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German mathematician (1826–1866)
Georg Friedrich Bernhard Riemann (/ˈriːmɑːn/; German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] ; 17 September 1826 – 20 July 1866) was a German mathematician
Bernhard_Riemann
Analytic function in mathematics
function over the reals in the first half of the eighteenth century. Bernhard Riemann's seminal 1859 article "On the Number of Primes Less Than a Given Magnitude"
Riemann_zeta_function
Basic integral in elementary calculus
suitably close to the limit can be used as numerical approximations. Bernhard Riemann introduced the integral in work presented to the faculty at the University
Riemann_integral
mathematician Bernhard Riemann (1826–1866) is the eponym of many things. Riemann bilinear relations Riemann conditions Riemann form Riemann function Riemann–Hurwitz
List of things named after Bernhard Riemann
List_of_things_named_after_Bernhard_Riemann
Generalization of the Riemann integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.
Riemann–Stieltjes_integral
Mathematical conjecture about zeros of L-functions
The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
One-dimensional complex manifold
Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces
Riemann_surface
Theorem in harmonic analysis
In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, states that the Fourier transform or Laplace transform of
Riemann–Lebesgue_lemma
Conjecture on zeros of the zeta function
proposed by Bernhard Riemann, after whom it is named. There is overwhelming numerical evidence for the hypothesis, but no proof is known. The Riemann hypothesis
Riemann_hypothesis
Characteristic property of holomorphic functions
Cauchy then used these equations to construct his theory of functions. Bernhard Riemann's dissertation on the theory of functions appeared in 1851. Suppose
Cauchy–Riemann_equations
Model of the extended complex plane plus a point at infinity
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the
Riemann_sphere
Approximation technique in integral calculus
a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann
Riemann_sum
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
Constants of the mathematical zeta function
s ) {\displaystyle \zeta (s)} and is named after the mathematician Bernhard Riemann. When the argument s {\displaystyle s} is a real number greater than
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Tensor field in Riemannian geometry
field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the
Riemann_curvature_tensor
Simpler variant of the Riemann zeta function
simple functional equation. The function is named in honour of Bernhard Riemann. Riemann's original lower-case "xi"-function, ξ {\displaystyle \xi } was
Riemann_xi_function
where they obtain the name invariant. They were first obtained by Bernhard Riemann in his work on plane waves in gas dynamics. Consider the set of conservation
Riemann_invariant
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
Mathematical formula
(1932) in unpublished manuscripts of Bernhard Riemann dating from the 1850s. Siegel derived it from the Riemann–Siegel integral formula, an expression
Riemann–Siegel_formula
Unconditionally convergent series converge absolutely
mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that
Riemann_series_theorem
Mathematical theorem
assumption that the boundary of U {\displaystyle U} is piecewise smooth) by Bernhard Riemann in 1851 in his PhD thesis. Lars Ahlfors wrote once, concerning the
Riemann_mapping_theorem
Mathematical problems related to differential equations
In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential
Riemann–Hilbert_problem
Concept in mathematics
Hilbert posed his twenty-first problem, referencing earlier work by Bernhard Riemann. The basic idea of this problem can be illustrated with an example:
Riemann–Hilbert correspondence
Riemann–Hilbert_correspondence
Complex vector of electromagnetic fields
physics, in particular electromagnetism, the Riemann–Silberstein vector or Weber vector named after Bernhard Riemann, Heinrich Martin Weber and Ludwik Silberstein
Riemann–Silberstein_vector
Book by John Derbyshire
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing
Prime_Obsession
Mathematical problem
A Riemann problem, named after Bernhard Riemann, is a specific initial value problem composed of a conservation equation together with piecewise constant
Riemann_problem
In mathematics, the grand Riemann hypothesis is a generalisation of both the Riemann hypothesis and the generalized Riemann hypothesis. It states that
Grand_Riemann_hypothesis
Integral transform
an iterated antiderivative of f of order α. The Riemann–Liouville integral is named for Bernhard Riemann and Joseph Liouville, the latter of whom was the
Riemann–Liouville_integral
Surname list
Riemann is a German surname. Notable people with this surname include the following: Bernhard Riemann (1826–1866), German mathematician, originator of
Riemann_(surname)
Branch of differential geometry
local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "Über die Hypothesen, welche der
Riemannian_geometry
Seven mathematical problems with a US$1 million prize for each solution
problem has been well known ever since it was originally posed by Bernhard Riemann in 1859. The Clay Institute's exposition of the problem was given by
Millennium_Prize_Problems
In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: A lattice Λ in a complex vector space Cg.
