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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
2013 film by Terry Gilliam
The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges.
The_Zero_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
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
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
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
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
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
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
Theorem in graph theory
the max-flow min-cut theorem, which is a weighted, edge version, and which in turn is a special case of the strong duality theorem for linear programs
Menger's_theorem
On distances between points on a circle
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n {\displaystyle n} points on a circle
Three-gap_theorem
All derivatives have the intermediate value property
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
Darboux's_theorem_(analysis)
American mathematician (1921–2005)
mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph
Frank_Harary
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)
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
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
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 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
Branch of mathematical combinatorics
either a blue triangle or a red triangle? It turns out that the answer is 6. See the article on Ramsey's theorem for a rigorous proof. Another way to express
Ramsey_theory
Number of times a curve wraps around a point in the plane
total number of counterclockwise turns that the object makes around the origin. When counting the total number of turns, counterclockwise motion counts
Winding_number
Theorem in real analysis
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
Rolle's_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
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
Theorem for proving more complex theorems
theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however, a lemma can also turn out
Lemma_(mathematics)
Theorem in number theory
complement forms the minor arcs. It turns out that these intervals dominate the integral, hence to prove the theorem one has to give an upper bound for
Vinogradov's_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
Ideals in a Boolean algebra can be extended to prime ideals
In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement
Boolean_prime_ideal_theorem
Describes statistically the splitting of primes in a given Galois extension of Q
mathematics, specifically in algebraic number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting
Chebotarev_density_theorem
Theorem in group theory
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
Grushko_theorem
Physics theorem
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
Virial_theorem
Mathematical group
subgroups is a permutation that swaps two corners and swaps two edges. It turns out that these generate all possible permutations, which means C p = ( A
Rubik's_Cube_group
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
Theorem in quantum mechanics
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
Gleason's_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
Counterintuitive result in probability
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
Infinite_monkey_theorem
Theorem in probability theory
Raikov’s theorem, named for Russian mathematician Dmitrii Abramovich Raikov, is a result in the probability theory. It is well known that if each of two
Raikov's_theorem
Every simple polygon with more than three vertices has at least two ears
In geometry, the two ears theorem states that every simple polygon with more than three vertices has at least two ears, vertices that can be removed from
Two_ears_theorem
Interactive theorem prover software
computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs
Proof_assistant
Foundational theorem of quantum information processing
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
No-deleting_theorem
Theorem in quantum mechanics
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
Haag'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
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
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 on polygon dissections
geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and P. Gerwien, is a theorem related to dissections of polygons
Wallace–Bolyai–Gerwien theorem
Wallace–Bolyai–Gerwien_theorem
Part of ring theory in mathematics
transfinite induction. The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zorn's lemma, which in turn is equivalent to the axiom
Krull's_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
Relation between the sides of a convex quadrilateral and its diagonals
law which in turn can be seen as generalisation of the Pythagorean theorem. Because of the latter the restatement of the Pythagorean theorem in terms of
Euler's_quadrilateral_theorem
Polyhedra are determined by surface distance
Alexandrov's theorem on polyhedra is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
Theorem constraining types of hidden-variable theories
quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon
Kochen–Specker_theorem
Theorem in probability theory
Cramér's decomposition theorem is a result in probability theory. It is well known that if random variables ξ 1 {\displaystyle \xi _{1}} and ξ 2 {\displaystyle
Cramér's decomposition theorem
Cramér's_decomposition_theorem
Gives a homomorphism from homotopy groups to homology groups
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
Hurewicz_theorem
Theorem in projective geometry
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in
Desargues's_theorem
Partial quantifier elimination for ordered fields with exponentials
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
Wilkie's_theorem
Invariance under simultaneous charge conjugation, parity transformation and time reversal
explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by
CPT_symmetry
Theorem in combinatorics
In combinatorics, the Dinitz theorem, formerly known as the Dinitz conjecture, is a statement about the extension of arrays to partial Latin squares,
Dinitz_theorem
Theorem in measure theory
