105 relations: Abelian variety, Adolf Hurwitz, Adolf Wüllner, Albert Einstein, Alfred Clebsch, Algebraic geometry, Analytic number theory, Arnold Sommerfeld, Bible, Carl Friedrich Gauss, Carl Gustav Jacob Jacobi, Carl Wolfgang Benjamin Goldschmidt, Cauchy–Riemann equations, Christian theology, Complex analysis, Complex manifold, Crelle's Journal, Dannenberg (Elbe), David Hilbert, Detlef Laugwitz, Differential geometry, Dimension, Dirichlet's principle, Eduard Selling, Elliptic integral, Felix Klein, Ferdinand Georg Frobenius, Fourier series, General relativity, Georg Cantor, Germany, Gotthold Eisenstein, Gustav Roch, Habilitation, Hanover, Harmonic function, HarperCollins, Henri Poincaré, Hermann Schwarz, Hermann von Helmholtz, Humboldt University of Berlin, Hypergeometric function, Injective function, Italy, Jacobian variety, Jakob Steiner, Jameln, Karl Weierstrass, Kingdom of Hanover, Kingdom of Italy, ..., Lake Maggiore, Laplace's equation, Least squares, Leonhard Euler, List of things named after Bernhard Riemann, Logarithm, Lutheranism, Lyceum, Manifold, Marcus du Sautoy, Mathematical analysis, Mathematical physics, Mathematics, Moduli (physics), Monodromy matrix, Moritz Abraham Stern, Napoleonic Wars, Non-Euclidean geometry, Number theory, On the Number of Primes Less Than a Given Magnitude, Pafnuty Chebyshev, Peter Gustav Lejeune Dirichlet, Philology, Physics, Prime number, Prime number theorem, Prime Obsession, Prime-counting function, Prussia, Real analysis, Riemann curvature tensor, Riemann hypothesis, Riemann integral, Riemann mapping theorem, Riemann surface, Riemann zeta function, Riemann–Lebesgue lemma, Riemann–Roch theorem, Riemann–Stieltjes integral, Riemannian geometry, Riemannian manifold, Romans 8, Set theory, Solomon Lefschetz, Square root, Tensor, The Music of the Primes, Theorema Egregium, Theta function, Topology, Tuberculosis, Uniformization theorem, University of Göttingen, Verbania, William Kingdon Clifford. Expand index (55 more) » « Shrink index
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.
Adolf Hurwitz (26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory.
Adolf Wüllner (13 June 1835, in Düsseldorf – 6 October 1908, in Aachen) was a German physicist.
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).
Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
Arnold Johannes Wilhelm Sommerfeld, (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored a large number of students for the new era of theoretical physics.
The Bible (from Koine Greek τὰ βιβλία, tà biblía, "the books") is a collection of sacred texts or scriptures that Jews and Christians consider to be a product of divine inspiration and a record of the relationship between God and humans.
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.
Carl Wolfgang Benjamin Goldschmidt (1807–February 15, 1851) was a German astronomer, mathematician, and physicist of Jewish descent who was a professor of astronomy at the University of Göttingen.
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
Christian theology is the theology of Christian belief and practice.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
Dannenberg is a town in the district Lüchow-Dannenberg, in Lower Saxony, Germany.
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
Detlef Laugwitz (1932–2000) was a German mathematician and historian, who worked in differential geometry, history of mathematics, functional analysis, and non-standard analysis.
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.
Eduard Selling (5. November 1834 in Ansbach – 31. January 1920 in Munich) was a German mathematician and inventor of calculating machines.
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.
Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory.
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a sovereign state in central-western Europe.
Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician.
Gustav Roch (9 December 1839 – 21 November 1866) was a German mathematician who made significant contributions to the theory of Riemann surfaces in a career that ended when he died at the age of 26.
Habilitation defines the qualification to conduct self-contained university teaching and is the key for access to a professorship in many European countries.
Hanover or Hannover (Hannover), on the River Leine, is the capital and largest city of the German state of Lower Saxony (Niedersachsen), and was once by personal union the family seat of the Hanoverian Kings of the United Kingdom of Great Britain and Ireland, under their title as the dukes of Brunswick-Lüneburg (later described as the Elector of Hanover).
