Bernhard Riemann
Mathematician · 1826-1866 · Mathematics, stage 3: Meet the mathematicians
Generalised geometry to spaces of any curvature and stated the outstanding open problem about the primes.
Overview
Riemann gave a habilitation lecture at Göttingen in 1854, with Gauss in the audience, on the hypotheses that lie at the foundations of geometry. It proposed that space of any number of dimensions can be described by how distance behaves locally, with curvature varying from point to point, and it contains almost no formulas; sixty years later it was the mathematics general relativity required. He also gave the definition of the integral taught in first courses, and in an 1859 paper of under ten pages on the number of primes below a given magnitude he connected the distribution of primes to the zeros of a function on the complex plane, stating in passing the conjecture about those zeros that remains unproved and is now the best known open problem in mathematics. He died of tuberculosis at thirty-nine. Start with the 1854 lecture in translation.
Where to start reading
On the Hypotheses Which Lie at the Foundations of Geometry 1854
The habilitation lecture that introduced manifolds and intrinsic curvature in any number of dimensions. Delivered in 1854 and published in 1868.
On the Number of Primes Less Than a Given Magnitude 1859
A short paper linking the count of primes to the zeta function on the complex plane, and the source of the Riemann hypothesis.
Part of
Sources
- Bernhard Riemann MacTutor History of Mathematics
- Bernhard Riemann Wikipedia
- Millennium Prize Problems Clay Mathematics InstituteThe official statement of the Riemann hypothesis, which is one of the seven.
