metric and curvature tensor. In four dimensions, he found, ten numbers at each point suffice to describe distance and curvature however warped the space. Published only in 1868, it later provided the mathematical language of general relativity, and Riemann was the first to suggest that physical reality might need more than three or four dimensions.
His other work was just as foundational. He gave the first rigorous definition of the integral, invented Riemann surfaces to turn many-valued complex functions into single-valued ones, and in an 1859 paper on counting prime numbers stated the Riemann hypothesis, still unresolved. That paper is regarded as a founding document of analytic number theory.
Recognition and security came slowly: in 1857 he finally received a regular salary, and in 1859 he succeeded Dirichlet as head of mathematics at Göttingen. A devout Christian, he saw mathematics as a way of serving God. In 1866, fleeing the clash of Hanoverian and Prussian armies at Göttingen, he travelled to Italy and died of tuberculosis at Selasca on Lake Maggiore.
Source: Bernhard Riemann
