View source for List of theorems

{{Short description|none}}

{{Reorganize|date=February 2024|reason=it should be sorted by subdiscipline rather than alphabetically for ease of navigation}}

This is a list of notable [[Theorem|theorem]]s. Lists of theorems and similar statements include:
*[[List of algebras]]
*[[List of algorithms]]
*[[List of axioms]]
*[[List of conjectures]]
*[[List of data structures]]
*List of derivatives and integrals in alternative calculi
*[[List of equations]]
*List of fundamental theorems
*List of hypotheses
*[[List of inequalities]]
*[[Lists of integrals]]
*List of laws
*[[List of lemmas]]
*[[List of limits]]
*[[List of logarithmic identities]]
*[[List of mathematical functions]]
*[[List of mathematical identities]]
*[[List of mathematical proofs]]
*[[List of misnamed theorems]]
*List of scientific laws
*List of theories

Most of the results below come from [[Pure mathematics|pure mathematics]], but some are from [[Physics:Theoretical physics|theoretical physics]], [[Finance:Economics|economics]], and other [[Applied mathematics|applied]] fields.

{{TOC left|limit=2}}

==Logics and foundations==

*[[Ax–Grothendieck theorem]] (''[[Model theory|model theory]]'')
*[[Barwise compactness theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Borel determinacy theorem]] (''[[Set theory|set theory]]'')
*[[Büchi-Elgot-Trakhtenbrot theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Cantor–Bernstein–Schröder theorem (''[[Set theory|set theory]]'', ''[[Cardinal number|cardinal number]]s'')
*[[Cantor's theorem]] (''[[Set theory|set theory]]'')
*[[Church–Rosser theorem]] (''[[Lambda calculus|lambda calculus]]'')
*[[Compactness theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Conservativity theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Craig's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Craig's interpolation theorem (''[[Mathematical logic|mathematical logic]]'')
*[[Cut-elimination theorem]] (''[[Proof theory|proof theory]]'')
*[[Deduction theorem]] (''[[Logic|logic]]'')
*[[Diaconescu's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Easton's theorem]] (''[[Set theory|set theory]]'')
*[[Erdős–Dushnik–Miller theorem]] (''[[Set theory|set theory]]'')
*[[Erdős–Rado theorem]] (''[[Set theory|set theory]]'')
*[[Feferman–Vaught theorem]] (''[[Model theory|model theory]]'')
*[[Friedberg–Muchnik theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Fundamental theorem of equivalence relations (''[[Set theory|set theory]]'')
*[[Philosophy:Double-negation translation#Propositional logic|Glivenko's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Gentzen's consistency proof]] (''[[Proof theory|proof theory]])''
*[[Gödel's completeness theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Gödel's incompleteness theorem (''[[Mathematical logic|mathematical logic]]'')
*[[Goodstein's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Herbrand's theorem]] (''[[Logic|logic]]'')
*Independence of the axiom of choice (''[[Mathematical logic|mathematical logic]]'')
*[[Continuum hypothesis#Independence from ZFC|Independence of the continuum hypothesis]] (''[[Mathematical logic|mathematical logic]]'')
*[[Kanamori–McAloon theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Kirby–Paris theorem (''[[Proof theory|proof theory]]'')
*[[Kleene's recursion theorem]] (''recursion theory'')
*[[König's theorem (set theory)|König's theorem]] (''[[Set theory|set theory]], [[Mathematical logic|mathematical logic]]'')
*[[Lindström's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Löb's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Łoś' theorem (''[[Model theory|model theory]]'')
*[[Löwenheim–Skolem theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Matiyasevich's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Morley's categoricity theorem]] (''[[Model theory|model theory]]'')
*[[Paris–Harrington theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Post's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Richardson's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Robinson's joint consistency theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Sahlqvist correspondence theorem (''[[Modal logic|modal logic]]'')
*Soundness theorem (''[[Mathematical logic|mathematical logic]]'')
*Tarski's indefinability theorem (''[[Mathematical logic|mathematical logic]]'')
*[[Tennenbaum's theorem]] (''[[Model theory|model theory]]'')
*[[Cardinality of the continuum#Uncountability|Uncountability of the continuum]] (''[[Set theory|set theory]]'')
*[[Unique homomorphic extension theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Well-ordering theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Wilkie's theorem]] (''[[Model theory|model theory]]'')
*[[Zorn's lemma]] (''[[Set theory|set theory]]'')

