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 Gauss at Göttingen
• 1859: Replaced Dirichlet 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
• Riemann P-symbol (also known as the Papperitz symbol for Erwin Papperitz)
• Riemann Sum
• Riemann Surface
• Riemann Sphere
• Riemann Zeta Function

• Riemann-Christoffel Tensor (with Elwin Bruno Christoffel), also known as Riemannian Curvature Tensor
• Zariski-Riemann Surface (with Oscar Zariski)

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

• Cauchy-Riemann Equations (with Augustin Louis Cauchy)
• Grothendieck-Hirzebruch-Riemann-Roch Theorem (with Alexander Grothendieck, Friedrich Hirzebruch and Gustav Roch)
• Hirzebruch-Riemann-Roch Theorem (with Friedrich Hirzebruch and Gustav Roch)

• Riemann-Hilbert Problem (with David Hilbert)
• Riemann-Hurwitz Formula (with Adolf Hurwitz)
• Riemann-Lebesgue Lemma (with Henri Léon Lebesgue)
• Riemann-Lebesgue Theorem (with Henri Léon Lebesgue)
• Riemann-Roch Theorem (with Gustav Roch)
• Riemann-Siegel Formula (with Carl Ludwig Siegel)
• Riemann-Siegel Integral Formula (with Carl Ludwig Siegel)
• Riemann-von Mangoldt Formula (with Hans Carl Friedrich von Mangoldt)

• Pseudo-Riemannian Metric (also known as Semi-Riemannian Metric

Results named for Georg Friedrich Bernhard Riemann can be found here.

Definitions of concepts named for Georg Friedrich Bernhard Riemann can be found here.

Publications

• 1851: Frundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse
• 1854: Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe
• 1854: Ueber die Hypothesen, welche der Geometrie zu Grande liegen
• 1859: Ueber die Anzahl der Primzahlen under einer gegebenen Grösse
• 1925: Die Differential- und Integralgleichungen der Mechanik und Physik (with Philipp Frank, Richard von Mises and Heinrich Weber) (2nd Edition: 1943)

Critical View

... an extraordinary mathematician.

-- Salomon Bochner

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.

-- Carl Friedrich Gauss

Also known as

Usually referred to as Bernhard Riemann.

Sources

• John J. O'Connor and Edmund F. Robertson: "Georg Friedrich Bernhard Riemann": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{XXVI}$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Riemann, Georg Friedrich Bernhard (1826-66)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.32$: Riemann ($\text {1826}$ – $\text {1866}$)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Riemann, Georg Friedrich Bernhard (1826-66)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Riemann, Georg Friedrich Bernhard (1826-66)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Riemann, (Georg Friedrich) Bernhard (1826-66)