# قائمة المبرهنات الرياضية

هذه هي **قائمة المبرهنات**. انظر أيضاً:

- fundamental theorem of algebra
- fundamental theorem of arbitrage-free pricing
- fundamental theorem of arithmetic
- fundamental theorem of calculus
- fundamental lemma of calculus of variations
- fundamental theorem of curves
- fundamental theorem of surfaces
- fundamental theorem of finitely generated abelian groups
- fundamental theorem of Galois theory
- fundamental theorem on homomorphisms
- fundamental theorem of linear algebra
- fundamental theorem of projective geometry
- fundamental theorem of Riemannian geometry
- fundamental theorem of vector analysis
- fundamental theorem of Linear Programming

- Summation by parts
*Abel's lemma* - Artin-Rees lemma (commutative algebra)
- Borel's lemma (partial differential equations)
- Borel-Cantelli lemma (probability theory)
- Burnside's lemma
- Covering lemma
- Dehn's lemma (geometric topology)
- Diagonalization lemma
- Dickson's lemma (combinatorics)
- Euclid's lemma
- Fatou's lemma
- Subadditive function
*Fekete's lemma* - Fitting lemma
- Five lemma
- Fixed-point lemma for normal functions
- Fodor's lemma
- Gauss's lemma
- Gödel's diagonal lemma
- Grönwall's inequality
*Grönwall's lemma* - Grothendieck lemma (differential forms)
- Handshaking lemma
- Hartogs' lemma (several complex variables)
- Hensel's lemma
- Injective module
*Injective test lemma* - Itō's lemma
- König's lemma
- Lambda lemma
- Lebesgue's number lemma (dimension theory)
- Lindelöf's lemma
- Lindenbaum's lemma
- Lovász local lemma
- Mautner's lemma (representation theory)
- Morse theory
*Morse lemma*(differential topology) - Nakayama lemma
- Newman's lemma (term rewriting)
- Neyman-Pearson lemma
- Nine lemma (homological algebra)
- Noether's normalization lemma (commutative algebra)
- Ogden's lemma
- Piling-up lemma
- Poincaré lemma of closed and exact differential forms (differential forms)
- Pumping lemma (formal languages)
*Bar-Hillel lemma* - Rasiowa-Sikorski lemma (set theory)
- Riemann lemma
- Sard's lemma (mathematical analysis, singularity theory)
- Schanuel's lemma (projective modules)
- Schreier's subgroup lemma
- Shephard's lemma
- Short five lemma (homological algebra)
- Siegel's lemma (Diophantine approximation)
- Snake lemma (homological algebra)
- Sperner's lemma (combinatorics)
- Splitting lemma (homological algebra)
- Stein's lemma (probability theory)
- Szemerédi regularity lemma (graph theory)
- Ultrafilter lemma
- Urysohn's lemma (general topology)
- Whitehead's lemma (Lie algebras)
- Yoneda lemma (category theory)
- Zassenhaus lemma (group theory)
- Zolotarev's lemma (number theory)
- Zorn's lemma (Kuratowski-Zorn lemma)

See also:

- Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators
- Unsolved problems in mathematics
- List of unsolved problems
- Millennium Prize Problems

and, for proved results,

also

for problems not subject to conventional proof nor disproof.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

## Proved (now theorems)

- Adams conjecture (J-homomorphism)
- Bieberbach conjecture (De Branges' theorem)
- Blattner's conjecture (Blattner formula)
- Catalan's conjecture (Mihailescu's theorem)
- Conway-Norton conjecture (Monstrous moonshine)
- Dinitz conjecture (Galvin's theorem)
- Dodecahedral conjecture (Hales-McLaughlin theorem)
- Epsilon conjecture (Ribet's theorem)
- Fermat's Last Theorem
- Gradient conjecture (Kurdyka-Mostowski-Parusinski theorem)
- Heawood conjecture (Ringel-Youngs' theorem)
- Kummer's conjecture on cubic Gauss sums (Kummer sum)
- Mahler-Manin conjecture
- Manin-Mumford conjecture (Raynaud's theorem)
- Milnor conjecture (Voevodsky's theorem)
- Mordell conjecture (Faltings' theorem)
- Mumford conjecture (Haboush's theorem)
- Oppenheim conjecture (Margulis' theorem)
- Ramanujan conjecture on the cusp form Δ (proved by the proof of the Weil conjectures)
- Segal's Burnside ring conjecture (Carlsson theorem)
- Serre's conjecture (Quillen-Suslin theorem)
- Seymour's conjecture
- Smith conjecture (Gordon's theorem)
- Star height problem (Hashiguchi theorem)
- Strong perfect graph conjecture (Chudnovsky-Robertson-Seymour-Thomas theorem)
- Sullivan conjecture
- Tameness conjecture (Agol or Calegari-Gabai theorem)
- Taniyama-Shimura conjecture (Shimura–Taniyama theorem)
- Wagner's conjecture (Robertson-Seymour theorem)
- Weil conjectures (Deligne's theorems)