==Combinatorics==

*[[2-factor theorem|2-factor theorem]] (''[[Graph theory|graph theory]]'')
*[[Abel's binomial theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Alspach's conjecture|Alspach's theorem]] (''[[Graph theory|graph theory]]'')
*Aztec diamond theorem (''[[Combinatorics|combinatorics]]'')
*[[BEST theorem]] (''[[Graph theory|graph theory]]'')
*[[Baranyai's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Berge's theorem]] (''[[Graph theory|graph theory]]'')
*[[Binomial theorem]] (''[[Algebra|algebra]], [[Combinatorics|combinatorics]]'')
*[[Bondy's theorem]] (''[[Graph theory|graph theory]]'', ''[[Combinatorics|combinatorics]]'')
*Bondy–Chvátal theorem (''[[Graph theory|graph theory]]'')
*Brooks's theorem (''[[Graph theory|graph theory]]'')
*Bruck–Chowla–Ryser theorem (''[[Combinatorics|combinatorics]]'')
*[[Cameron–Erdős conjecture|Cameron–Erdős theorem]] (''[[Discrete mathematics|discrete mathematics]]'')
*[[Corners theorem]] (''[[Arithmetic combinatorics|arithmetic combinatorics]]'')
*[[Courcelle's theorem]] (''[[Graph theory|graph theory]]'')
*[[De Bruijn–Erdős theorem (graph theory)]]
*Dirac's theorems (''[[Graph theory|graph theory]]'')
*[[Erdős–Gallai theorem]] (''[[Graph theory|graph theory]]'')
*Erdős–Ginzburg–Ziv theorem (''[[Number theory|number theory]]'')
*[[Erdős–Ko–Rado theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Erdős–Pósa theorem]] (''[[Graph theory|graph theory]]'')
*[[Erdős–Stone theorem]] (''[[Graph theory|graph theory]]'')
*Euler's partition theorem (''[[Number theory|number theory]]'')
*[[Fermat polygonal number theorem]] (''[[Number theory|number theory]]'')
*[[Five color theorem]] (''[[Graph theory|graph theory]]'')
*[[Four color theorem]] (''[[Graph theory|graph theory]]'')
*[[Freiman's theorem]] (''[[Number theory|number theory]]'')
*Friendship theorem (''[[Graph theory|graph theory]]'')
*[[Dinitz conjecture|Galvin's theorem]] (''[[Combinatorics|combinatorics]]'')
*Gomory's theorem (''[[Combinatorics|combinatorics]]'')
*[[Graph structure theorem]] (''[[Graph theory|graph theory]]'')
*[[Grinberg's theorem]] (''[[Graph theory|graph theory]]'')
*[[Grötzsch's theorem]] (''[[Graph theory|graph theory]]'')
*Hajnal–Szemerédi theorem (''[[Graph theory|graph theory]]'')
*[[Hales–Jewett theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Hall's marriage theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Halpern–Läuchli theorem]] (''[[Ramsey theory]]'')
*Hindman's theorem (''[[Ramsey theory]]'')
*[[Kirchhoff's theorem]] (''[[Graph theory|graph theory]]'')
*[[Kneser's theorem (combinatorics)|Kneser's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Kőnig's theorem (graph theory)|Kőnig's theorem]] (''[[Bipartite graph|bipartite graph]]s'')
*Kövari–Sós–Turán theorem (''[[Graph theory|graph theory]]'')
*[[Kruskal–Katona theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Kuratowski's theorem]] (''[[Graph theory|graph theory]]'')
*[[Lambek–Moser theorem]] (''[[Combinatorics|combinatorics]]'')
*[[MacMahon's master theorem]] (''[[Enumerative combinatorics|enumerative combinatorics]]'')
*[[Menger's theorem]] (''[[Graph theory|graph theory]]'')
*[[Milliken–Taylor theorem]] (''[[Ramsey theory]]'')
*[[Milliken's tree theorem]] (''[[Ramsey theory]]'')
*[[Multinomial theorem]] (''[[Algebra|algebra]]'', ''[[Combinatorics|combinatorics]]'')
*Mycielski's theorem (''[[Graph theory|graph theory]]'')
*Nicomachus's theorem (''[[Number theory|number theory]]'')
*[[Ore's theorem]] (''[[Graph theory|graph theory]]'')
*Paley's theorem (''[[Algebra|algebra]]'')
*[[Perfect graph theorem]] (''[[Graph theory|graph theory]]'')
*Perlis theorem (''[[Graph theory|graph theory]]'')
*[[Planar separator theorem]] (''[[Graph theory|graph theory]]'')
*[[Pólya enumeration theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Ramsey's theorem]] (''[[Graph theory|graph theory]], [[Combinatorics|combinatorics]]'')
*Ringel–Youngs theorem (''[[Graph theory|graph theory]]'')
*[[Robbins' theorem]] (''[[Graph theory|graph theory]]'')
*[[Robertson–Seymour theorem]] (''[[Graph theory|graph theory]]'')
*[[Schnyder's theorem]] (''[[Graph theory|graph theory]]'')
*[[Schur's theorem]] (''[[Ramsey theory]]'')
*[[Schwenk's theorem]] (''[[Graph theory|graph theory]]'')
*[[Sensitivity theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Sperner's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Stanley's reciprocity theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Star of David theorem]] (''[[Combinatorics|combinatorics]]'')
*Stirling's theorem (''[[Mathematical analysis|mathematical analysis]]'')
*[[Strong perfect graph theorem]] (''[[Graph theory|graph theory]]'')
*[[Symmetric hypergraph theorem]] (''[[Graph theory|graph theory]]'')
*[[Szemerédi's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Theorem on friends and strangers]] (''[[Ramsey theory]]'')
*Tutte's theorem on perfect matchings (''[[Graph theory|graph theory]]'')
*[[Turán's theorem]] (''[[Graph theory|graph theory]]'')
*[[Van der Waerden's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Vizing's theorem]] ([[Graph theory|graph theory]])
*[[Wagner's theorem]] (''[[Graph theory|graph theory]]'')
*Zeilberger–Bressoud theorem (''[[Combinatorics|combinatorics]]'')

==Order, lattices, ordered algebraic structures==

*[[Birkhoff's representation theorem]] (''lattice theory'')
*[[Boolean prime ideal theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Bourbaki–Witt theorem]] (''[[Order theory|order theory]]'')
*[[Cantor's isomorphism theorem]] (''[[Order theory|order theory]]'')
*[[Dilworth's theorem]] (''[[Combinatorics|combinatorics]]'', ''[[Order theory|order theory]]'')
*Four functions theorem (''[[Combinatorics|combinatorics]]'')
*[[Hahn embedding theorem]] (''[[Ordered group|ordered group]]s'')
*[[Hausdorff maximal principle|Hausdorff maximality theorem]] (''[[Set theory|set theory]]'')
*[[Kleene fixed-point theorem]] (''[[Order theory|order theory]]'')
*[[Knaster–Tarski theorem]] (''[[Order theory|order theory]]'')
*[[Kruskal's tree theorem]] (''[[Order theory|order theory]]'')
*Shannon's expansion theorem (''[[Boolean algebra]]'')
*[[Stone's representation theorem for Boolean algebras]] (''[[Mathematical logic|mathematical logic]]'')
*[[Szpilrajn extension theorem]] (''[[Axiom of choice|axiom of choice]]'')

==General algebraic systems==

*[[Fundamental theorem on homomorphisms]] (''[[Abstract algebra|abstract algebra]]'')
*Isomorphism theorem (''[[Abstract algebra|abstract algebra]]'')
*Lattice theorem (''[[Abstract algebra|abstract algebra]]'')

