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mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a...

Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities...

In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide...

Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with...

algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ⁠ ( x...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a...

In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions,...

In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions...

The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals...

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle...

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices...

In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating...

Marguerite's Theorem (French: Le Théorème de Marguerite) is 2023 French-Swiss drama film co-written and directed by Anna Novion [fr]. It is about a female...

Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that...

In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree...

geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because...

Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex...

In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges....

question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle...

In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)...

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid...

In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

Mazur's theorem may refer to: Ascoli–Mazur theorem, or Mazur's theorem, a corollary of the Hahn–Banach separation theorem in functional analysis Mazur's...

Separation theorem may refer to several theorems in different fields. Fisher separation theorem (corporation theory) - asserts that the objective of a...

Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to an + bn = cn...

stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources...

In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map...

compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important...

In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given...

In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:...

segment theorem. Ptolemy's theorem. The Milne-Thomson circle theorem in fluid dynamics. Five circles theorem Six circles theorem Seven circles theorem Gershgorin...

Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. It...

Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be...

Morton's theorem is a poker principle articulated by Andy Morton in a Usenet poker newsgroup. It states that in multi-way pots, a player's expectation...

Joyal's theorem may refer to: Joyal's extension theorem Joyal's lifting theorem Joyal's completeness theorem Quasi-category § Definition – with a result...

mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph....

In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative...

Thompson replacement theorem is a theorem about the existence of certain abelian subgroups of a p-group. The Glauberman replacement theorem is a generalization...

In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of...

derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem. If a real function...

hypothesis is true, then the theorem is true. If the generalized Riemann hypothesis is false, then the theorem is true. Thus, the theorem is true!! Care should...

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly...

In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from...

specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow...

Several theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the...

Sylvester's theorem or the Sylvester theorem may refer to any of several theorems named after James Joseph Sylvester: The Sylvester–Gallai theorem, on the...

mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality...

Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant...

equilibrium Lyapunov central limit theorem, variant of the central limit theorem Lyapunov vector-measure theorem, theorem in measure theory that the range...

In number theory, Proth's theorem is a theorem which forms the basis of a primality test for Proth numbers known as Proth's test. Proth numbers, sometimes...

In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations...

Tutte's theorem may refer to several theorems of W. T. Tutte, including: Tutte's theorem on Hamiltonian cycles, the existence of Hamiltonian cycles in...

In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain...

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...

In computability theory, the UTM theorem, or universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions...

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes or a prime and a semiprime...

known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,...

calculus, the squeeze theorem (also known as the sandwich theorem, the two policeman and a drunk theorem among other names) is a theorem regarding the limit...

Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems: Gromov's compactness theorem (geometry)...

mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of...

In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then...

The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will...

In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from...

probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker...

mathematical area of game theory and of convex optimization, a minimax theorem is a theorem that claims that max x ∈ X min y ∈ Y f ( x , y ) = min y ∈ Y max...

In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is...

In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of...

( x ) {\displaystyle \log _{e}(x)} . In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of prime numbers among the...

recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first...

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle...

In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about...

In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points...

mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of...

Reciprocity theorem may refer to: Quadratic reciprocity, a theorem about modular arithmetic Cubic reciprocity Quartic reciprocity Artin reciprocity Weil...

Carleson's theorem is a fundamental result in mathematical analysis establishing the (Lebesgue) pointwise almost everywhere convergence of Fourier series...

The Thomas theorem is a theory of sociology which was formulated in 1928 by William Isaac Thomas and Dorothy Swaine Thomas: If men define situations as...

Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f {\displaystyle...

The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no...

The honeycomb theorem, formerly the honeycomb conjecture, states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision...

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...

Slutsky's theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables. The theorem was...

Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This...

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic...

Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

Folkman's theorem is a theorem in mathematics, and more particularly in arithmetic combinatorics and Ramsey theory. According to this theorem, whenever...

In mathematics, Eisenstein's theorem, named after the German mathematician Gotthold Eisenstein, applies to the coefficients of any power series which...

representation theorem M. Riesz extension theorem Riesz–Thorin theorem Riesz–Fischer theorem Riesz's lemma Riesz–Markov–Kakutani representation theorem This disambiguation...

