Bernhard Riemann
1826–1866, Breselenz, Kingdom of Hanover (now Germany), Selasca, Italy
German mathematician whose 1854 lecture on the hypotheses underlying geometry founded Riemannian geometry, and whose 1859 paper on the prime-counting function posed the Riemann hypothesis, still one of the most important open problems in mathematics.
Riemann was the son of a Lutheran minister and studied theology at Göttingen before switching, with his father's permission, to mathematics. He moved to Berlin in 1847 to study under Dirichlet, Jacobi, Steiner and Eisenstein, then returned to Göttingen to complete a doctorate supervised by Gauss in 1851 on the theory of complex variables, introducing what are now called Riemann surfaces.
For his habilitation in 1854, Riemann delivered the lecture On the Hypotheses which Lie at the Foundations of Geometry, defining what is now called a Riemannian manifold and laying the groundwork later used by Einstein for general relativity; only Gauss in the audience fully grasped its significance at the time. In 1859, on his election to the Berlin Academy, he wrote a report on the number of primes less than a given magnitude, in which he studied the zeta function as a function of a complex variable and conjectured that all its nontrivial zeros have real part 1/2 — the Riemann hypothesis. He suffered from poor health for most of his life and died of tuberculosis in Selasca, Italy, in 1866, aged 39.
Workplaces: University of Göttingen
Germany