functions. The theorem is named after Pierre Fatou and Henri Léon Lebesgue. If the sequence of functions converges pointwise, the inequalities turn into equalities
Fatou–Lebesgue_theorem
Foundational law of electromagnetism relating electric field and charge distributions
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
Gauss's_law
Hypothesis about intelligent agents
complex mathematics problem like the Riemann hypothesis could attempt to turn the Earth (and in principle other celestial bodies) into additional computing
Instrumental_convergence
Result in dynamical systems
Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves
Kolmogorov–Arnold–Moser theorem
Kolmogorov–Arnold–Moser_theorem
On forbidden subgraphs in planar graphs
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states
Kuratowski's_theorem
Theorem
In mathematics, more specifically in differential geometry, the de Rham theorem says that the ring homomorphism from the de Rham cohomology to the singular
De_Rham_theorem
Theorem about zeros of holomorphic functions
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle
Rouché's_theorem
Tool for measuring area
auxiliary turns counter scale. As the area outline is traced, this wheel rolls on the surface of the drawing. The operator sets the wheel, turns the counter
Planimeter
On algebraic independence of logarithms
In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms
Baker's_theorem
On degree sums and Hamiltonian cycles
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
Ore's_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
Description of flat one-vertex origami
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
Kawasaki's_theorem
Every set is smaller than its power set
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
Cantor's_theorem
Thermodynamic theorem
In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to
H-theorem
In board games that cannot end in a draw, one of the two players has a winning strategy
take alternate turns; and there is no chance element present. Zermelo has stated that there are many games of this type; however his theorem has been applied
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Continuous real function on a closed interval has a maximum and a minimum
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
Extreme_value_theorem
The group of K-rational points of an abelian variety is a finitely-generated abelian group
In mathematics, the Mordell–Weil theorem states that for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A
Mordell–Weil_theorem
Used in the summation of divergent series
In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named
Abelian and Tauberian theorems
Abelian_and_Tauberian_theorems
Statistical physics theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed-point theorem for maps of a complete
Caristi_fixed-point_theorem
2019 Mathematics book
Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other is a mathematics book on "some surprising
Finding_Ellipses
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is
Classification of finite simple groups
Classification_of_finite_simple_groups
Branch of mathematics
curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite
Calculus
Formula for number of orbits of a group action
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
Pólya_enumeration_theorem
Theorem in graph theory
The Gale–Ryser theorem is a result in graph theory and combinatorial matrix theory, two branches of combinatorics. It provides one of two known approaches
Gale–Ryser_theorem
Operation in calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
Mathematical graph theorem
Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every cubic
Petersen's_theorem
Mathematician and philosopher (1906–1978)
theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two
Kurt_Gödel
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
Theorem in dynamical system mathematics
the study of dynamical systems, the Hartman–Grobman theorem or linearization theorem is a theorem about the local behaviour of dynamical systems in the
Hartman–Grobman_theorem
Theorem that any three objects in space can be simultaneously bisected by a plane
mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space
Ham_sandwich_theorem
Temperley–Lieb algebra give representations of the braid group, which in turn often give invariants for knots. Popa, Sorin (1994), "Classification of amenable
Subfactor
Game of strategy
combinatorial game in which two players take turns removing (or "nimming") objects from distinct heaps or piles. On each turn, a player must remove at least one
Nim
On polynomial rings over fields
In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in
Hilbert's_syzygy_theorem
American actress, mathematics writer, and education advocate (born 1975)
\mathbb {Z} ^{2}} ." Their results are termed the "Chayes–McKellar–Winn theorem". Later, when Chayes was asked to comment about the mathematical abilities
Danica_McKellar
Relationship between the rational roots of a polynomial and its extreme coefficients
In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational
Rational_root_theorem
Theorem that every set can be well-ordered
In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict
Well-ordering_theorem
Result in algebraic geometry
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
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
Complex analysis theorem
The Sokhotski–Plemelj theorem (Polish spelling is Sochocki) is a theorem in complex analysis, which helps in evaluating certain integrals. The real-line
Sokhotski–Plemelj_theorem
Theorem used in quantum mechanics for angular momentum calculations
The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in
Wigner–Eckart_theorem
Fundamental combinatorial result of Ramsey theory
In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, named after Alfred W. Hales and Robert I. Jewett, that
Hales–Jewett_theorem
10th episode of the 6th season of Futurama
episode by what David X. Cohen described in an interview as a mathematical theorem proved by Keeler, who has a Ph.D. in Mathematics. The title and the story's
The_Prisoner_of_Benda
Three-dimensional analog of the Pythagorean theorem
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron
De_Gua's_theorem
Mathematical theorem
and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem can be applied to show that any primitive
Jacobson_density_theorem
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