Riemann_form
Result in algebraic geometry
the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
Smooth manifold with an inner product on each tangent space
manifolds. Riemannian manifolds take their name from German mathematician Bernhard Riemann, who first conceptualized them in 1854. Formally, a Riemannian metric
Riemannian_manifold
Sum of inverse squares of natural numbers
considerably, and his ideas were taken up more than a century later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given
Basel_problem
Numerical method used to solve a Riemann problem
A Riemann solver is a numerical method used to solve a hyperbolic partial differential equation based on the solution of the corresponding Riemann problem
Riemann_solver
Conformal mapping in complex analysis
polygon. Such a map is guaranteed to exist by the Riemann mapping theorem (stated by Bernhard Riemann in 1851); the Schwarz–Christoffel formula provides
Schwarz–Christoffel_mapping
Operation in calculus
under a curve as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann later gave a rigorous definition of integrals, which is based on a
Integral
1859 mathematics paper by Bernhard Riemann
Primes Less Than a Given Magnitude") is a seminal 9-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich
On the Number of Primes Less Than a Given Magnitude
On_the_Number_of_Primes_Less_Than_a_Given_Magnitude
Mathematical function
In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as θ ( t ) = arg ( Γ ( 1 4 + i t 2 ) ) − log π 2 t {\displaystyle
Riemann–Siegel_theta_function
Topics referred to by the same term
Riemann function may refer to one of the several functions named after the mathematician Bernhard Riemann, including: Riemann zeta function Thomae's function
Riemann_function
Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann
Riemann–von_Mangoldt_formula
Study of space and shapes locally given by a convergent power series
include Riemann surfaces for algebraic functions and zeros for algebraic functions. A Riemann surface, first studied by and named after Bernhard Riemann, is
Geometric_function_theory
Property of a mathematical space
of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen
Dimension
Mathematical formula of two surfaces
In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of
Riemann–Hurwitz_formula
Concept in algebraic geometry
them Riemann manifolds or Riemann surfaces. They were named Zariski–Riemann spaces after Oscar Zariski and Bernhard Riemann by Nagata (1962) who used
Zariski–Riemann_space
Name list
American football player Bernhard Riemann (1826–1866), German mathematician Bernhard Seidenath (born 1968), German politician Bernhard Siebken (1910–1949)
Bernhard
Generalization of the hypergeometric differential equation
In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing
Riemann's differential equation
Riemann's_differential_equation
Mathematics award
International School of Mathematics in Italy. The award is named in honor of Bernhard Riemann. Established in 2019, it was first awarded to Terence Tao in 2020.