==Number theory==

*[[15 and 290 theorems|15 and 290 theorems]] (''[[Number theory|number theory]]'')
*[[Albert–Brauer–Hasse–Noether theorem]] (''[[Algebra|algebra]]s'')
*Ankeny&ndash;Artin&ndash;Chowla theorem (''[[Number theory|number theory]]'')
*[[Apéry's theorem]] (''[[Number theory|number theory]]'')
*[[Artin–Verdier duality|Artin–Verdier duality theorem]] (''[[Number theory|number theory]]'')
*[[ATS theorem]] (''[[Number theory|number theory]]'')
*Auxiliary polynomial theorem (''[[Diophantine approximation]]'')
*[[Ax–Kochen theorem]] (''[[Number theory|number theory]]'')
*[[Baker's theorem]] (''[[Number theory|number theory]]'')
*[[Barban–Davenport–Halberstam theorem]] (''[[Analytic number theory|analytic number theory]]'')
*[[Basel problem]] (''[[Mathematical analysis|mathematical analysis]]'')
*Beatty's theorem (''[[Diophantine approximation]]'')
*[[Behrend's theorem]] (''[[Number theory|number theory]]'')
*[[Bertrand's postulate]] (''[[Number theory|number theory]]'')
*[[Birch's theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Schneider–Lang theorem|Bombieri's theorem]] (''[[Number theory|number theory]]'')
*Bombieri–Friedlander–Iwaniec theorem (''[[Number theory|number theory]]'')
*[[Brauer–Siegel theorem]] (''[[Number theory|number theory]]'')
*[[Brun's theorem]] (''[[Number theory|number theory]]'')
*[[Brun–Titchmarsh theorem]] (''[[Number theory|number theory]]'')
*[[Carmichael's theorem]] (''[[Fibonacci number]]s'')
*[[Chebotarev's density theorem]] (''[[Number theory|number theory]]'')
*[[Chen's theorem]] (''[[Number theory|number theory]]'')
*[[Chowla–Mordell theorem]] (''[[Number theory|number theory]]'')
*[[Cohn's irreducibility criterion]] (''[[Polynomials|polynomials]]'')
*Critical line theorem (''[[Number theory|number theory]]'')
*[[Davenport–Schmidt theorem]] (''[[Number theory|number theory]]'', ''[[Diophantine approximations]]'')
*[[Dirichlet's approximation theorem]] (''[[Diophantine approximations]]'')
*[[Dirichlet's theorem on arithmetic progressions]] (''[[Number theory|number theory]]'')
*[[Dirichlet's unit theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Equidistribution theorem]] (''[[Ergodic theory|ergodic theory]]'')
*[[Erdős–Kac theorem]] (''[[Number theory|number theory]]'')
*[[Euclid's theorem]] (''[[Number theory|number theory]]'')
*[[Euclid–Euler theorem]] (''[[Number theory|number theory]]'')
*[[Euler's theorem]] (''[[Number theory|number theory]]'')
*[[Fermat's Last Theorem]] (''[[Number theory|number theory]]'')
*[[Fermat's little theorem]] (''[[Number theory|number theory]]'')
*[[Fermat's theorem on sums of two squares]] (''[[Number theory|number theory]]'')
*[[Ferrero–Washington theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Euler's totient function#Ford's theorem|Ford's theorem]] (''[[Number theory|number theory]]'')
*[[Farey sequence#Riemann hypothesis|Franel–Landau theorem]] (''[[Number theory|number theory]]'')
*[[Gelfond–Schneider theorem]] (''[[Transcendental number theory|transcendental number theory]]'')
*[[Glaisher's theorem]] (''[[Number theory|number theory]]'')
*[[Green–Tao theorem]] (''[[Number theory|number theory]]'')
*Gross–Zagier theorem (''[[Number theory|number theory]]'')
*[[Grunwald–Wang theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Hardy–Ramanujan theorem]] (''[[Number theory|number theory]]'')
*[[Hasse norm theorem]] (''[[Number theory|number theory]]'')
*[[Hasse–Minkowski theorem]] (''[[Number theory|number theory]]'')
*[[Herbrand–Ribet theorem]] (''[[Cyclotomic field|cyclotomic field]]s'')
*[[Hilbert–Speiser theorem]] (''[[Cyclotomic field|cyclotomic field]]s'')
*Hilbert–Waring theorem (''[[Number theory|number theory]]'')
*[[Hilbert's irreducibility theorem]] (''[[Number theory|number theory]]'')
*[[Hurwitz's theorem (number theory)|Hurwitz's theorem]] (''[[Number theory|number theory]]'')
*[[Jacobi's four-square theorem]] (''[[Number theory|number theory]]'')
*[[Jurkat–Richert theorem]] (''[[Analytic number theory|analytic number theory]]'')
*[[Kaplansky's theorem on quadratic forms]] (''[[Number theory|number theory]]'')
*Khinchin's theorem (''[[Probability|probability]]'')
*[[Kronecker's theorem]] (''[[Diophantine approximation]]'')
*[[Kronecker–Weber theorem]] (''[[Number theory|number theory]]'')
*[[Kummer's theorem]] (''[[Number theory|number theory]]'')
*[[Lafforgue's theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Lagrange's four-square theorem]] (''[[Number theory|number theory]]'')
*[[Landau prime ideal theorem]] (''[[Number theory|number theory]]'')
*[[Lindemann–Weierstrass theorem]] (''[[Transcendental number theory|transcendental number theory]]'')
*[[Linnik's theorem]] (''[[Number theory|number theory]]'')
*[[Lochs's theorem]] (''[[Number theory|number theory]]'')
*[[Lucas's theorem]] (''[[Number theory|number theory]]'')
*[[Mahler's compactness theorem]] (''[[Geometry of numbers|geometry of numbers]]'')
*[[Mahler's theorem]] (''[[P-adic analysis|p-adic analysis]]'')
*[[Maier's theorem]] (''[[Analytic number theory|analytic number theory]]'')
*[[Mann's theorem]] (''[[Number theory|number theory]]'')
*[[Mazur's control theorem]] (''[[Number theory|number theory]]'')
*Mertens's theorems (''[[Number theory|number theory]]'')
*[[Midy's theorem]] (''[[Number theory|number theory]]'')
*[[Mihăilescu's theorem]] (''[[Number theory|number theory]]'')
*Mirsky–Newman theorem (''[[Group theory|group theory]]'')
*[[Modularity theorem]] (''[[Number theory|number theory]]'')
*[[Mordell–Weil theorem]] (''[[Number theory|number theory]]'')
*[[Multiplicity-one theorem]] (''[[Group representation|group representation]]s'')
*[[Nagell–Lutz theorem]] (''[[Elliptic curve|elliptic curve]]s'')
*[[Niven's theorem]] (''[[Number theory|number theory]]'')
*[[Ostrowski's theorem]] (''[[Number theory|number theory]]'')
*[[Pentagonal number theorem]] (''[[Number theory|number theory]]'')
*[[Prime number theorem]] (''[[Number theory|number theory]]'')
*[[Principal ideal theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Proth's theorem]] (''[[Number theory|number theory]]'')
*Quadratic reciprocity theorem
*Ramanujan–Skolem's theorem (''[[Diophantine equations]]'')
*[[Reflection theorem]] (''[[Algebraic number theory|algebraic number theory]]'')
*[[Ribet's theorem]] (''[[Elliptic curve|elliptic curve]]s'')
*Robin's theorem (''[[Number theory|number theory]]'')
*[[Rosser's theorem]] (''[[Number theory|number theory]]'')
*[[Siegel–Walfisz theorem]] (''[[Analytic number theory|analytic number theory]]'')
*[[Six exponentials theorem]] (''[[Transcendental number theory|transcendental number theory]]'')
*[[Skolem–Mahler–Lech theorem]] (''[[Number theory|number theory]]'')
*[[Pell's equation|Solutions to Pell's equation]] (''[[Number theory|number theory]]'')
*[[Sophie Germain's theorem]] (''[[Number theory|number theory]]'')
*[[Sphere packing#Hypersphere packing|Sphere packing theorems in dimensions 8 and 24]] (''[[Geometry|geometry]]'', ''modular forms'')
*[[Stark–Heegner theorem]] (''[[Number theory|number theory]]'')
*[[Subspace theorem]] (''[[Diophantine approximation]]'')
*[[Bertrand's postulate#Sylvester.27s theorem|Sylvester's theorem]] (''[[Number theory|number theory]]'')
*[[Takagi existence theorem]] (''[[Number theory|number theory]]'')
*[[Thabit number|Thabit ibn Qurra's theorem]] (''amicable numbers'')
*[[Thue equation|Thue's theorem]] (''[[Diophantine equation]]'')
*Thue–Siegel–Roth theorem (''[[Diophantine approximation]]'')
*[[Tijdeman's theorem]] (''[[Diophantine equations]]'')
*[[Tunnell's theorem]] (''[[Number theory|number theory]]'')
*[[Turán–Kubilius inequality|Turán–Kubilius theorem]] (''[[Number theory|number theory]]'')
*[[Vantieghems theorem]] (''[[Number theory|number theory]]'')
*[[Vinogradov's theorem]] (''[[Number theory|number theory]]'')
*[[Von Staudt–Clausen theorem]] (''[[Number theory|number theory]]'')
*[[Wilson's theorem]] (''[[Number theory|number theory]]'')
*[[Wolstenholme's theorem]] (''[[Number theory|number theory]]'')
*[[Zeckendorf's theorem]] (''[[Number theory|number theory]]'')
*[[Zsigmondy's theorem]] (''[[Number theory|number theory]]'')