In probability theory, Maxwell's theorem (known also as Herschel-Maxwell's theorem and Herschel-Maxwell's derivation) states that if the probability distribution...

In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms...

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

Inductive Constructions), the foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source...

In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square...

In mathematics, representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract...

impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a...

In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow: Chow's theorem: Any analytic subvariety in projective space is...

mathematics, Tonelli's theorem may refer to Tonelli's theorem (measure theory), a successor of Fubini's theorem Tonelli's theorem (functional analysis)...

In mathematics, the disintegration theorem is a result in measure theory and probability theory. It rigorously defines the idea of a non-trivial "restriction"...

In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization...

mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an...

theorems associated with the name König or Kőnig: Kőnig's theorem (set theory), named after the Hungarian mathematician Gyula Kőnig. Kőnig's theorem (complex...

Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The theorem is especially...

Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram...

In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a (univariate) polynomial...

Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa. It relates to flat-foldable origami crease patterns and states...

Cauchy theorem may refer to: Cauchy's integral theorem in complex analysis, also Cauchy's integral formula Cauchy's mean value theorem in real analysis...

generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about...

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the...

In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if a > b > 0 {\displaystyle a>b>0} are coprime integers, then for any integer...

In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result...

shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular...

In the mathematical field of analysis, Dini's theorem says that if a monotone sequence of continuous functions converges pointwise on a compact space...

x ) {\displaystyle \log _{e}(x)} . In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by...

In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often...

Stone's theorem may refer to a number of theorems of Marshall Stone: Stone's representation theorem for Boolean algebras Stone–Weierstrass theorem Stone–von...

In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order...

Dirac's theorem may refer to: Dirac's theorem on Hamiltonian cycles, the statement that an n-vertex graph in which each vertex has degree at least n/2...

Higman's theorem may refer to: Hall–Higman theorem in group theory, proved in 1956 by Philip Hall and Graham Higman Higman's embedding theorem in group...

In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number...

specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal...

In algebra, Schlessinger's theorem is a theorem in deformation theory introduced by Schlessinger (1968) that gives conditions for a functor of artinian...

theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected...

as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the...

In electrodynamics, Poynting's theorem is a statement of conservation of energy for electromagnetic fields that was developed by British physicist John...

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length. It is named after...

In geometry, Stewart's theorem yields a relation between the lengths of the sides and the length of a cevian in a triangle. Its name is in honour of the...

In geometric topology, a branch of mathematics, Moise's theorem, proved by Edwin E. Moise in Moise (1952), states that any topological 3-manifold has...

The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry...

Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic...

In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number...

Ginsberg's theorem is an epigrammatic paraphrase and parody "theorem" which restates or analogizes the consequences of the four laws of thermodynamics...

Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important...

The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded...

Skorokhod's theorem may refer to: Skorokhod's embedding theorem Skorokhod's representation theorem List of things named after Anatoliy Skorokhod This disambiguation...

Wick's theorem is a method of reducing high-order derivatives to a combinatorics problem. It is named after Italian physicist Gian Carlo Wick. It is used...

In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n {\displaystyle n} points on a circle...

In mathematics, the Plancherel theorem (sometimes called the Parseval–Plancherel identity) is a result in harmonic analysis, proven by Michel Plancherel...

In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter...

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability...

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete...

Glivenko's theorem may refer to: Glivenko's theorem (probability theory) Glivenko's theorem or Glivenko's translation, a double-negation translation for...

ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ring has at least one maximal ideal. The theorem was proved in 1929 by...

In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than...

"Witt's theorem" or "the Witt theorem" may also refer to the Bourbaki–Witt fixed point theorem of order theory. In mathematics, Witt's theorem, named after...

In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit...

Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented...

computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the...

mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher. In complex analysis, the theorem states that the...

Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used...

mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur...

Komlós' theorem is a theorem from probability theory and mathematical analysis about the Cesàro convergence of a subsequence of random variables (or functions)...

Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds...

Bernstein's theorem (approximation theory) Bernstein's theorem (polynomials) Bernstein's lethargy theorem Bernstein–von Mises theorem Cantor–Bernstein theorem in...