Riemann_Prize
Algebraic object with geometric applications
Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard Riemann, Elwin Bruno Christoffel, and others – as part of the absolute differential
Tensor
German polymath and scholar (1777–1855)
on his own work, some of his students, such as Richard Dedekind and Bernhard Riemann, became well-known and influential mathematicians in their own right
Carl_Friedrich_Gauss
groups. The term "manifold" comes from German Mannigfaltigkeit, by Bernhard Riemann. In English, "manifold" refers to spaces with a differentiable or topological
History of manifolds and varieties
History_of_manifolds_and_varieties
Topological space that locally resembles Euclidean space
consider special types of complex manifolds, now known as Jacobians. Bernhard Riemann further contributed to their theory, clarifying the geometric meaning
Manifold
Theorem in geometric topology
precluding an easy resolution of the Poincaré conjecture. In the 1800s, Bernhard Riemann and Enrico Betti initiated the study of topological invariants of manifolds
Poincaré_conjecture
differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published
Riemann's_minimal_surface
t ) , {\displaystyle P(t)=\prod _{i=1}^{2g}(1-\omega _{i}t)\ ,} the Riemann hypothesis for curves over finite fields states | ω i | = q 1 / 2 . {\displaystyle
Local_zeta_function
Branch of mathematics
his student, Bernhard Riemann in his Habilitationsschrift, On the hypotheses which lie at the foundation of geometry. In this work Riemann introduced the
Differential_geometry
Tensor index notation for tensor-based calculations
twentieth century. The basis of modern tensor analysis was developed by Bernhard Riemann in a paper from 1861. A component of a tensor is a real number that
Ricci_calculus
Comune in Piedmont, Italy
until her death on 15 April 2017 Daniele Ranzoni (1843-1889), artist Bernhard Riemann (1826–1866), mathematician Giovanni Domenico Zucchinetti, organist
Verbania
Crater on the Moon
the surface. This crater is named after German mathematician G. F. Bernhard Riemann (1826–1866). By convention these features are identified on lunar maps
Riemann_(crater)
Sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n
work was extended into the complex plane by Bernhard Riemann in 1859, leading directly to the celebrated Riemann hypothesis about the distribution of prime
Harmonic_number
functional equation of the Dedekind eta function, in a commentary to Bernhard Riemann's collected papers.. They have subsequently been much studied in number
Dedekind_sum
Characterization of how many integers are prime
la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is
Prime_number_theorem
Use of a Dirichlet series expansion to calculate the complex function
Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations
Proof of the Euler product formula for the Riemann zeta function
Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function
German mathematician
studying under Wilhelm Eduard Weber, but also attending lectures by Bernhard Riemann. After three terms in Göttingen, Roch went to the University of Berlin
Gustav_Roch
Geometric space whose points represent algebro-geometric objects of some fixed kind
as spaces of objects. A variant of moduli spaces is formal moduli. Bernhard Riemann first used the term "moduli" in 1857. Every point of a moduli space
Moduli_space
German mathematician (1805–1859)
especially Richard Dedekind and Bernhard Riemann. After moving to Göttingen he was able to obtain a small annual stipend for Riemann to retain him in the teaching
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Meromorphic function on the complex plane
Leonhard Euler (which is now known as the Riemann zeta function). Most notably, the mathematicians Bernhard Riemann (1826–1866), Richard Dedekind (1831–1916)
L-function
Infinitely detailed mathematical structure
functions in the 19th century by the seminal work of Bernard Bolzano, Bernhard Riemann, and Karl Weierstrass, and on to the coining of the word fractal in
Fractal
Algebraic operation on coordinate vectors
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Dot_product
German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian
History_of_mathematics
Bertrand (1822–1900) Delfino Codazzi (1824–1873) – differential geometry Bernhard Riemann (1826–1866) – elliptic geometry (a non-Euclidean geometry) and Riemannian
List_of_geometers
Mathematics of smooth surfaces
the emergence of the concepts of Riemannian manifold initiated by Bernhard Riemann in the mid-nineteenth century and of connection developed by Tullio
Differential geometry of surfaces
Differential_geometry_of_surfaces
Function that is continuous everywhere but differentiable nowhere
function. While Bernhard Riemann strongly claimed that the function is differentiable nowhere, no evidence of this was published by Riemann, and Weierstrass
Weierstrass_function
Differentiable manifold with nondegenerate metric tensor
In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is
