Mathematician:Georg Friedrich Bernhard Riemann

Mathematician
German mathematician most famous for the Riemann Hypothesis, which is (at time of writing, early $21$st century) one of the most highly sought-after results in mathematics.

Nationality
German

History

 * Born: 17 Sept 1826, Breselenz, Hanover (now Germany)
 * 1845: Went to University of Göttingen to study theology, but soon switched to mathematics.
 * 1851: Received doctorate from Berlin University
 * 1854: Appointed Privatdozent (unpaid lecturer) at Göttingen
 * 1855: Replaced at Göttingen
 * 1859: Replaced as full professor
 * Died: 20 July 1866, Selasca, Italy

Theorems and Definitions

 * Riemann Condition
 * (Small) Riemann Function (also known as the Thomae Function or Modified Dirichlet Function)
 * Riemannian Geometry
 * Riemannian Geometry (Mathematical Branch)
 * Riemann Integral
 * Riemannian Manifold


 * Riemannian Metric
 * Pseudo-Riemannian Metric (also known as Semi-Riemannian Metric)


 * Riemann P-symbol (also known as the Papperitz symbol for )
 * Riemann Sum
 * Riemann Surface
 * Riemann Sphere
 * Riemann Zeta Function


 * Cauchy-Riemann Equations (with )
 * Riemann-Christoffel Tensor (with ), also known as Riemannian Curvature Tensor
 * Zariski-Riemann Surface (with )


 * Riemann Hypothesis
 * Riemann's Rearrangement Theorem
 * Riemann Removable Singularities Theorem
 * Riemann Uniformization Theorem


 * Grothendieck-Hirzebruch-Riemann-Roch Theorem (with, and )
 * Hirzebruch-Riemann-Roch Theorem (with and )


 * Riemann-Hilbert Problem (with )
 * Riemann-Hurwitz Formula (with )
 * Riemann-Lebesgue Lemma (with )
 * Riemann-Lebesgue Theorem (with )
 * Riemann-Roch Theorem (with )
 * Riemann-Siegel Formula (with )
 * Riemann-Siegel Integral Formula (with )
 * Riemann-von Mangoldt Formula (with )

Publications

 * 1851: Frundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse
 * 1854: Über die Hypothesen, welche der Geometrie zu Grunde liegen
 * 1925: Die Differential- und Integralgleichungen der Mechanik und Physik (with, and ) (2nd Edition: 1943)
 * 1925: Die Differential- und Integralgleichungen der Mechanik und Physik (with, and ) (2nd Edition: 1943)
 * 1925: Die Differential- und Integralgleichungen der Mechanik und Physik (with, and ) (2nd Edition: 1943)

Critical View

 * ... an extraordinary mathematician.


 * The dissertation [ of $1851$ ] submitted by Herr Riemann offers convincing evidence of the author's thorough and penetrating investigations in those parts of the subject treated in the dissertation, of a creative, active, truly mathematical mind, and of a gloriously fertile originality.

Also known as
Usually referred to as Bernhard Riemann.