## Disproved

## Recent work

## Open problems

- abc conjecture
- Andrews-Curtis conjecture
- Agoh-Giuga conjecture
- Artin conjectures
- Atiyah conjecture
- Bateman-Horn conjecture
- Baum-Connes conjecture
- Beal's conjecture
- Beilinson conjecture
- Berry-Tabor conjecture
- Birch and Swinnerton-Dyer conjecture
- Birch-Tate conjecture
- Bloch-Beilinson conjectures
- Borel conjecture
- Bost conjecture
- Collatz conjecture
- Cramér's conjecture
- Deligne conjecture disambiguation
- Eilenberg-Ganea conjecture
- Elliott-Halberstam conjecture
- Erdős-Burr conjecture
- Erdős-Gyárfás conjecture
- Farrell-Jones conjecture
- Frankl conjecture
- Gilbreath conjecture
- Goldbach's conjecture
- Goldbach's weak conjecture
- Grimm's conjecture
- Hadamard conjecture
- Hopf conjecture
- Hodge conjecture
- Homological conjectures in commutative algebra
- Jacobian conjecture
- Keating-Snaith conjecture
- Lawson's conjecture
- Lenstra-Pomerance-Wagstaff conjecture
- Lichtenbaum conjecture
- List coloring conjecture
- Littlewood conjecture
- Lovász conjecture
- Marshall Hall's conjecture
- Mazur's conjectures
- Monodromy conjecture
- New Mersenne conjecture
- Novikov conjecture
- Petersen coloring conjecture
- Pierce-Birkhoff conjecture
- Pillai's conjecture
- De Polignac's conjecture
- Quillen-Lichtenbaum conjecture
- Reconstruction conjecture
*Riemann Hypotheses*: see also Weil conjectures, above- Schanuel's conjecture
- Schinzel's hypothesis H
- Scholz conjecture
- Second Hardy-Littlewood conjecture
- Selfridge's conjecture
- Serre's multiplicity conjectures
- Singmaster's conjecture
- Tate conjecture
- Twin prime conjecture
- Vandiver's conjecture
- Weight-monodromy conjecture

This page lists Wikipedia articles about named mathematical inequalities.

## Pure mathematics

- Bernoulli's inequality
- Bessel's inequality
- Bishop-Gromov inequality
- Cauchy-Schwarz inequality
- Chebyshev's sum inequality
- Fenchel's inequality
- Friedrichs' inequality
- Gronwall's inequality
- Hadamard's inequality
- Hardy's inequality
- Harnack's inequality
- Hölder's inequality
- Inequality of arithmetic and geometric means
- Jensen's inequality
- Kantorovich inequality
- Kraft's inequality
- Ky Fan inequality
- Large sieve inequality
- Lubell-Yamamoto-Meshalkin inequality
- Minkowski's inequality
- Muirhead's inequality
- Nesbitt's inequality
- Pedoe's inequality
- Peetre's inequality
- Poincaré inequality
- Pólya-Vinogradov inequality
- Ptolemy's inequality
- Rearrangement inequality
- Schur's inequality
- Shapiro inequality
- Sobolev inequality
- Triangle inequality
- Weyl's inequality
- Wirtinger's inequality
- Young's inequality
- Zaimi-Marku inequality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### Inequalities in probability theory

## Inequalities particular to physics

- Bell's inequality — see Bell's theorem
- Heisenberg's inequality
- Rushbrooke inequality
- Tsirelson's inequality

A list of articles with mathematical proofs:

## Theorems of which articles are primarily devoted to proving them

- Bertrand's postulate and a proof
- Estimation of covariance matrices
- Fermat's little theorem and some proofs
- Gödel's completeness theorem and its original proof
- Mathematical induction and a proof
- Proof that 0.999... equals 1
- Proof that 22/7 exceeds π
- Proof that e is irrational
- Proof that the sum of the reciprocals of the primes diverges