==Field theory and polynomials==

*[[Abel–Ruffini theorem]] (''[[Theory of equations|theory of equations]]'', ''[[Galois theory]]'')
*Artin–Schreier theorem (''[[Real closed field|real closed field]]s'')
*[[Chevalley–Warning theorem]] (''[[Field theory (mathematics)|field theory]]'')
*Diller–Dress theorem (''[[Field theory (mathematics)|field theory]]'')
*[[Fundamental theorem of Galois theory]] (''[[Galois theory]]'')
*[[Hasse–Arf theorem]] (''[[Local class field theory|local class field theory]]'')
*Hilbert's theorem 90 (''[[Number theory|number theory]]'')
*[[Isomorphism extension theorem]] (''[[Abstract algebra|abstract algebra]]'')
*[[Joubert's theorem]] (''[[Algebra|algebra]]'')
*[[Lagrange's theorem (number theory)|Lagrange's theorem]] (''[[Number theory|number theory]]'')
*[[Mason–Stothers theorem]] (''[[Polynomials|polynomials]]'')
*Polynomial remainder theorem (''[[Polynomials|polynomials]]'')
*[[Primitive element theorem]] (''[[Field theory (mathematics)|field theory]]'')
*[[Rational root theorem]] (''[[Algebra|algebra]], [[Polynomials|polynomials]]'')
*[[Cubic equation|Solutions of a general cubic equation]] (''[[Algebra|algebra]]'')
*[[Quartic equation|Solutions of a general quartic equation]] (''[[Algebra|algebra]]'')
*[[Strassmann's theorem]] (''[[Field theory (mathematics)|field theory]]'')
*[[Sturm's theorem]] (''[[Theory of equations|theory of equations]]'')
*[[Vieta's formulas]] (''quadratics'')

==Commutative algebra==

*[[Artin approximation theorem]] (''[[Commutative algebra|commutative algebra]]'')
*Bézout's identity (''[[Number theory|number theory]]'')
*[[Chinese remainder theorem]] (''[[Number theory|number theory]]'')
*[[Cohen structure theorem]] (''[[Commutative algebra|commutative algebra]]'')
*[[Factor theorem]] (''[[Polynomials|polynomials]]'')
*[[Fundamental theorem of arithmetic]] (''[[Number theory|number theory]]'')
*[[Going up and going down|Going-up and going-down theorems]] (''[[Commutative algebra|commutative algebra]]'')
*[[Hilbert's basis theorem]] (''[[Commutative algebra|commutative algebra]]'',''[[Invariant theory|invariant theory]]'')
*[[Hilbert's syzygy theorem]] (''[[Commutative algebra|commutative algebra]]'')
*Integral root theorem (''[[Algebra|algebra]], [[Polynomials|polynomials]]'')
*[[Krull's principal ideal theorem]] (''[[Commutative algebra|commutative algebra]]'')
*Lasker–Noether theorem (''[[Commutative algebra|commutative algebra]]'')
*Linear congruence theorem (''[[Number theory|number theory]]'', ''[[Modular arithmetic|modular arithmetic]]'')
*[[Quillen–Suslin theorem]] (''[[Abstract algebra|abstract algebra]]'')
*Rédei's theorem (''[[Group theory|group theory]]'')
*Schwartz–Zippel theorem (''[[Polynomials|polynomials]]'')
*Structure theorem for finitely generated modules over a principal ideal domain (''[[Abstract algebra|abstract algebra]]'')
*Unmixedness theorem (''[[Algebraic geometry|algebraic geometry]]'')

==Algebraic geometry==

*[[AF+BG theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Abel–Jacobi theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Abhyankar–Moh theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Addition theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Andreotti–Frankel theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Arithmetic Riemann–Roch theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Decomposition theorem of Beilinson, Bernstein and Deligne|BBD decomposition theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Base change theorems]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Beauville–Laszlo theorem]] (''vector bundles'')
*[[Belyi's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Bertini's theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Bézout's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Borel fixed-point theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Castelnuovo theorem (''[[Algebraic geometry|algebraic geometry]]'')
*Cayley–Salmon theorem (''[[Algebraic surface|algebraic surface]]s'')
*[[Chasles' theorem (geometry)|Chasles' theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Chevalley's structure theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Faltings' theorem (''[[Diophantine geometry]]'')
*[[Fulton–Hansen connectedness theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Grauert–Riemenschneider vanishing theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Grothendieck–Hirzebruch–Riemann–Roch theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Grothendieck's connectedness theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Haboush's theorem]] (''[[Algebraic group|algebraic group]]s'', ''[[Representation theory|representation theory]]'', ''[[Invariant theory|invariant theory]]'')
*[[Harnack's curve theorem]] (''[[Real algebraic geometry|real algebraic geometry]]'')
*[[Hasse's theorem on elliptic curves]] (''[[Number theory|number theory]]'')
*[[Hilbert's Nullstellensatz]] (theorem of zeroes) (''[[Commutative algebra|commutative algebra]]'', ''[[Algebraic geometry|algebraic geometry]]'')
*Hironaka theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Hodge index theorem]] (''[[Algebraic surface|algebraic surface]]s'')
*[[Katz–Lang finiteness theorem]] (''[[Number theory|number theory]]'')
*[[Lefschetz hyperplane theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Leray's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Manin–Drinfeld theorem]] (''[[Number theory|number theory]]'')
*[[Algebraic surface|Max Noether's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*Mazur's torsion theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Mumford vanishing theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Nagata's compactification theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Noether's theorem on rationality for surfaces]] (''[[Algebraic surface|algebraic surface]]s'')
*Proper base change theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Puiseux series#Newton–Puiseux theorem|Puiseux's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Ramanujam vanishing theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Reider's theorem]] (''[[Algebraic surface|algebraic surface]]s'')
*[[Riemann–Roch theorem for surfaces]] (''[[Algebraic surface|algebraic surface]]s'')
*Sylvester pentahedral theorem (''[[Invariant theory|invariant theory]]'')
*[[Theorem of the cube]] (''algebraic varieties'')
*[[Torelli theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Tsen's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Weber's theorem (Algebraic curves)|Weber's theorem]] (''[[Algebraic curve|algebraic curve]]s'')
*[[Zariski's connectedness theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Zariski's main theorem]] (''[[Algebraic geometry|algebraic geometry]]'')