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R where U is an open subset of Rn that satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or.
HarperCollins Publishers L.L.C. is one of the world's largest publishing companies and is one of the Big Five English-language publishing companies, alongside Hachette, Macmillan, Penguin Random House, and Simon & Schuster.
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
Karl Hermann Amandus Schwarz (25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist who made significant contributions in several scientific fields.
The Humboldt University of Berlin (Humboldt-Universität zu Berlin, abbreviated HU Berlin), is a university in the central borough of Mitte in Berlin, Germany.
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.
In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.
Jameln is a municipality in the district Lüchow-Dannenberg, in Lower Saxony, Germany.
Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
The Kingdom of Hanover (Königreich Hannover) was established in October 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian territories after the Napoleonic era.
The Kingdom of Italy (Regno d'Italia) was a state which existed from 1861—when King Victor Emmanuel II of Sardinia was proclaimed King of Italy—until 1946—when a constitutional referendum led civil discontent to abandon the monarchy and form the modern Italian Republic.
Lake Maggiore (Lago Maggiore, literally 'Greater Lake') or Lago Verbàno (Lacus Verbanus) is a large lake located on the south side of the Alps.
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
The German mathematician Bernhard Riemann (1826–1866) is the eponym of many things.
In mathematics, the logarithm is the inverse function to exponentiation.
Lutheranism is a major branch of Protestant Christianity which identifies with the theology of Martin Luther (1483–1546), a German friar, ecclesiastical reformer and theologian.
The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe.
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Marcus Peter Francis du Sautoy (born 26 August 1965) is a British mathematician, author, and populariser of science and mathematics.
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In quantum field theory, the term moduli (or more properly moduli fields) is sometimes used to refer to scalar fields whose potential energy function has continuous families of global minima.
In mathematics, and particularly ordinary differential equations (ODEs), a monodromy matrix is the fundamental matrix of a system of ODEs evaluated at the period of the coefficients of the system.
Moritz Abraham Stern (29 June 1807 – 30 January 1894) was a German mathematician.
The Napoleonic Wars (1803–1815) were a series of major conflicts pitting the French Empire and its allies, led by Napoleon I, against a fluctuating array of European powers formed into various coalitions, financed and usually led by the United Kingdom.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
" die Anzahl der Primzahlen unter einer gegebenen " (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 10-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.
Pafnuty Lvovich Chebyshev (p) (–) was a Russian mathematician.
Johann Peter Gustav Lejeune Dirichlet (13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function.
Philology is the study of language in oral and written historical sources; it is a combination of literary criticism, history, and linguistics.
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number pi).
Prussia (Preußen) was a historically prominent German state that originated in 1525 with a duchy centred on the region of Prussia.
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk This mapping is known as a Riemann mapping.
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, is of importance in harmonic analysis and asymptotic analysis.
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles.
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
Romans 8 is the eighth chapter of the Epistle to the Romans in the New Testament of the Christian Bible.
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
Solomon Lefschetz (Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
The Music of the Primes (British subtitle: Why an Unsolved Problem in Mathematics Matters; American subtitle: Searching to Solve the Greatest Mystery in Mathematics) is a 2003 book by Marcus du Sautoy, a professor in mathematics at the University of Oxford, on the history of prime number theory.
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces.
In mathematics, theta functions are special functions of several complex variables.
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
Tuberculosis (TB) is an infectious disease usually caused by the bacterium Mycobacterium tuberculosis (MTB).
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of the three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere.
The University of Göttingen (Georg-August-Universität Göttingen, GAU, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany.
Verbania (Verbania, Verbania) is the most populous comune (municipality) and the capital city of the province of Verbano-Cusio-Ossola in the Piedmont region of northwest Italy.
William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher.
Berhardt Riemann, Bernhard Georg Friedrich Riemann, Bernhard riemann, G F Bernhard Riemann, G. Bernhard F. Riemann, G. F. B. Riemann, Georg Bernhard Riemann, Georg Friedrich Bernhard Riemann, Georg Friedrich-Bernard Riemann, Georg Riemann, Riemann, Riemann, Georg Friedrich Bernhard, Riemman, Whatever-his-first-name-is Riemann.