When1: 1854
When2: 1859
Who: Georg Bernhard Riemann [Riemann, Georg Bernhard]
What: mathematician
Where: Germany
works\ On the hypotheses that lie at the foundations of geometry [1854]; Theory of Abelian functions [1857]; On the number of primes less than given magnitude [1859]
Detail: He lived 1826 to 1866. He studied non-Euclidean geometry, differential geometry, complex functions, multiple-valued functions, mapping, prime-number theorems, analytic number theory, and singularities. He invented Riemann surfaces, Riemann-Darboux integral, Riemann zeta function, Riemann mapping theorem, and Riemann hypothesis. Riemann integrals are sums over infinity of step functions. All closed line segments have the same number of points. All points, in plane touching Riemann sphere at South Pole, map to sphere points, with points at infinity mapping to North Pole. Compact-plane points can thus map to limited, closed, and bounded surfaces.
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Date Modified: 2022.0224