In fluid dynamics, Squire's theorem states that of all the perturbations that may be applied to a shear flow (i.e. a velocity field of the form U = (...

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral...

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published...

In Euclidean geometry, the butterfly theorem is a classical result which can be stated as follows: Let M be the midpoint of a chord PQ of a circle, through...

Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely related theorems, which...

See also Gap theorem (disambiguation) for other gap theorems in mathematics. In computational complexity theory, the gap theorem, also known as the Borodin–Trakhtenbrot...

In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in...

Frucht's theorem is a result in algebraic graph theory, conjectured by Dénes Kőnig in 1936 and proved by Robert Frucht in 1939. It states that every finite...

In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly...

In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician...

In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the...

In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician...

In quantum mechanics, Kramers' theorem or Kramers' degeneracy theorem states that for every energy eigenstate of a time-reversal symmetric system with...

The transport theorem (or transport equation, rate of change transport theorem or basic kinematic equation or Bour's formula, named after: Edmond Bour)...

The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) is an influential element of economic theory; it forms the basis for modern thinking...

In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz...

dots and dividers) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems, such as how many...

The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently...

In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear force vectors, which keeps an object...

theorem may refer to any of several theorems developed by the mathematician Kurt Gödel: Gödel's incompleteness theorems Gödel's completeness theorem Gödel's...

Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville: In complex analysis, see Liouville's theorem (complex analysis)...

Invariance theorem may refer to: Invariance of domain, a theorem in topology A theorem pertaining to Kolmogorov complexity A result in classical mechanics...

fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus...

Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory. It concerns properties of Galois representations associated...

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

The Kantorovich theorem, or Newton–Kantorovich theorem, is a mathematical statement on the semi-local convergence of Newton's method. It was first stated...

In mathematics, the (exponential) shift theorem is a theorem about polynomial differential operators (D-operators) and exponential functions. It permits...

Recursion theorem can refer to: The recursion theorem in set theory Kleene's recursion theorem, also called the fixed point theorem, in computability...

Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states...

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf...

In mathematics, Wolstenholme's theorem states that for a prime number p ≥ 5, the congruence ( 2 p − 1 p − 1 ) ≡ 1 ( mod p 3 ) {\displaystyle {2p-1 \choose...

Poincaré theorem may refer to: Poincaré conjecture, on homeomorphisms to the sphere; Poincaré recurrence theorem, on sufficient conditions for recurrence...

In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg in 1966, is the result that sufficiently many points in Euclidean space can be...

Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl. These include the Peter–Weyl theorem Weyl's theorem on complete...

In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation...

For computer science, in statistical learning theory, a representer theorem is any of several related results stating that a minimizer f ∗ {\displaystyle...

In mathematics, Sharkovskii's theorem (also spelled Sharkovsky, Sharkovskiy, Šarkovskii or Sarkovskii), named after Oleksandr Mykolayovych Sharkovsky...

In probability theory, Isserlis's theorem or Wick's probability theorem is a formula that allows one to compute higher-order moments of the multivariate...

Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states...

In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x...

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime...

In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic...

Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime...

There are several mathematical theorems named after Ferdinand Georg Frobenius. They include: Frobenius theorem (differential topology) in differential...

In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement...

In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic...

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified...

In number theory, Rosser's theorem states that the n {\displaystyle n} th prime number is greater than n log ⁡ n {\displaystyle n\log n} , where log {\displaystyle...

In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point...

In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of...

Myers's theorem, also known as the Bonnet–Myers theorem, is a celebrated, fundamental theorem in the mathematical field of Riemannian geometry. It was...

Hilbert's theorem may refer to: Hilbert's theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian...

In mathematics, Belyi's theorem on algebraic curves states that any non-singular algebraic curve C, defined by algebraic number coefficients, represents...

Levinson's theorem is an important theorem of scattering theory. In non-relativistic quantum mechanics, it relates the number of bound states in channels...

In number theory, the Green–Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long...

Erdős–Ginzburg–Ziv theorem after its discoverers. It may also be deduced from the Cauchy–Davenport theorem. More general results than this theorem exist, such...