==Linear and multilinear algebra; matrix theory==

*[[Amitsur–Levitzki theorem]] (''[[Linear algebra|linear algebra]]'')
*Binomial inverse theorem (''[[Linear algebra|linear algebra]]'')
*Birkhoff–Von Neumann theorem (''[[Linear algebra|linear algebra]]'')
*[[Bregman–Minc inequality]] (''[[Discrete mathematics|discrete mathematics]]'')
*Cauchy-Binet formula (''[[Linear algebra|linear algebra]]'')
*[[Cayley–Hamilton theorem]] (''[[Linear algebra]]'')
*[[Dimension theorem for vector spaces]] (''[[Vector space|vector space]]s, [[Linear algebra|linear algebra]]'')
*[[Euler's rotation theorem]] (''[[Geometry|geometry]]'')
*Exchange theorem (''[[Linear algebra|linear algebra]]'')
*[[Gamas's Theorem]] (''[[Multilinear algebra|multilinear algebra]]'')
*[[Gershgorin circle theorem]] (''[[Physics:Matrix theory|matrix theory]]'')
*Inverse eigenvalues theorem (''[[Linear algebra|linear algebra]]'')
*[[Perron–Frobenius theorem]] (''[[Physics:Matrix theory|matrix theory]]'')
*[[Principal axis theorem]] (''[[Linear algebra|linear algebra]]'')
*[[Rank–nullity theorem]] (''[[Linear algebra|linear algebra]]'')
*[[Rouché–Capelli theorem]] (''[[Linear algebra]]'')
*[[Sinkhorn's theorem]] (''[[Physics:Matrix theory|matrix theory]]'')
*[[Specht's theorem]] (''[[Physics:Matrix theory|matrix theory]]'')
*[[Spectral theorem]] (''[[Linear algebra|linear algebra]]'', ''[[Functional analysis|functional analysis]]'')
*Sylvester's determinant theorem (''determinants'')
*[[Sylvester's law of inertia]] (''quadratic forms'')
*[[Witt's theorem]] (''[[Quadratic form|quadratic form]]s'')

==Associative rings and algebras==

*[[Artin–Wedderburn theorem]] (''[[Abstract algebra|abstract algebra]]'')
*[[Artin–Zorn theorem]] (''[[Algebra|algebra]]'')
*Brauer–Cartan–Hua theorem (''[[Ring theory|ring theory]]'')
*[[Frobenius theorem (real division algebras)|Frobenius theorem]] (''[[Abstract algebra|abstract algebra]]s'')
*[[Goldie's theorem]] (''[[Ring theory|ring theory]]'')
*[[Jacobson density theorem]] (''[[Ring theory|ring theory]]'')
*[[Jacobson–Bourbaki theorem]] (''[[Algebra|algebra]]'')
*[[Levitzky's theorem]] (''[[Ring theory|ring theory]]'')
*[[Regev's theorem]] (''[[Ring theory|ring theory]]'')
*[[Skolem–Noether theorem]] (''[[Simple algebra|simple algebra]]s'')
*[[Wedderburn's little theorem]] (''[[Ring theory|ring theory]]'')
*[[Artin–Wedderburn theorem|Wedderburn's theorem]] (''[[Abstract algebra|abstract algebra]]'')

==Nonassociative rings and algebras==

*[[Ado's theorem]] (''[[Lie algebra]]'')
*[[Goddard–Thorn theorem]] (''vertex algebras'')
*[[Hurwitz's theorem (normed division algebras)|Hurwitz's theorem]] (''normed division algebras'')
*[[Jacobson–Morozov theorem]] (''[[Lie algebra]]'')
*Levi's theorem (''Lie groups'')
*[[Lie's theorem]] (''[[Lie algebra]]'')
*[[Poincaré–Birkhoff–Witt theorem]] (''[[Universal enveloping algebra|universal enveloping algebra]]s'')
*Shirshov–Cohn theorem (''[[Jordan algebra]]s'')
*Shirshov–Witt theorem (''[[Lie algebra]]s'')

==Category theory and homological algebra==
*[[Beck's monadicity theorem]] (''[[Category theory|category theory]]'')
*[[Bruguières modularity theorem]] (''[[Category theory|category theory]]'')
*Freyd's adjoint functor theorem (''[[Category theory|category theory]]'')
*[[Golod–Shafarevich theorem]] (''[[Group theory|group theory]]'')
*[[Lawvere's fixed-point theorem]] (''[[Mathematical logic|mathematical logic]]'')
*[[Mitchell's embedding theorem]] (''[[Category theory|category theory]]'')
*[[Stone duality#The duality theorem|The duality theorem]] (''[[Topology|topology]]'')
*[[Yoneda lemma]] (''[[Category theory|category theory]]'')

==K-theory==

*[[Atiyah–Segal completion theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Snaith's theorem]] (''[[Algebraic topology|algebraic topology]]'')

==Group theory and generalizations==

*[[Alperin–Brauer–Gorenstein theorem]] (''finite groups'')
*[[Gromov's theorem on groups of polynomial growth#Growth rates of nilpotent groups|Bass-Guirvarc'h formula]] (''[[Group theory|group theory]]'')
*[[Bass–Serre theory#Fundamental theorem of Bass–Serre theory|Bass-Serre theorem]] (''[[Group theory|group theory]]'')
*Borel–Bott–Weil theorem (''[[Representation theory|representation theory]]'')
*Borel–Weil theorem (''[[Representation theory|representation theory]]'')
*[[Brauer–Nesbitt theorem]] (''[[Representation theory of finite groups|representation theory of finite groups]]'')
*[[Brauer–Suzuki theorem]] (''finite groups'')
*[[Brauer–Suzuki–Wall theorem]] (''[[Group theory|group theory]]'')
*Brauer's theorem (''[[Number theory|number theory]]'')
*[[Brauer's theorem on induced characters]] (''[[Representation theory of finite groups|representation theory of finite groups]]'')
*[[Burnside's theorem]] (''[[Group theory|group theory]]'')
*[[Cartan–Dieudonné theorem]] (''[[Group theory|group theory]]'')
*[[Cauchy's theorem (group theory)|Cauchy's theorem]] (''finite groups'')
*[[Cayley's theorem]] (''[[Group theory|group theory]]'')
*[[Chevalley–Shephard–Todd theorem]] (''[[Finite group|finite group]]'')
*[[Classification of finite simple groups]] (''[[Group theory|group theory]]'')
*[[Feit–Thompson theorem]] (''[[Finite group|finite group]]s'')
*[[Fitting's theorem]] (''[[Group theory|group theory]]'')
*[[Preissmann's theorem#Flat torus theorem|Flat torus theorem]] (''[[Geometric group theory|geometric group theory]]'')
*[[Focal subgroup theorem]] (''[[Abstract algebra|abstract algebra]]'')
*[[Frobenius determinant theorem]] (''[[Group theory|group theory]]'')
*[[Frobenius reciprocity theorem]] (''[[Group representation|group representation]]s'')
*[[Frucht's theorem]] (''[[Graph theory|graph theory]]'')
*Great orthogonality theorem (''[[Group theory|group theory]]'')
*[[Gromov's theorem on groups of polynomial growth]] (''[[Geometric group theory|geometric group theory]]'')
*[[Grushko theorem]] (''[[Group theory|group theory]]'')
*[[Higman's embedding theorem]] (''[[Group theory|group theory]]'')
*[[Dehn function#Known results|Isoperimetric gap]] (''[[Geometric group theory|geometric group theory]]'', ''metric geometry'')
*Jordan–Hölder theorem (''[[Group theory|group theory]]'')
*[[Jordan–Schur theorem]] (''[[Group theory|group theory]]'')
*Jordan's theorem (multiply transitive groups) (''[[Group theory|group theory]]'')
*[[Krull–Schmidt theorem]] (''[[Group theory|group theory]]'')
*[[Kurosh subgroup theorem]] (''[[Group theory|group theory]]'')
*[[L-balance theorem]] (''finite groups'')
*[[Lagrange's theorem (group theory)|Lagrange's theorem]] (''[[Group theory|group theory]]'')
*[[Lie–Kolchin theorem]] (''[[Algebraic group|algebraic group]]s'', ''[[Representation theory|representation theory]]'')
*[[Maschke's theorem]] (''[[Group representation|group representation]]s'')
*[[Moufang loop#Associativity|Moufang's theorem]] (''loop theory'')
*[[Nagao's theorem]] (''[[Group theory|group theory]]'')
*[[Nielsen–Schreier theorem]] (''[[Free group|free group]]s'')
*Orbit-stabilizer theorem (''[[Group theory|group theory]]'')
*[[Schreier refinement theorem]] (''[[Group theory|group theory]]'')
*[[Schur's lemma]] (''[[Representation theory|representation theory]]'')
*[[Schur–Zassenhaus theorem]] (''[[Group theory|group theory]]'')
*[[Biography:Zlil Sela#Mathematical contributions|Sela's theorem]] (''[[Hyperbolic group|hyperbolic group]]s'')
*[[Stallings theorem about ends of groups]] (''[[Group theory|group theory]]'')
*Superrigidity theorem (''algebraic groups'')
*[[Švarc–Milnor lemma|Švarc-Milnor lemma]] (''[[Geometric group theory|geometric group theory]]'')
*[[Sylow theorems]] (''[[Group theory|group theory]]'')
*[[Thompson transitivity theorem]] (''finite groups'')
*[[Thompson uniqueness theorem]] (''finite groups'')
*[[Tits alternative]] (''[[Geometric group theory|geometric group theory]]'')
*[[Trichotomy theorem]] (''finite groups'')
*[[Walter theorem]] (''finite groups'')
*[[Z* theorem]] (''finite groups'')
*[[ZJ theorem]] (''finite groups'')