## Articles devoted to theorems of which a (sketch of a) proof is given

- Banach fixed point theorem
- Banach–Tarski paradox
- Basel problem
- Bolzano-Weierstrass theorem
- Brouwer fixed point theorem
- Buckingham π theorem (proof in progress)
- Burnside's lemma
- Cantor's theorem
- Cantor–Bernstein–Schroeder theorem
- Cayley's formula
- Cayley's theorem
- Clique problem (to do)
- Compactness theorem (very compact proof)
- Erdős-Ko-Rado theorem
- Euler's formula
- Euler's four-square identity
- Euler's theorem
- Five color theorem
- Five lemma
- Fundamental theorem of arithmetic
- Gauss-Markov theorem (brief pointer to proof)
- Gödel's incompleteness theorem
- Gödel's first incompleteness theorem
- Gödel's second incompleteness theorem

- Goodstein's theorem
- Green's theorem (to do)
- Green's theorem when D is a simple region

- Heine-Borel theorem
- Intermediate value theorem
- Itô's lemma
- König's lemma
- König's theorem (to do)
- Lagrange's theorem
- Liouville's theorem (brief pointer to proof)
- Markov's inequality (proof of a generalization)
- Mean value theorem
- Multivariate normal distribution (to do)
- Holomorphic functions are analytic
- Pythagorean theorem
- Quadratic equation
- Quotient rule
- Ramsey's theorem
- Rao-Blackwell theorem
- Rice's theorem
- Rolle's theorem
- Splitting lemma
- squeeze theorem
- Sum rule in differentiation
- Sum rule in integration
- Sylow theorem
- Transcendence of
*e*and π (as corollaries of Lindemann-Weierstrass) - Tychonoff's theorem (to do)
- Ultrafilter lemma
- Ultraparallel theorem
- Urysohn's lemma
- Van der Waerden's theorem
- Wilson's theorem
- Zorn's lemma

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

## Articles devoted to algorithms in which their correctness is proven

- Bellman-Ford algorithm (to do)
- Euclidean algorithm
- Kruskal's algorithm
- Prim's algorithm
- Shor's algorithm (incomplete)

## Articles where example statements are proven

## Other articles containing proofs

- Addition in N
- associativity of addition in N
- commutativity of addition in N
- uniqueness of addition in N

- Algorithmic information theory
- Boolean ring
- commutativity of a boolean ring

- Boolean satisfiability problem
- NP-completeness of the Boolean satisfiability problem

- Calculus with polynomials
- Cantor's diagonal argument
- set is smaller than its power set
- uncountability of the real numbers

- Combinatorics
- Combinatory logic
- Co-NP
- Coset
- Countable
- countability of a subset of a countable set (to do)

- Counter
- Angle of parallelism
- Galois group
- Fundamental theorem of Galois theory (to do)

- Gödel number
- Gödel's incompleteness theorem

- Group (mathematics)
- Halting problem
- insolubility of the halting problem

- Harmonic series (mathematics)
- divergence of the (standard) harmonic series

- Highly composite number
- Area of hyperbolic sector, basis of hyperbolic angle
- Infinite series
- convergence of the geometric series with first term 1 and ratio 1/2

- Integer partition
- Irrational number
- irrationality of log
_{2}3 - irrationality of the square root of 2

- irrationality of log
- Limit point
- Mathematical induction
- sum identity

- Prime number
- Infinitude of the prime numbers

- Primitive recursive function
- Principle of bivalence
- no propositions are neither true nor false in intuitionistic logic

- Recursion
- Relational algebra (to do)
- Solvable group
- Tetris
- Algebra of sets
- idempotent laws for set union and intersection

## Articles which mention dependencies of theorems

## Articles giving mathematical proofs within a physical model

This is a **list of misnamed theorems** in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object) that are well known in mathematics, but which are not named for the originator. That is, these items on this list illustrate Stigler's law of eponymy (which is not, of course, due to Stigler, who credits Merton!).

- Benford's law. This was first stated in 1881 by Simon Newcomb,
^{[1]}and rediscovered in 1938 by Frank Benford.^{[2]}The first rigorous formulation and proof seems to be due to Ted Hill in 1988.^{[3]}

- Bézout's theorem. The statement may have been made first by Isaac Newton in 1665. The matter of a proof was taken up by Colin MacLaurin (c. 1720) and Leonhard Euler as well as Etienne Bézout (c. 1750). However, Bézout's "proof" was
*incorrect*. The first correct proof seems to be due mostly to Georges-Henri Halphen in the 1870s.^{[4]}

- Burnside's lemma. This was stated and proven without attribution in Burnside's 1897 textbook,
^{[5]}but it has previously been discussed by Augustin Cauchy, in 1845, and by Georg Frobenius in 1887.