Suslin's theorem may refer to: The Quillen–Suslin theorem (formerly the Serre conjecture), due to Andrei Suslin. Any of several theorems about analytic...

Chasles' theorem may refer to any of several mathematical results attributed to Michel Chasles (1793–1880): Chasles' theorem (kinematics), about translation...

In the area of mathematics known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected...

In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity...

In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the...

Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that...

In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani...

Carnot's theorem or Carnot's principle may refer to: In geometry: Carnot's theorem (inradius, circumradius), describing a property of the incircle and...

In the mathematical field of mathematical analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an...

In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that...

branch of mathematics, the Goldstine theorem, named after Herman Goldstine, is stated as follows: Goldstine theorem. Let X {\displaystyle X} be a Banach...

Hurwitz's theorem can refer to several theorems named after Adolf Hurwitz: Hurwitz's theorem (complex analysis) Riemann–Hurwitz formula in algebraic geometry...

Wiener's theorem is any of several theorems named after Norbert Wiener: Paley–Wiener theorem Wiener's 1/ƒ theorem about functions with absolutely convergent...

Euclidean theorem may refer to: Any theorem in Euclidean geometry Any theorem in Euclid's Elements, and in particular: Euclid's theorem that there are...

In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class...

In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to...

Clifford's theorem may refer to: Clifford's theorem on special divisors Clifford theory in representation theory Hammersley–Clifford theorem in probability...

Theorem prover may refer to: Automated theorem prover Proof assistant, an interactive theorem prover This disambiguation page lists articles associated...

In mathematics, Favard's theorem, also called the Shohat–Favard theorem, states that a sequence of polynomials satisfying a suitable three-term recurrence...

Cartan's theorem may refer to several mathematical results by Élie Cartan: Closed-subgroup theorem, 1930, that any closed subgroup of a Lie group is a...

Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical...

Dirichlet's theorem may refer to any of several mathematical theorems due to Peter Gustav Lejeune Dirichlet. Dirichlet's theorem on arithmetic progressions...

Faltings' theorem is a result in arithmetic geometry, according to which a non-singular algebraic curve of genus greater than 1 over the field Q {\displaystyle...

Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. According to the four-color theorem, every...

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval...

Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with...

In economics, Holmström's theorem is an impossibility theorem or trilemma attributed to Bengt R. Holmström proving that no incentive system for a team...

In mathematics, Brauer's theorem, named for Richard Brauer, may refer to: Brauer's theorem on forms Brauer's theorem on induced characters (also called...

Tennenbaum's theorem, named for Stanley Tennenbaum who presented the theorem in 1959, is a result in mathematical logic that states that no countable...

In number theory, Lucas's theorem expresses the remainder of division of the binomial coefficient ( m n ) {\displaystyle {\tbinom {m}{n}}} by a prime...

n  theorem, written also as "smn-theorem" or "s-m-n theorem" (also called the translation lemma, parameter theorem, and the parameterization theorem) is...

sequential use of Bayes' theorem: as more data become available, calculate the posterior distribution using Bayes' theorem; subsequently, the posterior...

In mathematics, the subspace theorem says that points of small height in projective space lie in a finite number of hyperplanes. It is a result obtained...

theorem Kawamata–Viehweg vanishing theorem Kodaira vanishing theorem Le Potier's vanishing theorem Mumford vanishing theorem Nakano vanishing theorem...

extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees...

theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. This type of theorem imposes boundaries on...

In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier-Stieltjes transform of a positive finite Borel measure on the...

Folk theorem or folklore theorem may refer to: Mathematical folklore, theorems that are widely known to mathematicians but cannot be traced back to an...

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated...

The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering...

In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle △ABC, let the lines AO, BO, CO be drawn from the vertices to a common...

Wedderburn's theorem may refer to: Artin–Wedderburn theorem, classifying semisimple rings and semisimple algebras Wedderburn's theorem on simple rings...

The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot...

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in...

In mathematics, a classification theorem answers the classification problem: "What are the objects of a given type, up to some equivalence?". It gives...

theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which...

Leibniz theorem (named after Gottfried Wilhelm Leibniz) may refer to one of the following: Product rule in differential calculus General Leibniz rule...