Pseudo-Riemannian_manifold
In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function
Measurable Riemann mapping theorem
Measurable_Riemann_mapping_theorem
Branch of mathematics
distinct area of study in the work of Bernhard Riemann in his study of Riemann surfaces. Work in the spirit of Riemann was carried out by the Italian school
Geometry
Geometric space
algebraic curves. The term "modulus" was introduced for this purpose by Bernhard Riemann, and means "parameter"; thus a "moduli space" means a space giving
Moduli_of_algebraic_curves
Henry David Thoreau – American naturalist and author, aged 44. 1866: Bernhard Riemann – German mathematician, aged 39. 1867: Takasugi Shinsaku — Japanese
List of deaths due to tuberculosis
List_of_deaths_due_to_tuberculosis
2D surface which extends indefinitely
venture into abstraction in geometry was followed by Felix Klein and Bernhard Riemann leading to non-Euclidean geometry and Riemannian geometry. In mathematics
Plane_(mathematics)
associated Riemann theta-function. It is therefore an algebraic subvariety of A of dimension dim A − 1. Classical results of Bernhard Riemann describe Θ
Theta_divisor
Undefined point on a holomorphic function which can be made regular
extendable over U {\displaystyle U} if such a g {\displaystyle g} exists. Riemann's theorem on removable singularities is as follows: Theorem— Let D ⊂ C {\displaystyle
Removable_singularity
Proposition in mathematics that is unproven
mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture that the non-trivial zeros of the Riemann zeta function all
Conjecture
Branch of mathematics
by Augustin-Louis Cauchy, Ludwig Schläfli, Johann Benedict Listing, Bernhard Riemann and Enrico Betti. Listing introduced the term "Topologie" in Vorstudien
Topology
Method of mathematical integration
foundation. The Riemann integral—proposed by Bernhard Riemann (1826–1866)—is a broadly successful attempt to provide such a foundation. Riemann's definition
Lebesgue_integral
German mathematician (1807–1894)
Christianity long before then. As a professor, Stern taught Gauss's student Bernhard Riemann. Stern was very helpful to Gotthold Eisenstein in formulating a proof
Moritz_Abraham_Stern
the set of algebraic numbers ( ℵ 0 {\displaystyle \aleph _{0}} ). Bernhard Riemann, at the end of his famous 1859 paper "On the Number of Primes Less
List_of_conjectures
Diagram of harmonic relations in music
Oettingen and the influential musicologist Hugo Riemann (not to be confused with the mathematician Bernhard Riemann) explored the capacity of the space to chart
Tonnetz
List of scientists who are Christians
he was an old-earth creationist who openly rejected materialism. Bernhard Riemann (1826–1866): son of a pastor, he entered the University of Göttingen
List of Christians in science and technology
List_of_Christians_in_science_and_technology
ISBN 978-0-06-093558-0. Derbyshire, John (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
specifically, the study of Riemannian manifolds. It is named after Bernhard Riemann and it features many generalizations of concepts from Euclidean geometry
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Tensor in differential geometry
Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric. In Riemannian
Ricci_curvature
Number divisible only by 1 and itself
{\displaystyle 2n} , proved in 1852 by Pafnuty Chebyshev. Ideas of Bernhard Riemann in his 1859 paper on the zeta-function sketched an outline for proving
Prime_number
French mathematician (1875–1941)
addressing Augustin-Louis Cauchy, Peter Gustav Lejeune Dirichlet, and Bernhard Riemann. Lebesgue presents six conditions which it is desirable that the integral
Henri_Lebesgue
German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian
19th_century_in_science
Series of three books by E. T. Whittaker on the history of electromagnetic theory
of the contributions made by Franz Neumann, Wilhelm Eduard Weber, Bernhard Riemann, James Prescott Joule, Hermann von Helmholtz, Lord Kelvin, Gustav Kirchhoff
A History of the Theories of Aether and Electricity
A_History_of_the_Theories_of_Aether_and_Electricity
Property of infinite series
series). Bernhard Riemann proved that a conditionally convergent series may be rearranged to converge to any value at all, including ∞ or −∞; see Riemann series
Conditional_convergence
Lasse Rempe-Gillen Theodor Reye Hans-Egon Richert Michael M. Richter Bernhard Riemann Adam Ries Willi Rinow Abraham Robinson Michael Röckner Werner Wolfgang
List_of_German_mathematicians
Branch of mathematics
the subject is still occasionally called "infinitesimal calculus". Bernhard Riemann used these ideas to give a precise definition of the integral. It was
Calculus
Algebra associated to any vector space
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Exterior_algebra
travel, tourism, insurance
BERNHARD RIEMANN
BERNHARD RIEMANN
Boy/Male
Gaelic, German, Scottish
Bear or Courageous; Bear Strong; Form of Bernard
Boy/Male
English
The Old EnglishGerman Bernard, meaning bear-hard.