- Cramer's paradox. This was first noted by Colin MacLaurin in 1720, and then rediscovered by Leonhard Euler in 1748 (whose paper was not published for another two years, as Euler wrote his papers faster than his printers could print them). It was also discussed by Gabriel Cramer in 1750, who independently suggested the essential idea needed for the resolution, although providing a rigorous proof remained an outstanding open problem for much of the 19th century. Even though Cramer had cited McLaurin, the paradox became known after Cramer rather than McLaurin. Halphen, Arthur Cayley, and several other luminaries contributed to the earliest more or less correct proof. See
^{[6]}for an excellent review.

- Fermat's last theorem. This was stated in 1637 in a marginal note in one of his books by Pierre de Fermat, who famously wrote that he had proven it but that the margin was too small to write out the proof there. After Fermat's death, this intriguing notation was mentioned c. 1670 by his son in a new edition of Fermat's collected works, and it became known by its present name. However, the "theorem" remained a conjecture until in 1995 it was finally proven by Andrew Wiles.

- Frobenius theorem. This fundamental theorem was stated and proven in 1840 by Feodor Deahna.
^{[7]}Even though Frobenius cited Deahna's paper in his own 1875 paper,^{[8]}it became known after Frobenius, not Deahna. See^{[9]}for a historical review.

- Pell's equation. The solution of the equation where are unknown positive integers and where is a known positive integer which is not a perfect square, which is nominally ascribed to John Pell, was in fact known to Hindu mathematicians far earlier. In Europe, it seems to have been rediscovered by Fermat, who set it as a challenge problem in 1657. The first European solution is found in a joint work in 1658 by John Wallis and Lord Brouncker; in 1668, a shorter solution was given in an edition of a third mathemathecians work by Pell; see
^{[10]}The first rigorous proof may be due to Lagrange. The misnomer apparently came about when Euler confused Brouncker and Pell; see^{[11]}for an extensive account of the history of this equation.

- Poincaré lemma. This was mentioned in 1886 by Henri Poincaré,
^{[12]}but was first proven in a series of 1889 papers by the distinguished Italian mathematician Vito Volterra. Nonetheless it has become known after Poincaré. See^{[9]}for the twisted history of this lemma.

- Pólya enumeration theorem. This was proven in 1927 in a difficult paper by J. H. Redfield.
^{[13]}Despite the prominence of the venue (the American Journal of Mathematics), the paper was overlooked. Eventually, the theorem was independently rediscovered in 1936 by George Pólya.^{[14]}Not until 1960 did Frank Harary unearth the much earlier paper by Redfield. See^{[15]}for historical and other information.

## انظر أيضاً

Most of the results below come from pure mathematics, but some are from theoretical physics, علم الاقتصاد, and other applied fields.

فهرست: | أعلى - 0-9 | ا | ب | ت | ث | ج | ح | خ | د | ذ | ر | ز | س | ش | ص | ض | ط | ظ | ع | غ | ف | ق | ك | ل | م | ن | ه | و | ي |
---|

## A

- Abel's theorem (
*mathematical analysis*) - Abelian and tauberian theorems (
*mathematical analysis*) - Abel-Ruffini theorem (
*theory of equations*,*Galois theory*) - Abouabdillah's theorem (
*هندسة رياضية*,*number theory*) - Ankeny-Artin-Chowla theorem (
*number theory*) - Arrow's impossibility theorem (
*game theory*) - Artin-Schreier theorem (
*real closed fields*) - Artin-Wedderburn theorem (
*abstract algebra*) - Arzelà-Ascoli theorem (
*functional analysis*) - Atiyah-Singer index theorem (
*elliptic differential operators*,*harmonic analysis*)

## B

- Baire category theorem (
*topology*,*metric spaces*) - Banach-Alaoglu theorem (
*functional analysis*) - Banach fixed point theorem (
*metric spaces, differential equations*) - Banach-Steinhaus theorem (
*functional analysis*) - Barbier's theorem (
*هندسة رياضية*) - Bass's theorem (
*group theory*) - Bayes' theorem (
*probability*) - Beatty's theorem (
*diophantine approximation*) - Beck's monadicity theorem (
*category theory*) - Beck's theorem (
*incidence geometry*) - Bell's theorem (
*quantum theory - physics*) - Bendixson-Dulac theorem (
*dynamical systems*) - Berry-Esséen theorem (
*probability theory*) - Bertrand's ballot theorem (
*probability theory*,*combinatorics*) - Bertrand's postulate (
*prime numbers*) - Bézout's theorem (
*algebraic curves*) - Binomial theorem (
*algebra, combinatorics*) - Birkhoff's theorem (
*ergodic theory*) - Bohr-Mollerup theorem (
*gamma function*) - Bolyai-Gerwien theorem (
*هندسة رياضية*) - Bolzano's theorem (
*real analysis, calculus*) - Bolzano-Weierstrass theorem (
*real analysis, calculus*) - Boolean prime ideal theorem (
*mathematical logic*) - Borel-Bott-Weil theorem (
*representation theory*) - Bott periodicity theorem (
*homotopy theory*) - Borsuk-Ulam theorem (
*topology*) - Brouwer fixed point theorem (
*topology*) - Brown's representability theorem (
*homotopy theory*) - Bruck-Chowla-Ryser theorem (
*combinatorics*) - Buckingham π theorem (
*dimensional analysis*)

