Georg Friedrich Bernhard Riemann (; September 17, 1826 – July 20, 1866) was an influential
German mathematician who made lasting and revolutionary contributions to
analysis,
number theory, and
differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the
Riemann integral, and his work on
Fourier series. His contributions to
complex analysis include most notably the introduction of
Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous
1859 paper on the
prime-counting function, containing the original statement of the
Riemann hypothesis, is regarded, although it is his only paper in the field, as one of the most influential papers in
analytic number theory. Through his pioneering
contributions to differential geometry, Riemann laid the foundations of the mathematics of
general relativity.