The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately...

In mathematics, the Wielandt theorem characterizes the gamma function, defined for all complex numbers z {\displaystyle z} for which R e z > 0 {\displaystyle...

Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of...

Pósa's theorem, in graph theory, is a sufficient condition for the existence of a Hamiltonian cycle based on the degrees of the vertices in an undirected...

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

In general relativity, Birkhoff–Jebsen's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically...

In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that...

mathematics, the Shafarevich theorem, named for Igor Shafarevich, may refer to: Néron–Ogg–Shafarevich criterion Golod–Shafarevich theorem about class field towers...

mathematics, Kakutani's theorem may refer to: the Kakutani fixed-point theorem, a fixed-point theorem for set-valued functions; Kakutani's theorem (geometry): the...

In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under...

mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping), about...

theorem may refer to several theorems named for the American mathematician George David Birkhoff: Birkhoff's theorem (relativity) Birkhoff's theorem (electromagnetism)...

Lagrange's theorem usually refers to any of the following theorems, attributed to Joseph Louis Lagrange: Lagrange's theorem (group theory) Lagrange's theorem (number...

In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts...

Kronecker's theorem is a theorem about diophantine approximation, introduced by Leopold Kronecker (1884). Kronecker's approximation theorem had been firstly...

In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers...

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices...

In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle...

In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a one-dimensional political...

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial...

mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of...

In mathematics, a Paley–Wiener theorem is a theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier...

Jackson's theorem may refer to: Jackson networks, in queueing theory (after James R. Jackson) Jackson's inequality, in analysis (after Dunham Jackson)...

Hodge theorem may refer to: Hodge theory Hodge index theorem This disambiguation page lists mathematics articles associated with the same title. If an...

fundamental theorems on polynomials, the Nullstellensatz (zero-locus theorem) and the syzygy theorem (theorem on relations). These three theorems were the...

In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase...

The no-hair theorem, also known as the black hole uniqueness theorem, states that all stationary black hole solutions of the Einstein–Maxwell equations...

The free will theorem of John H. Conway and Simon B. Kochen states that if we have free will in the sense that our choices are not a function of the past...

In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary...

In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers...

mathematics, Nash's theorem may refer to one of the following: the Nash embedding theorems in differential geometry Nash's theorem on the existence of...

In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after...

In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures...

In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points...

Pappus's theorem may refer to: Pappus's area theorem Pappus's centroid theorem Pappus's hexagon theorem This disambiguation page lists mathematics articles...

the Poincaré Recurrence Theorem is a foundational result in both dynamical systems and statistical mechanics. The theorem is named after Henri Poincaré...

In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W....

In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of...

In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that...

In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It was first...

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there...

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations...

Cramér's theorem may refer to Cramér’s decomposition theorem, a statement about the sum of normal distributed random variable Cramér's theorem (large deviations)...

quantum chemistry, Brillouin's theorem, proposed by the French physicist Léon Brillouin in 1934, is a fundamental theorem that simplifies theoretical calculations...

In information geometry, Chentsov's theorem states that the Fisher information metric is, up to rescaling, the unique Riemannian metric on a statistical...

Tarski's theorem may refer to the following theorems of Alfred Tarski: Tarski's theorem about choice Tarski's undefinability theorem Tarski's theorem on the...

physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field of complex...

The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient...

In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite...

In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it...

Bang's theorem may refer to: The solution to Tarski's plank problem by Thøger Bang (1917–1997) A special case of Zsigmondy's theorem, on unique divisors...

In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of...

Cover's theorem is a statement in computational learning theory and is one of the primary theoretical motivations for the use of non-linear kernel methods...

generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by...

Denjoy–Luzin theorem Denjoy–Luzin–Saks theorem Denjoy–Riesz theorem Denjoy–Wolff theorem Denjoy–Young–Saks theorem Denjoy's theorem on rotation number This disambiguation...

In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's...

In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result...

In mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the...

In mathematics, the equidistribution theorem is the statement that the sequence a, 2a, 3a, ... mod 1 is uniformly distributed on the circle R / Z {\displaystyle...

In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (equivalently...

In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval...

In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics...