## C

- Cantor–Bernstein–Schroeder theorem (
*Set theory*,*cardinal numbers*) - Cantor's theorem (
*Set theory*,*Cantor's diagonal argument*) - Carathéodory-Jacobi-Lie theorem (
*symplectic topology*) - Carathéodory's theorem (
*conformal mapping*) - Carathéodory's theorem (
*convex hull*) - Carathéodory's theorem (
*measure theory*) - Cartan's theorem (
*Lie group*) - Cartan's theorems A and B (
*several complex variables*) - Cauchy integral theorem (
*Complex analysis*) - Cayley-Hamilton theorem (
*Linear algebra*) - Cayley's theorem (
*group theory*) - Central limit theorem (
*probability*) - Ceva's theorem (
*هندسة رياضية*) - Chebotarev's density theorem (
*number theory*) - Chen's theorem (
*number theory*) - Chern-Gauss-Bonnet theorem (
*differential geometry*) - Chinese remainder theorem (
*number theory*) - Chowla-Mordell theorem (
*number theory*) - Church-Rosser theorem (
*lambda calculus*) - Closed graph theorem (
*functional analysis*) - Cluster decomposition theorem (
*quantum field theory*) - Coase theorem (
*علم الاقتصاد*) - Cochran's theorem (
*statistics*) - Compactness theorem (
*mathematical logic*) - Conservativity theorem (
*mathematical logic*) - Convolution theorem (
*Fourier transforms*) - Cook's theorem (
*computational complexity theory*) - Cox's theorem (
*probability foundations*) - Crystallographic restriction theorem (
*group theory*,*crystallography*) - Cut-elimination theorem (
*proof theory*)

## D

- Dandelin's theorem (
*هندسة رياضية*) - Darboux's theorem (
*symplectic topology*) - De Branges' theorem (
*complex analysis*) - De Finetti's theorem (
*probability*) - De Rham's theorem (
*differential topology*) - Deduction theorem (
*logic*) - Desargues' theorem (
*هندسة رياضية*) - Descartes' theorem (
*هندسة رياضية*) - Dilworth's theorem (
*combinatorics*,*order theory*) - Dimension theorem for vector spaces (
*vector spaces, linear algebra*) - Dirichlet's theorem on arithmetic progressions (
*number theory*) - Dirichlet's unit theorem (
*algebraic number theory*) - Divergence theorem (
*vector calculus*) - Dominated convergence theorem (
*Lebesgue integration*)

## E

- Earnshaw's theorem (
*electrostatics*) - Ehresmann's theorem (
*differential topology*) - Equipartition theorem (
*ergodic theory*) - Erdős-Ko-Rado theorem (
*combinatorics*) - Euler's rotation theorem (
*هندسة رياضية*) - Euler's theorem (
*number theory*) - Euler's theorem on homogeneous functions (
*multivariate calculus*) - Extreme value theorem

## F

- Faltings' theorem (
*diophantine geometry*) - Feit-Thompson theorem (
*finite groups*) - Fermat's last theorem (
*number theory*) - Fermat's little theorem (
*number theory*) - Fisher separation theorem (
*علم الاقتصاد*) - Five color theorem (
*graph theory*) - Fixed point theorems in infinite-dimensional spaces
- Fluctuation dissipation theorem (
*physics*) - Fluctuation theorem
- Four color theorem (
*graph theory*) - Fourier inversion theorem (
*harmonic analysis*) - Frobenius reciprocity theorem (
*group representations*) - Frobenius theorem (
*foliations*) - Fubini's theorem (
*integration*) - Fuglede's theorem (
*functional analysis*) - Fundamental theorem of algebra (
*complex analysis*) - Fundamental theorem of arbitrage-free pricing (
*financial mathematics*) - Fundamental theorem of arithmetic (
*number theory*) - Fundamental theorem of calculus (
*calculus*) - Fundamental theorem on homomorphisms (
*abstract algebra*)

