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Social choice theorem on superiority of majority voting
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function
May's_theorem
Theorem about prime numbers
In number theory, Maier's theorem is a theorem due to Helmut Maier about the numbers of primes in short intervals for which Cramér's probabilistic model
Maier's_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
In mathematics, a statement that has been proven
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
Theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Relationship between derivatives and integrals
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
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Impossibility of straightforward game forms
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
Gibbard's_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
Decision rule that selects alternatives that have a majority
even to "an aggressive culture and conflict"; however, the median voter theorem guarantees that majority-rule will tend to elect "compromise" or "consensus"
Majority_rule
Mathematical rule for inverting probabilities
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities
Bayes'_theorem
Well-quasi-ordering of finite trees
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
Kruskal's_tree_theorem
Planar maps require at most four colors
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
Four_color_theorem
DC circuit analysis technique
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
Norton's_theorem
Theorem in calculus
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
Divergence_theorem
Theorem in vector calculus
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
Stokes'_theorem
1995 publication in mathematics
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
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Every polynomial has a real or complex root
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
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Key result in Hamiltonian mechanics and statistical mechanics
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics
Liouville's theorem (Hamiltonian)
Liouville's_theorem_(Hamiltonian)
Theorem in political science
In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a one-dimensional political
Median_voter_theorem
Theorem in quantum information science
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
No-cloning_theorem
Concerns the decomposition of representations of a finite group into irreducible pieces
In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations
Maschke's_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Bound on eigenvalues
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
Gershgorin_circle_theorem
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices
Ptolemy's_theorem
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
A prime p divides a^p–a for any integer a
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
Fermat's_little_theorem
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
Result about when a matrix can be diagonalized
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
Spectral_theorem
Topics referred to by the same term
Joyal's theorem may refer to: Joyal's extension theorem Joyal's lifting theorem Joyal's completeness theorem Quasi-category § Definition – with a result
Joyal's_theorem
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
On when a family of real, continuous functions has a uniformly convergent subsequence
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence
Arzelà–Ascoli_theorem
Continuous function on an interval takes on every value between its values at the ends
In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval
Intermediate_value_theorem
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result
Bolzano–Weierstrass_theorem
Study of rational collective decision-making
and B better than C, but C is also better than A. This contrasts with May's theorem, which shows that simple majority is the optimal voting mechanism when
Social_choice_theory
About simultaneous modular congruences
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
Chinese_remainder_theorem
Conjecture on zeros of the zeta 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
Riemann_hypothesis
Description of flat one-vertex origami
theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be
Kawasaki's_theorem
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
Relates rational elliptic curves to modular forms
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
Modularity_theorem
Need to sacrifice consistency or availability in the presence of network partitions
In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide
CAP_theorem
Theorem in physics
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
Bell's_theorem
Formula for inverting a Taylor series
In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse
Lagrange_inversion_theorem
On representability of a contravariant functor on the category of connected CW complexes
In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy
Brown's representability theorem
Brown's_representability_theorem
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
On triangles inscribed in a circle with a diameter as an edge
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
Thales's_theorem
Approximation of a function by a polynomial
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
Taylor's_theorem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded
Nash_embedding_theorems
Theorem in calculus relating line and double integrals
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
Green's_theorem
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
On chains and antichains in partial orders
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
Dilworth's_theorem
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Theorem in projective geometry
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points
Pascal's_theorem
Explicitly describes the universal enveloping algebra of a Lie algebra
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
Poincaré–Birkhoff–Witt theorem
Poincaré–Birkhoff–Witt_theorem
Theorem in dimensional analysis
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
Buckingham_pi_theorem
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Algebraic expansion of powers of a binomial
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ( x
Binomial_theorem
Result in combinatorics and graph theory
mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and
Hall's_marriage_theorem
British mathematician who proved Fermat's Last Theorem
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
Andrew_Wiles
Proof assistant and programming language
Constructions), the foundational type theory originally developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source
Lean_(proof_assistant)
Conditions for switching order of integration in calculus
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
Fubini's_theorem
Mathematical theorem in the study of analysis
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly
Stone–Weierstrass_theorem
Number of intersection points of algebraic curves and hypersurfaces
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
Bézout's_theorem
Non-fiction book by Simon Singh
Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured
Fermat's_Last_Theorem_(book)
Theorem on operator interpolation
analysis, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation
Riesz–Thorin_theorem
Polynomial ideals are finitely generated
fundamental theorems on polynomials, the Nullstellensatz (zero-locus theorem) and the syzygy theorem (theorem on relations). These three theorems were the
Hilbert's_basis_theorem
Metatheorem in mathematical logic
In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly
Deduction_theorem
Theorem about the range of an analytic function
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
Picard_theorem
Theorem pertaining to the ontology of quantum mechanics
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)
Pusey–Barrett–Rudolph_theorem
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Algebraic tool for computing topological spaces' invariants
very simple patches, a theorem such as that of Mayer and Vietoris is potentially of broad and deep applicability. Walther Mayer was introduced to topology
Mayer–Vietoris_sequence
Theorem in mathematics
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is
Convolution_theorem
Product of any collection of compact topological spaces is compact
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
Tychonoff's_theorem
Generalization of the binomial theorem to other polynomials
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
Multinomial_theorem
American mathematician and historian of mathematics (1915–1977)
Ownsworth May (July 8, 1915 – December 1, 1977) was an American mathematician and historian of mathematics, who developed May's theorem. May was a prime
Kenneth_O._May
Topics referred to by the same term
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
Mazur's_theorem
Result in social choice theory
The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space
McKelvey–Schofield chaos theorem
McKelvey–Schofield_chaos_theorem
Relates the length of a median of a triangle to the lengths of its sides
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
Apollonius's_theorem
Statement in mathematical combinatorics
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)
Ramsey's_theorem
Equality of areas of a sliced disk
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
Pizza_theorem
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Theorem in differential geometry
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
Gauss–Bonnet_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Theorem in complex analysis
factorization theorem asserts that every entire function can be represented as a (possibly infinite) product involving its zeroes. The theorem may be viewed
Weierstrass factorization theorem
Weierstrass_factorization_theorem
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Process of creating equivalent circuits
connected in series, may be split into two grounded elements with corresponding impedances. There is also a dual Miller theorem with regards to impedance
Miller_theorem
Theorem in measure theory
In mathematics, the disintegration theorem is a result in measure theory and probability theory. It rigorously defines the idea of a non-trivial "restriction"
Disintegration_theorem
Theorem on extension of bounded linear functionals
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace
Hahn–Banach_theorem
Complete, full information, perfectly competitive markets are Pareto efficient
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Characterization of how many integers are prime
( x ) {\displaystyle \log _{e}(x)} . In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of prime numbers among the
Prime_number_theorem
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Topics referred to by the same term
theorem may refer to any of several theorems developed by the mathematician Kurt Gödel: Gödel's incompleteness theorems Gödel's completeness theorem Gödel's
Gödel's_theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
German mathematician
mathematical analysis and particularly for the so-called Maier's matrix method as well as Maier's theorem for primes in short intervals. He has also done important
Helmut_Maier
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