==Topological groups, Lie groups==

*Cartan's theorem (''[[Lie group]]'')
*[[Discrete series representation|Harish–Chandra theorem]] (''[[Representation theory|representation theory]]'')
*Harish–Chandra's regularity theorem (''[[Representation theory|representation theory]]'')
*[[Iwasawa decomposition]] (''[[Lie theory]]'')
*[[Kempf–Ness theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Lie's third theorem]] (''[[Lie group]]'')
*[[Hilbert's fifth problem|Montgomery-Zippin-Gleason theorem]] (''Transformation groups'')
*[[Plancherel theorem for spherical functions]] (''[[Representation theory|representation theory]]'')
*[[Trombi–Varadarajan theorem]] (''[[Lie group]]'')

==Real functions==

*[[Anderson's theorem]] (''[[Real analysis|real analysis]]'')
*[[Bernstein's theorem on monotone functions|Bernstein's theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Bohr–Mollerup theorem]] (''[[Gamma function|gamma function]]'')
*Bolzano's theorem (''[[Real analysis|real analysis]], [[Calculus|calculus]]'')
*Constant rank theorem (''multivariate calculus'')
*[[Cousin's theorem#In Henstock–Kurzweil integration|Cousin's lemma]] (''[[Real analysis|real analysis]]'')
*[[Danskin's theorem]] (''[[Convex analysis|convex analysis]]'')
*[[Darboux's theorem (analysis)|Darboux's theorem]] (''[[Real analysis|real analysis]]'')
*Denjoy–Carleman theorem (''[[Functional analysis|functional analysis]]'')
*[[Denjoy–Young–Saks theorem]] (''[[Real analysis|real analysis]]'')
*[[Dini's theorem]] (''[[Mathematical analysis|analysis]]'')
*[[Divergence theorem]] (''[[Vector calculus|vector calculus]]'')
*[[Fermat's theorem (stationary points)]] (''[[Real analysis|real analysis]]'')
*[[Fraňková–Helly selection theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Froda's theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Fubini's theorem on differentiation]] (''[[Real analysis|real analysis]]'')
*[[Fundamental theorem of calculus]] (''[[Calculus|calculus]]'')
*Gauss theorem (''[[Vector calculus|vector calculus]]'')
*[[Gradient theorem]] (''[[Vector calculus|vector calculus]]'')
*[[Green's theorem]] (''[[Vector calculus|vector calculus]]'')
*[[Helly's selection theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Implicit function theorem]] (''[[Vector calculus|vector calculus]]'')
*[[Increment theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Intermediate value theorem]] (''[[Calculus|calculus]]'')
*[[Inverse function theorem]] (''[[Vector calculus|vector calculus]]'')
*[[Kolmogorov–Arnold representation theorem]] (''[[Real analysis|real analysis]]'', ''[[Approximation theory|approximation theory]]'')
*[[Lebesgue differentiation theorem]] (''[[Real analysis|real analysis]]'')
*Luzin's theorem (''[[Real analysis|real analysis]]'')
*[[Malgrange preparation theorem]] (''[[Singularity theory|singularity theory]]'')
*[[Mean value theorem]] (''[[Calculus|calculus]]'')
*[[Monotone convergence theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Müntz–Szász theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Rademacher's theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Rising sun lemma]] (''[[Real analysis|real analysis]]'')
*[[Rolle's theorem]] (''[[Calculus|calculus]]'')
*[[Squeeze theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*Stokes's theorem (''[[Vector calculus|vector calculus]], [[Differential topology|differential topology]]'')
*[[Titchmarsh convolution theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Whitney extension theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Zahorski theorem]] (''[[Real analysis|real analysis]]'')

==Measure and integration==

*Banach–Tarski theorem (''measure theory'')
*[[Brunn–Minkowski theorem]] (''[[Riemannian geometry]]'')
*[[Cameron–Martin theorem]] (''measure theory'')
*[[Carathéodory's extension theorem]] (''measure theory'')
*[[Cramér–Wold theorem]] (''measure theory'')
*[[Disintegration theorem]] (''measure theory'')
*[[Dominated convergence theorem]] (''[[Lebesgue integration]]'')
*[[Egorov's theorem]] (''measure theory'')
*[[Fatou–Lebesgue theorem]] (''[[Real analysis|real analysis]]'')
*[[Fubini's theorem]] (''[[Integral|integration]]'')
*[[Hahn decomposition theorem]] (''measure theory'')
*[[Hahn–Kolmogorov theorem]] (''measure theory'')
*[[Ham sandwich theorem]] (''[[Topology|topology]]'')
*[[Hobby–Rice theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Kōmura's theorem]] (''measure theory'')
*[[Lebesgue's decomposition theorem]] (''measure theory'')
*[[Lebesgue's density theorem]] (''measure theory'')
*[[Maharam's theorem]] (''measure theory'')
*[[Minlos's theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Monotone class theorem]] (''measure theory'')
*[[Prokhorov's theorem]] (''measure theory'')
*[[Radon–Nikodym theorem]] (''measure theory'')
*[[Schilder's theorem]] (''stochastic processes'')
*[[Schröder–Bernstein theorem for measurable spaces]] (''measure theory'')
*[[Stein–Strömberg theorem]] (''measure theory'')
*[[Steinhaus theorem]] (''measure theory'')
*Stone–Tukey theorem (''[[Topology|topology]]'')
*[[Structure theorem for Gaussian measures]] (''measure theory'')
*[[Vitali convergence theorem]] (''measure theory'')
*[[Vitali set|Vitali theorem]] (''measure theory'')
*[[Vitali–Hahn–Saks theorem]] (''measure theory'')