## G

- Gauss theorem (
*vector calculus*) - Gauss's Theorema Egregium (
*differential geometry*) - Gauss-Bonnet theorem (
*differential geometry*) - Gauss-Markov theorem (
*statistics*) - Gauss-Wantzel theorem (
*هندسة رياضية*) - Gelfand-Naimark theorem (
*functional analysis*) - Gelfond-Schneider theorem (
*transcendence theory*) - Gibbard-Satterthwaite theorem (
*voting methods*) - Girsanov's theorem (
*stochastic processes*) - Goddard-Thorn theorem (
*vertex algebras*) - Gödel's completeness theorem (
*mathematical logic*) - Gödel's incompleteness theorem (
*mathematical logic*) - Going-up and going-down theorems (
*commutative algebra*) - Goodstein's theorem (
*mathematical logic*) - Green's theorem (
*vector calculus*) - Gromov's compactness theorem (
*Riemannian geometry*) - Gromov's theorem (
*group theory*) - Gromov-Ruh theorem (
*differential geometry*)

## H

- H-theorem (
*thermodynamics*) - Haag's theorem (
*quantum field theory*) - Haboush's theorem (
*algebraic groups*,*representation theory*,*invariant theory*) - Hadwiger's theorem (
*هندسة رياضية*,*measure theory*) - Hahn embedding theorem (
*ordered groups*) - Hairy ball theorem (
*algebraic topology*) - Hahn-Banach theorem (
*functional analysis*) - Hales-Jewett theorem (
*combinatorics*) - Ham sandwich theorem (
*topology*) - Heine-Borel theorem (
*real analysis*) - Hellinger-Toeplitz theorem (
*functional analysis*) - Helly's theorem (
*convex sets*) - Herbrand-Ribet theorem (
*cyclotomic fields*) - Hilbert's basis theorem (
*commutative algebra*,*invariant theory*) - Hilbert's Nullstellensatz (theorem of zeroes) (
*commutative algebra*,*algebraic geometry*) - Hilbert-Speiser theorem (
*cyclotomic fields*) - Hinge theorem (
*هندسة رياضية*) - Hopf-Rinow theorem (
*differential geometry*) - Hurewicz theorem (
*algebraic topology*) - Hurwitz's automorphisms theorem (
*algebraic curves*)

## I

## J

## K

- Kirchhoff's theorem (
*graph theory*) - Kirszbraun theorem (
*Lipschitz continuity*) - Kleene's recursion theorem (
*recursion theory*) - Knaster-Tarski theorem (
*order theory*) - Kolmogorov-Arnold-Moser theorem (
*dynamical systems*) - Kolmogorov extension theorem
- König's theorem (
*mathematical logic*) - Kronecker's theorem (
*diophantine approximation*) - Kronecker-Weber theorem (
*number theory*) - Krull's principal ideal theorem (
*commutative algebra*) - Künneth theorem (
*algebraic topology*)

## L

- Lagrange's theorem (
*group theory*) - Lagrange's four-square theorem (
*number theory*) - Lagrange inversion theorem (
*mathematical analysis*,*combinatorics*) - Lagrange reversion theorem (
*mathematical analysis*,*combinatorics*) - Lami's theorem (
*statics*) - Laurent expansion theorem (
*complex analysis*) - Lefschetz fixed point theorem (
*algebraic topology*) - Lehmann-Scheffé theorem (
*statistics*) - Lindemann-Weierstrass theorem (
*transcendence theory*) - Lie-Kolchin theorem (
*algebraic groups*,*representation theory*) - Linear congruence theorem (
*number theory*,*modular arithmetic*) - Linear speedup theorem (
*computational complexity theory*) - Linnik's theorem (
*number theory*) - Liouville's theorem (complex analysis) (
*entire functions*) - Liouville's theorem (Hamiltonian) (
*Hamiltonian mechanics*) - Löb's theorem (
*mathematical logic*) - Löwenheim-Skolem theorem (
*mathematical logic*) - Lyapunov's central limit theorem (
*probability theory*)

