German mathematician whose short career reshaped analysis, geometry and number theory. His 1854 habilitation lecture, On the Hypotheses which lie at the Foundations of Geometry, founded what is now called Riemannian geometry, curved spaces of any dimension described by a metric, which became the mathematical language of Einstein's general relativity six decades later. His 1859 paper on the distribution of primes introduced the Riemann zeta function and conjectured, without proving, what is now called the Riemann Hypothesis: that all its nontrivial zeros lie on a single critical line. He died of tuberculosis at thirty nine.
Facts
BirthplaceBreselenz, Kingdom of Hanover 2 Death PlaceSelasca, Kingdom of Italy, of tuberculosis 2 Nationality / Culture Defining ContributionFounded Riemannian geometry, the mathematics of curved space later used by general relativity; conjectured the Riemann Hypothesis about the zeta function and the primes. 2 Notable WorkUeber die Hypothesen, welche der Geometrie zu Grunde liegen (1854); Ueber die Anzahl der Primzahlen unter einer gegebenen Groesse (1859) 2 Connections
Associated With
Source Manifold (Wikipedia)
Named for Bernhard Riemann and arising from his work on complex analysis in the 1850s.
Source Riemann Sphere (Wikipedia)
Riemann's 1859 paper extended the function to the complex plane and is the work the function's name commemorates.
Source Riemann Zeta Function (Wikipedia)
Attributed Works
Source Riemann Sphere (Wikipedia)
Source Wikipedia: Riemann surface
Source Riemann-Stieltjes Integral (Wikipedia)
Conjectures Posed
Source MacTutor History of Mathematics Archive
Additional Source Riemann Hypothesis (Wikipedia)Opening paragraph
In Branch
Source MacTutor History of Mathematics Archive
Source Complex Analysis (Wikipedia)
Source Differential Geometry (Wikipedia)
Source MacTutor History of Mathematics Archive
Source MacTutor History of Mathematics Archive
Namesake Of
Proofs Credited
Source Riemann-Hurwitz formula, Wikipedia
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Sources
1. Wikipedia: Bernhard Riemann
WikipediaLead section, gender referenceQuote, Lead section, gender reference
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.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statistics
Manifold (Wikipedia)
Wikimedia FoundationAssociated With: Manifold, history sectionQuote, Associated With: Manifold, history section
Riemann was the first one to do extensive work generalizing the idea of a surface to higher dimensions.
Complex Analysis (Wikipedia)
WikipediaIn Branch: Complex Analysis, History sectionQuote, In Branch: Complex Analysis, History section
Important mathematicians associated with complex numbers include Euler, Gauss, Riemann, Cauchy, Weierstrass, and many more in the 20th century.
Differential Geometry (Wikipedia)
WikipediaIn Branch: Differential Geometry, Intrinsic geometry sectionQuote, In Branch: Differential Geometry, Intrinsic geometry section
Riemann introduced the notion of a Riemannian metric and the Riemannian curvature tensor for the first time, and began the systematic study of differential geometry in higher dimensions.
Riemann Hypothesis (Wikipedia)
Wikimedia FoundationConjectures Posed: Riemann Hypothesis, Opening paragraphQuote, Conjectures Posed: Riemann Hypothesis, Opening paragraph
It was proposed by Bernhard Riemann, after whom it is named.
Riemann Zeta Function (Wikipedia)
Riemann Sphere (Wikipedia)
Wikimedia Foundation- Associated With: Riemann Sphere
Attributed Works: Riemann Sphere, Lead section
the Riemann sphere, named after Bernhard Riemann
View the Source Wikipedia: Riemann surface
Attributed Works: Riemann Surface, Lead sectionQuote, Attributed Works: Riemann Surface, Lead section
These surfaces were first studied by and are named after Bernhard Riemann.
Riemann-Stieltjes Integral (Wikipedia)
Attributed Works: Riemann-Stieltjes Integral, Lead sectionQuote, Attributed Works: Riemann-Stieltjes Integral, Lead section
the Riemann-Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann
Riemann-Hurwitz formula, Wikipedia
Proofs Credited: Riemann-Hurwitz Formula, Lead sectionQuote, Proofs Credited: Riemann-Hurwitz Formula, Lead section
the Riemann-Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz
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