==Functions of a complex variable==

*[[Akhiezer's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Arakelyan's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Area theorem (conformal mapping)]] (''[[Complex analysis|complex analysis]]'')
*[[Beurling–Lax theorem]] (''[[Hardy space]]s'')
*[[Bloch's theorem (complex variables)|Bloch's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Bôcher's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Borel–Carathéodory theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Branching theorem]] (''[[Complex manifold|complex manifold]]'')
*[[Carathéodory's theorem (conformal mapping)|Carathéodory's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Carleson–Jacobs theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Carlson's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Cauchy integral theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Cauchy–Hadamard theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Clifford's theorem on special divisors]] (''[[Algebraic curve|algebraic curve]]s'')
*[[Corona theorem]] (''[[Complex analysis|complex analysis]]'')
*[[De Branges's theorem|de Branges's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[De Franchis theorem]] (''Riemann surfaces'')
*[[Edge-of-the-wedge theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Farrell–Markushevich theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Fatou's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Fundamental theorem of algebra]] (''[[Complex analysis|complex analysis]]'')
*[[Gauss–Lucas theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Grunsky's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hadamard three-circle theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hadamard three-lines theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hardy's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hartogs–Rosenthal theorem]] (''[[Complex analysis|complex analysis]]'')
*Harnack's theorem (''[[Complex analysis|complex analysis]]'')
*[[Hurwitz's automorphisms theorem]] (''[[Algebraic curve|algebraic curve]]s'')
*[[Hurwitz's theorem (complex analysis)|Hurwitz's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Identity theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Identity theorem for Riemann surfaces]] (''Riemann surfaces'')
*Koebe 1/4 theorem (''[[Complex analysis|complex analysis]]'')
*[[Lagrange inversion theorem]] (''[[Mathematical analysis|mathematical analysis]]'', ''[[Combinatorics|combinatorics]]'')
*[[Lagrange reversion theorem]] (''[[Mathematical analysis|mathematical analysis]]'', ''[[Combinatorics|combinatorics]]'')
*Laurent expansion theorem (''[[Complex analysis|complex analysis]]'')
*[[Lindelöf's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Liouville's theorem (complex analysis)|Liouville's theorem]] (''[[Complex analysis|complex analysis]], entire functions'')
*[[Liouville's theorem (conformal mappings)|Liouville's theorem]] (''[[Conformal mapping|conformal mapping]]s'')
*[[Looman–Menchoff theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Marden's theorem]] (''[[Polynomials|polynomials]]'')
*[[Mergelyan's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Quasiconformal mapping#Measurable Riemann mapping theorem|Measurable Riemann mapping theorem]] (''[[Conformal mapping|conformal mapping]]'')
*[[Mittag-Leffler's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Monodromy theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Montel's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Morera's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Nachbin's theorem]](''[[Complex analysis|complex analysis]]'')
*[[Open mapping theorem (complex analysis)|Open mapping theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Ostrowski–Hadamard gap theorem]] (''[[Complex analysis|complex analysis]]'')
*Phragmén–Lindelöf theorem (''[[Complex analysis|complex analysis]]'')
*[[Picard theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Residue theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Riemann mapping theorem]] (''[[Complex analysis|complex analysis]]'')
*Riemann's existence theorem (''[[Algebraic geometry|algebraic geometry]]'')
*Riemann's theorem on removable singularities (''[[Complex analysis|complex analysis]]'')
*[[Riemann–Roch theorem]] (''[[Riemann surface]]s'', ''[[Algebraic curve|algebraic curve]]s'')
*[[Rouché's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Routh–Hurwitz theorem]] (''[[Polynomials|polynomials]]'')
*[[Runge's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Siu's semicontinuity theorem]] (''[[Complex analysis|complex analysis]]'')
*Sokhatsky–Weierstrass theorem (''[[Complex analysis|complex analysis]]'')
*[[Uniformization theorem]] (''[[Complex analysis|complex analysis]]'', ''[[Differential geometry|differential geometry]]'')
*[[Convergence problem#Van Vleck.27s theorem|Van Vleck's theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*Weierstrass–Casorati theorem (''[[Complex analysis|complex analysis]]'')
*[[Weierstrass factorization theorem]] (''[[Complex analysis|complex analysis]]'')

==Several complex variables and analytic spaces==

*[[Appell–Humbert theorem]] (''[[Complex manifold|complex manifold]]'')
*Baily–Borel theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Behnke–Stein theorem]] (''[[Several complex variables|several complex variables]]'')
*[[Birkhoff–Grothendieck theorem]] (''[[Complex geometry|complex geometry]]'')
*[[Bochner's tube theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Cartan's theorems A and B]] (''[[Several complex variables|several complex variables]]'')
*[[Castelnuovo–de Franchis theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Algebraic geometry and analytic geometry#Chow.27s theorem|Chow's theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Cramer's theorem (algebraic curves)]] (''[[Analytic geometry|analytic geometry]]'')
*[[Hartogs's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hartogs's extension theorem]] (''[[Several complex variables|several complex variables]]'')
*[[Hirzebruch–Riemann–Roch theorem]] (''complex manifolds'')
*[[Kawamata–Viehweg vanishing theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Kodaira embedding theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Kodaira vanishing theorem]] (''[[Complex manifold|complex manifold]]'')
*[[Lefschetz theorem on (1,1)-classes]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Local invariant cycle theorem]] (''[[Algebraic geometry|algebraic geometry]]'')
*[[Malgrange–Zerner theorem]] (''[[Complex analysis|complex analysis]]'')
*Newlander–Niremberg theorem (''[[Differential geometry|differential geometry]]'')
*[[Remmert–Stein theorem]] (''[[Complex analysis|complex analysis]]'')
*Riemann singularity theorem (''[[Algebraic geometry|algebraic geometry]]'')
*[[Skoda–El Mir theorem]] (''[[Complex geometry|complex geometry]]'')
*[[Weierstrass preparation theorem]] (''[[Several complex variables|several complex variables]]'', ''[[Commutative algebra|commutative algebra]]'')

==Special functions==

*[[De Moivre's formula|De Moivre's theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Hölder's theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Multiplication theorem]] (''special functions'')