## M

- Mahler's compactness theorem (
*geometry of numbers*) - Mahler's theorem (
*p-adic analysis*) - Marcinkiewicz theorem (
*functional analysis*) - Marriage theorem (
*combinatorics*) - Master theorem (
*recurrence relations*,*asymptotic analysis*) - Maschke's theorem (
*group representations*) - Matiyasevich's theorem (
*mathematical logic*) - Max flow min cut theorem (
*graph theory*) - Maximum power theorem (
*electrical circuits*) - Maxwell's theorem (
*probability theory*) - Mean value theorem (
*calculus*) - Menger's theorem (
*graph theory*) - Mercer's theorem (
*functional analysis*) - Mertens' theorems (
*number theory*) - Metrization theorems (
*topological spaces*) - Min-max theorem (
*functional analysis*) - Minimax theorem
- Minkowski's theorem (
*geometry of numbers*) - Mitchell's embedding theorem (
*category theory*) - Mittag-Leffler's theorem (
*complex analysis*) - Modigliani-Miller theorem (
*finance theory*) - Mohr-Mascheroni theorem (
*هندسة رياضية*) - Monotone convergence theorem (
*mathematical analysis*) - Mordell-Weil theorem (
*number theory*) - Morera's theorem (
*complex analysis*) - Morley's categoricity theorem (
*model theory*) - Morley's trisector theorem (
*هندسة رياضية*) - Multinomial theorem (
*algebra*,*combinatorics*) - Myers theorem (
*differential geometry*) - Myhill-Nerode theorem (
*formal languages*)

## N

- Nagell-Lutz theorem (
*elliptic curves*) - Nash embedding theorem (
*differential geometry*) - Nielsen-Schreier theorem (
*free groups*) - No cloning theorem (
*quantum computation*) - Noether's theorem (
*Lie groups*,*calculus of variations*,*differential invariants*,*physics*) - No-ghost theorem (
*vertex algebras*) - Norton's theorem (
*electrical networks*) - Nyquist-Shannon sampling theorem (
*information theory*)

## O

## P

- Paley-Wiener theorem (
*Fourier transforms*) - Pappus's centroid theorem (
*هندسة رياضية*) - Parseval's theorem (
*Fourier analysis*) - Pascal's theorem (
*conics*) - Pentagonal number theorem (
*number theory*) - Perfect graph theorem (
*graph theory*) - Peter-Weyl theorem (
*representation theory*) - Picard theorem (
*complex analysis*) - Picard-Lindelöf theorem (
*ordinary differential equations*) - Pick's theorem (
*هندسة رياضية*) - Pitman-Koopman-Darmois theorem (
*statistics*) - Plancherel theorem (
*Fourier analysis*) - Poincaré-Bendixson theorem (
*dynamical systems*) - Poincaré-Birkhoff-Witt theorem (
*universal enveloping algebras*) - Poincaré duality theorem (
*algebraic topology of manifolds*) - Poncelet-Steiner theorem (
*هندسة رياضية*) - Post's theorem (
*mathematical logic*) - Prime number theorem (
*number theory*) - Primitive element theorem (
*field theory*) - Ptolemaios' theorem (
*هندسة رياضية*) - Pythagorean theorem (
*هندسة رياضية*)

## R

- Radon's theorem (
*convex sets*) - Radon-Nikodym theorem (
*measure theory*) - Ramsey's theorem (
*graph theory,combinatorics*) - Rank-nullity theorem (
*linear algebra*) - Rao-Blackwell theorem (
*statistics*) - Rational root theorem (
*algebra,polynomials*) - Reeh-Schlieder theorem (
*local quantum field theory*) - Residue theorem (
*complex analysis*) - Rice's theorem (
*recursion theory, computer science*) - Riemann mapping theorem (
*complex analysis*) - Riemann-Roch theorem (
*Riemann surfaces*,*algebraic curves*) - Riesz representation theorem (
*functional analysis,Hilbert space*) - Riesz-Thorin theorem (
*functional analysis*) - Robertson-Seymour theorem (
*graph theory*) - Rolle's theorem (
*calculus*) - Roth's theorem (
*diophantine approximation*) - Rouché's theorem (
*complex analysis*)