In mathematics, Fuglede's theorem is a result in operator theory, named after Bent Fuglede. Theorem (Fuglede) Let T and N be bounded operators on a complex...

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic...

functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz...

In Riemannian geometry, a field of mathematics, Preissmann's theorem is a statement that restricts the possible topology of a negatively curved compact...

Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family...

In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature...

the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential...

In mathematics, Busemann's theorem is a theorem in Euclidean geometry and geometric tomography. It was first proved by Herbert Busemann in 1949 and was...

In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in...

in finding these patterns in Conway's Game of Life. The Garden of Eden theorem of Moore and Myhill asserts that a cellular automaton on the square grid...

Several theorems proved by the French mathematician Claude Chevalley bear his name. Chevalley–Shephard–Todd theorem in invariant theory of finite groups...

In mathematics, the Radon–Nikodym theorem, named after Johann Radon and Otto M. Nikodym, is a result in measure theory that expresses the relationship...

In projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and...

a comparison theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is closely related to Myers' theorem, and is the key...

In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing...

In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given...

In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given...

There are several theorems known as the Helmholtz theorem: Helmholtz decomposition, also known as the fundamental theorem of vector calculus Helmholtz...

Riemann's Theorem or Riemann Theorem may refer to: Riemann's theorem on conformal mappings. Riemann's theorem on removable singularities. Riemann's theorem on...

languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and...

In cosmology, the Gurzadyan theorem, proved by Vahe Gurzadyan, states the most general functional form for the force satisfying the condition of identity...

In mathematics, Schilder's theorem is a generalization of the Laplace method from integrals on R n {\displaystyle \mathbb {R} ^{n}} to functional Wiener...

Pusey–Barrett–Rudolph (PBR) theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named)...

In mathematics, Goldie's theorem is a basic structural result in ring theory, proved by Alfred Goldie during the 1950s. What is now termed a right Goldie...

mathematics, diamond theorem may refer to: Aztec diamond theorem on tilings Diamond isomorphism theorem on modular lattices Haran's diamond theorem on Hilbertian...

dimensions. The Hales–Jewett theorem implies Van der Waerden's theorem. A theorem similar to van der Waerden's theorem is Schur's theorem: for any given c there...

In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers. It was originally proved independently in 1934...

In number theory, Størmer's theorem, named after Carl Størmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for...

In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to...

The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics...

mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space...

Brokard's theorem (also known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. It is...

Khinchin's theorem may refer to any of several different results by Aleksandr Khinchin: Wiener–Khinchin theorem Khinchin's constant Khinchin's theorem on the...

theorem. Alternatively, the requirement that det(Dφ) ≠ 0 can be eliminated by applying Sard's theorem. For Lebesgue measurable functions, the theorem...

In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose...

In mathematical logic, Craig's theorem (also known as Craig's trick) states that any recursively enumerable set of well-formed formulas of a first-order...

In higher category theory in mathematics, the pasting theorem guarantees that each pasting diagram has a uniquely defined composite that independent of...

In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such...

In probability theory, Lévy’s continuity theorem, or Lévy's convergence theorem, named after the French mathematician Paul Lévy, connects convergence in...

Nevertheless, a group of results known under the general name Jordan–Hölder theorem asserts that whenever composition series exist, the isomorphism classes...

Jacobi's theorem can refer to: Maximum power theorem, in electrical engineering The result that the determinant of skew-symmetric matrices with odd size...

In commutative algebra and algebraic geometry, Popescu's theorem, introduced by Dorin Popescu, states: Let A be a Noetherian ring and B a Noetherian algebra...

The Miller theorem refers to the process of creating equivalent circuits. It asserts that a floating impedance element, supplied by two voltage sources...

there are several finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical logic This...

representation theorem In probability theory Hahn–Kolmogorov theorem Kolmogorov extension theorem Kolmogorov continuity theorem Kolmogorov's three-series theorem Kolmogorov's...

In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence...

Kneser's theorem may refer to: Kneser's theorem (combinatorics) Kneser's theorem (differential equations) Tait–Kneser theorem This disambiguation page...

the Bondy–Chvátal theorem, which generalizes earlier results by G. A. Dirac (1952) and Øystein Ore. Both Dirac's and Ore's theorems can also be derived...