Male
Gaelic
Gaelic form of French Bernard, BEARNARD means "bold as a bear."
Male
German
Variant spelling of German Leonhardt, LEONHARD means "lion-strong."
Male
English
 English form of Anglo-Saxon Beornheard, BERNARD means "bold as a bear." Compare with another form of Bernard.
Male
Italian
 Italian and Spanish form of Latin Bernardus, BERNARDO means "bold as a bear."
Girl/Female
French
Feminine of Bernard, meaning strong as a bear, or bear hard.
Boy/Male
Australian, Chinese, Danish, Dutch, Finnish, French, German, Swedish
Bear; Courageous; Brave Like a Bear
Boy/Male
German American
Brave as a bear.
Surname or Lastname
English, French, Dutch, Polish, Czech, and Slovenian
English, French, Dutch, Polish, Czech, and Slovenian : from a Germanic personal name (see Bernhard). The popularity of the personal name was greatly increased by virtue of its having been borne by St. Bernard of Clairvaux (c.1090–1153), founder and abbot of the Cistercian monastery at Clairvaux.Americanized form of German Bernhard or any of the other cognates in European languages; for forms see Hanks and Hodges 1988.The first bearer of the name in Canada was from the Lorraine region of France. He is documented in Quebec city in 1666 as Jean Bernard. He and some of his descendants bore the secondary surnames Anse and Hanse, because his original forename must have been Hans (the German equivalent of French Jean, English John). Another bearer, from La Rochelle, is documented in Quebec city in 1676; and a third, from the Poitou region of France, was also documented in Quebec city, in 1713, with the secondary surname Léveillé. Other documented secondary names are Jolicoeur, Larivière, and Lajoie.
Male
German
Variant spelling of Old High German Bernhard, BERNHARDT means "bold as a bear."
Surname or Lastname
English
English : variant of Bernard.
Boy/Male
American, Australian, British, English, French, German
Strong as a Bear; Form of Bernard; Grim Bear; Bear; Courageous
Surname or Lastname
English
English : from the Old English personal name Burgheard (see Burkett).Dutch and German : variant of Burkhardt.Thomas Burchard came from London, England, to MA in 1635 aboard the True Love, and by 1652 he was in Edgartown on Martha’s Vineyard.
Girl/Female
Australian, French, German, Italian
Feminine of Bernard
Male
French
 Norman French form of Old High German Bernhard, BERNARD means "bold as a bear." Compare with another form of Bernard.
Boy/Male
German
Brave as a bear.
Female
French
Feminine form of French Bernard, BERNARDE means "bold as a bear."
Boy/Male
British, English
The Old English Variant of the German Bernard
Male
German
Contracted form of German Reginhard, REINHARD means "wise and strong."
BERNHARD RIEMANN
BERNHARD RIEMANN
BERNHARD RIEMANN
BERNHARD RIEMANN
BERNHARD RIEMANN
BERNHARD RIEMANN
BERNHARD RIEMANN
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