## S

- Sahlqvist correspondence theorem (
*modal logic*) - Sarkovskii's theorem (
*dynamical systems*) - Savitch's theorem (
*computational complexity theory*) - Schauder fixed point theorem (
*functional analysis*) - Schreier refinement theorem (
*group theory*) - Schur's lemma (
*representation theory*) - Schur's theorem (
*Ramsey theory*) - Seifert-van Kampen theorem (
*algebraic topology*) - Shannon's theorem (
*information theory*) - Simplicial approximation theorem (
*algebraic topology*) - Skolem-Noether theorem (
*simple algebras*) - Soundness theorem (
*mathematical logic*) - Space hierarchy theorem (
*computational complexity theory*) - Spectral theorem (
*functional analysis*) - Speedup theorem (
*computational complexity theory*) - Sperner's theorem (
*combinatorics*) - Spin-statistics theorem (
*physics*) - Sprague-Grundy theorem (
*combinatorial game theory*) - Squeeze theorem (
*mathematical analysis*) - Stanley's reciprocity theorem (
*combinatorics*) - Stark-Heegner theorem (
*number theory*) - Stokes' theorem (
*vector calculus, differential topology*) - Stolper-Samuelson theorem (
*علم الاقتصاد*) - Stone's representation theorem for Boolean algebras (
*mathematical logic*) - Stone's theorem on one-parameter unitary groups (
*functional analysis*) - Stone-Tukey theorem (
*topology*) - Stone-von Neumann theorem (
*functional analysis*,*representation theory*of the*Heisenberg group*,*quantum mechanics*) - Stone-Weierstrass theorem (
*functional analysis*) - Sturm's theorem (
*theory of equations*) - Swan's theorem (
*module theory*) - Sylow theorem (
*group theory*) - Sylvester's theorem (
*number theory*) - Sylvester-Gallai theorem (
*plane geometry*) - Szemerédi's theorem (
*combinatorics*) - Szemerédi-Trotter theorem (
*combinatorics*)

## T

- Takagi existence theorem (
*number theory*) - Taniyama-Shimura theorem (
*number theory*) - Tarski's indefinability theorem (
*mathematical logic*) - Taylor's theorem (
*calculus*) - Thales' theorem (
*هندسة رياضية*) - Thevenin's theorem (
*electrical circuits*) - Thue-Siegel-Roth theorem (
*diophantine approximation*) - Tietze extension theorem (
*general topology*) - Tikhonov fixed point theorem (
*functional analysis*) - Time hierarchy theorem (
*computational complexity theory*) - Tutte theorem (
*graph theory*) - Turán's theorem (
*graph theory*) - Tychonoff's theorem (
*general topology*)

## U

## V

## W

- Weierstrass-Casorati theorem (
*complex analysis*) - Weierstrass preparation theorem (
*several complex variables*,*commutative algebra*) - Well-ordering theorem (
*mathematical logic*) - Whitehead theorem (
*homotopy theory*) - Whitney embedding theorem (
*differential manifolds*) - Wigner-Eckhart theorem (
*Clebsch-Gordan coefficients*) - Wilson's theorem (
*number theory*) - Wolstenholme's theorem (
*number theory*)

## Z

**^**Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers".*Amer. J. Math*.**4**: 39–40.**^**Benford, F. (1938). "The law of anomalous numbers".*Proc. Amer. Phil. Soc*.**78**: 551–572.**^**Hill, Theodore P. (1995). "The Significant Digit Phenomenon".*Am. Math. Monthly*.**102**(4): 322–327. Unknown parameter`|month=`

ignored (help)**^**Bix, Robert (1998).*Conics and Cubics*. Springer. ISBN 0-387-98401-1.**^**Burnside, William (1897).*Theory of groups of finite order*. Cambridge University Press.**^**Scott, Charlotte Agnas (1898). "On the Intersection of Plane Curves".*Bull. Am. Math. Soc*.**4**: 260–273. Unknown parameter`|month=`

ignored (help)**^**Deahna, F. (1840). "Über die Bedingungen der Integrabilität".*J. Reine Angew. Math*.**20**. Text "pages-340-350" ignored (help)**^**Frobenius, Georg (1895). "Ūber die Pfaffsche Problem".*J. Reine Angew. Math.*: 230–315.- ^
^{أ}^{ب}Samelson, Hans (2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem".*Am. Math. Monthly*.**108**(6): 552–530. Unknown parameter`|month=`

ignored (help) **^**Cajori, Florian (1999).*A History of Mathematics*. New York: Chelsea. (reprint of fifth edition, 1891).**^**Whitford, Edward Everett (1912).*The Pell Equation*. New York: E. E. Whitford. This is Whitford's 1912 Ph.D. dissertation, written at Columbia University and published at his own expense in 1912.**^**Poincaré, H. (1886–1887). "Sur les residus des intégrales doubles".*Acta Math*.**9**: 321–380.CS1 maint: date format (link)**^**Redfield, J. H. (1927). "The theory of group related distributions".*Amer. J. Math*.**49**: 433–445.**^**Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen".*Z. für Krystallogr. A*.**93**: 414.**^**Read, R. C. (1987). "Pólya's Theorem and its Progeny".*Mathematics Magazine*.**60**(5): 275–282. Unknown parameter`|month=`

ignored (help)