Several theorems in mathematical analysis bear the name of Giuseppe Vitali: Vitali covering theorem in the foundations of measure theory Various theorems concerning...

The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence...

In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function...

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...

In abstract algebra, Ado's theorem is a theorem characterizing finite-dimensional Lie algebras. Ado's theorem states that every finite-dimensional Lie...

In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives...

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein...

In algebraic geometry, the seesaw theorem, or seesaw principle, says roughly that a limit of trivial line bundles over complete varieties is a trivial...

In differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying...

In thermodynamics and thermal physics, the Gouy–Stodola theorem is an important theorem for the quantification of irreversibilities in an open system...

In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician...

sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising...

In mathematics, the pseudoisotopy theorem is a theorem of Jean Cerf's which refers to the connectivity of a group of diffeomorphisms of a manifold. Given...

of games on the unit square – Parthasarathy's theorem is a generalization of Von Neumann's minimax theorem. It states that a particular class of games has...

The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity...

Morley's theorem may refer to: Morley's trisector theorem, a theorem in geometry, discovered by Frank Morley Morley's categoricity theorem, a theorem in model...

sufficient regularity and decay properties is given by the Fourier inversion theorem, i.e., Inverse transform The functions f {\displaystyle f} and f ^ {\displaystyle...

In mathematics, Dieudonné's theorem, named after Jean Dieudonné, is a theorem on when the Minkowski sum of closed sets is closed. Let X {\displaystyle...

In mathematics, Birch's theorem, named for Bryan John Birch, is a statement about the representability of zero by odd degree forms. Let K be an algebraic...

mathematics, specifically in algebraic number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting...

x2) such that x1 < x2. Matiyasevich's theorem, also called the Matiyasevich–Robinson–Davis–Putnam or MRDP theorem, says: Every computably enumerable set...

In mathematics, the tameness theorem states that every complete hyperbolic 3-manifold with finitely generated fundamental group is topologically tame...

has been made in automated theorem proving in first-order logic. First-order logic also satisfies several metalogical theorems that make it amenable to...

In differential geometry, Vermeil's theorem essentially states that the scalar curvature is the only (non-trivial) absolute invariant among those of prescribed...

In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H...

mathematical economics, Topkis's theorem is a result that is useful for establishing comparative statics. The theorem allows researchers to understand...

approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [...

Campbell's theorem may refer to: Campbell's theorem (geometry), which concerns the embedding of Riemannian manifolds and is named after J. E. Campbell...

In mathematics, Marden's theorem, named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between...

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some...

theorem is a theorem on a triangle in Euclidean geometry proved by the Swiss mathematician Simon Antoine Jean L'Huilier in 1809. L'Huilier's theorem—Let...

Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves...

The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic...

In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source...

In computability theory, the Rice–Shapiro theorem is a generalization of Rice's theorem, named after Henry Gordon Rice and Norman Shapiro. It states that...

Rado's theorem or Radó's theorem may refer to: Tibor Radó's theorem (harmonic functions) Tibor Radó's theorem (Riemann surfaces) Richard Rado's theorem (Ramsey...

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative...

In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include:...

specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping...

In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω ( n ) {\displaystyle...

In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is a result used to establish bounds on the growth rates...

four major theorems which are sometimes called the four pillars of functional analysis: the Hahn–Banach theorem the open mapping theorem the closed graph...

Hegerfeldt's theorem is a no-go theorem that demonstrates the incompatibility of the existence of spatially localized discrete particles with the combination...

The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists...

existence of the interaction picture, a result now commonly known as Haag's theorem. Haag's original proof relied on the specific form of then-common field...

In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton-Dyer conjecture, a...

In mathematics, Wedderburn's little theorem states that every finite division ring is a field; thus, every finite domain is a field. In other words, for...

In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of...

Prigogine's theorem is a theorem of non-equilibrium thermodynamics, originally formulated by Ilya Prigogine. The formulation of Prigogine's theorem is: In...

Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula...

The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose...

In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}}...

The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior...

In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a...

proof of the Vitali covering theorem. The covering theorem is credited to the Italian mathematician Giuseppe Vitali. The theorem states that it is possible...

In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle...

In quantum field theory, the C-theorem states that there exists a positive real function, C ( g i , μ ) {\displaystyle C(g_{i}^{},\mu )} , depending on...

In mathematics, the annulus theorem (formerly called the annulus conjecture) states roughly that the region between two well-behaved spheres is an annulus...

the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections...

Masreliez theorem describes a recursive algorithm within the technology of extended Kalman filter, named after the Swedish-American physicist John Masreliez...

Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply...

equation, known as the equation of the circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the...

incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and consistent. Gödel's theorem applies...

h-cobordism theorem showed that (simply connected) manifolds of dimension at least 5 are much easier than those of dimension 3 or 4. The proof of the theorem depends...

A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely...

In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln ⁡...

integration. This relationship is commonly characterized (by the fundamental theorem of calculus) in the framework of Riemann integration, but with absolute...

Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since measurable...

In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph...

In mathematics, the (linear) Peetre theorem, named after Jaak Peetre, is a result of functional analysis that gives a characterisation of differential...

In the mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight...

The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The...

In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938. Every locally...

In mathematics, particularly functional analysis, James's theorem, named for Robert C. James, states that a Banach space X {\displaystyle X} is reflexive...

Bing's theorem may refer to Bing's recognition theorem Bing metrization theorem R. H. Bing This disambiguation page lists mathematics articles associated...

In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two...

smaller than c {\displaystyle c} . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its...

impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it...

In statistics and econometrics, the Frisch–Waugh–Lovell (FWL) theorem is a theorem of ordinary least squares estimators which states that estimates of...

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete...

Schmidt's theorem may refer to: Krull–Schmidt theorem Wolfgang M. Schmidt's subspace theorem This disambiguation page lists mathematics articles associated...

Beck's theorem may refer to either of two mathematical results: Beck's monadicity theorem or the Beck tripleability theorem (1964/2003), by Jonathan Mock...

In differential topology in mathematics, the Quinn theorem is a result about topological 4-manifolds. It shows the importance of the topological property...

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named...

In mathematical analysis, the Szegő limit theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. They were first proved...

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are...

It's a consequence of Gödel's completeness theorem (not to be confused with his incompleteness theorems) that a theory has a model if and only if it...

mathematical complex analysis, Schottky's theorem, introduced by Schottky (1904) is a quantitative version of Picard's theorem. It states that for a holomorphic...

In real analysis, the extreme value theorem states that if a real-valued function f {\displaystyle f} is continuous on the closed and bounded interval...

fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, the first isomorphism theorem, or just the homomorphism theorem, relates...

area of Fourier analysis, the Titchmarsh theorem may refer to: The Titchmarsh convolution theorem The theorem relating real and imaginary parts of the...

In mathematics, Sard's theorem, also known as Sard's lemma or the Morse–Sard theorem, is a result in mathematical analysis that asserts that the set of...

an analytic object to an algebraic one is a functor. The prototypical theorem relating X {\displaystyle X} and X a n {\displaystyle X^{\mathrm {an} }}...

In geometry, Jung's theorem is an inequality between the diameter of a set of points in any Euclidean space and the radius of the minimum enclosing ball...

mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a closed, oriented, smooth...

by d {\displaystyle d} is τ . {\displaystyle \tau .} Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable...

In real analysis, Darboux's theorem states that the derivative of any real-valued function of a real variable has the intermediate value property, that...

In mathematics, Hall's theorem may refer to: Hall's marriage theorem One of several theorems about Hall subgroups This disambiguation page lists mathematics...

In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result that characterizes the transformation...

Canonical Form is a characterization, or structure theorem, for complex matrices, and the spectral theorem is likewise for symmetric matrices (if real) or...

mathematics, specifically real analysis and functional analysis, the Kirszbraun theorem states that if U is a subset of some Hilbert space H1, and H2 is another...

Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian...

In mathematics, Sazonov's theorem, named after Vyacheslav Vasilievich Sazonov (Вячесла́в Васи́льевич Сазо́нов), is a theorem in functional analysis. It...

Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. This theorem was first published...