==Ordinary differential equations==

*[[Carathéodory's existence theorem]] (''ordinary differential equations'')
*[[Floquet theory#Floquet theorem|Floquet's theorem]] (''differential equations'')
*Fuchs's theorem (''differential equations'')
*[[Kharitonov's theorem]] (''[[Control theory|control theory]]'')
*[[Kneser's theorem (differential equations)|Kneser's theorem]] (''differential equations'')
*Liénard's theorem (''[[Dynamical system|dynamical system]]s'')
*Markus−Yamabe theorem (''dynamical systems'')
*[[Peano existence theorem]] (''ordinary differential equations'')
*Picard&ndash;Lindelöf theorem (''ordinary differential equations'')
*[[Shift theorem]] (''[[Differential operator|differential operator]]s'')
*[[Sturm–Picone comparison theorem]] (''differential equations'')

==Partial differential equations==

*[[Cartan–Kähler theorem]] (''[[Partial differential equation|partial differential equation]]s'')
*[[Cartan–Kuranishi prolongation theorem]] (''[[Partial differential equation|partial differential equation]]s'')
*[[Cauchy–Kowalevski theorem]] (''[[Partial differential equation|partial differential equation]]s'')
*[[Malgrange–Ehrenpreis theorem]] (''differential equations'')

==Dynamical systems and ergodic theory==

*[[Autonomous convergence theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Banach fixed-point theorem]] (''[[Metric space|metric space]]s, [[Differential equation|differential equation]]s'')
*[[Bendixson–Dulac theorem]] (''[[Dynamical system|dynamical system]]s'')
*Birkhoff's theorem (''[[Ergodic theory|ergodic theory]]'')
*[[Conley–Zehnder theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Curtis–Hedlund–Lyndon theorem]] (''[[Cellular automata|cellular automata]]'')
*[[Hartman–Grobman theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Physics:Kolmogorov–Arnold–Moser theorem|Kolmogorov–Arnold–Moser theorem]] (''dynamical systems'')
*[[Krylov–Bogolyubov theorem]] (''dynamical systems'')
*[[Maximal ergodic theorem]] (''[[Ergodic theory|ergodic theory]]'')
*No wandering domain theorem (''[[Ergodic theory|ergodic theory]]'')
*[[Physics:Noether's theorem|Noether's theorem]] (''[[Lie group]]s'', ''[[Calculus of variations|calculus of variations]]'', ''[[Differential invariant|differential invariant]]s'', ''[[HandWiki:Physics|physics]]'')
*Ornstein theorem (''[[Ergodic theory|ergodic theory]]'')
*Oseledec theorem (''[[Ergodic theory|ergodic theory]]'')
*[[Peixoto's theorem]] (''dynamical systems'')
*[[Poincaré–Bendixson theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Poincaré recurrence theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Ratner's theorems]] (''[[Ergodic theory|ergodic theory]]'')
*Sarkovskii's theorem (''[[Dynamical system|dynamical system]]s'')
*[[Physics:Takens's theorem|Takens's theorem]] (''[[Dynamical system|dynamical system]]s'')

==Difference and functional equations==

*Euler's theorem on homogeneous functions (''multivariate calculus'')

==Sequence, series, summability==

*[[Abel's theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Abelian and Tauberian theorems]] (''[[Mathematical analysis|mathematical analysis]]'')
*Absolute convergence theorem (''mathematical series'')
*[[Cesàro summation|Cesàro's theorem]] (''[[Real analysis|real analysis]]'')
*[[Hardy–Littlewood tauberian theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Riemann series theorem]] (''mathematical series'')
*[[Silverman–Toeplitz theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Śleszyński–Pringsheim theorem]] (''[[Continued fraction|continued fraction]]'')
*[[Stolz–Cesàro theorem]] (''[[Calculus|calculus]]'')

==Approximations and expansions==

*[[Stone–Weierstrass theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Taylor's theorem]] (''[[Calculus|calculus]]'')

==Harmonic analysis on Euclidean spaces==

*[[Balian–Low theorem]] (''[[Fourier analysis]]'')
*[[Bernstein's theorem (approximation theory)|Bernstein's theorem]] (''[[Approximation theory|approximation theory]]'')
*[[Carleson's theorem]] (''[[Harmonic analysis|harmonic analysis]]'')
*[[Convolution theorem]] (''[[Fourier transform]]s'')
*[[Denjoy–Luzin theorem|Denjoy theorem]] (''[[Dynamical system|dynamical system]]s'')
*[[Fourier inversion theorem]] (''[[Harmonic analysis|harmonic analysis]]'')
*Fourier theorem (''[[Harmonic analysis|harmonic analysis]]'')
*Hausdorff-Young inequality (''[[Fourier analysis]]'')
*[[Lauricella's theorem]] (''[[Functional analysis|functional analysis]]'')
*Paley&ndash;Wiener theorem (''[[Fourier transform]]s'')
*[[Parseval's theorem]] (''[[Fourier analysis]]'')
*[[Plancherel theorem]] (''[[Fourier analysis]]'')
*[[Riesz–Fischer theorem]] (''[[Real analysis|real analysis]]'')
*[[Szegő limit theorems]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Wiener's tauberian theorem]] (''[[Real analysis|real analysis]]'')
*[[Wiener–Ikehara theorem]] (''[[Number theory|number theory]]'')

==Abstract harmonic analysis==

*[[F. and M. Riesz theorem]] (''measure theory'')
*[[Peter–Weyl theorem]] (''[[Representation theory|representation theory]]'')
*[[Pontryagin duality#Pontryagin duality theorem|Pontryagin duality theorem]] (''[[Representation theory|representation theory]]'')

==Integral transforms, operational calculus==

*[[Final value theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Initial value theorem]] (''[[Integral transform|integral transform]]'')
*[[Mellin inversion theorem]] (''[[Complex analysis|complex analysis]]'')
*[[Stahl's theorem]] (''[[Matrix analysis|matrix analysis]]'')
*[[Hilbert transform#Titchmarsh's theorem|Titchmarsh theorem]] (''[[Integral transform|integral transform]]'')

==Integral equations==

*[[Fredholm's theorem]] (''[[Linear algebra|linear algebra]]'')

==Functional analysis==

*[[Analytic Fredholm theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Banach–Alaoglu theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Banach–Mazur theorem]] (''[[Functional analysis|functional analysis]]'')
*Banach–Steinhaus theorem (''[[Functional analysis|functional analysis]]'')
*Choquet–Bishop–de Leeuw theorem (''[[Functional analysis|functional analysis]]'')
*[[Closed range theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Dunford–Schwartz theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Eberlein–Šmulian theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Goldstine theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Hahn–Banach theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Hilbert projection theorem]] (''[[Convex analysis|convex analysis]]'')
*[[Kachurovskii's theorem]] (''[[Convex analysis|convex analysis]]'')
*[[Kirszbraun theorem]] (''[[Lipschitz continuity]]'')
*[[M. Riesz extension theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Milman–Pettis theorem]] (''[[Banach space]]'')
*Moore–Aronszajn theorem (''[[Hilbert space]]'')
*[[Orlicz–Pettis theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Quotient of subspace theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Riesz representation theorem]] (''[[Functional analysis|functional analysis]], [[Hilbert space]]'')
*[[Schauder fixed-point theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Schwartz kernel theorem]] (''[[Generalized function|generalized function]]s'')
*Sobczyk's theorem (''[[Functional analysis|functional analysis]]'')
*Sobolev embedding theorem (''[[Mathematical analysis|mathematical analysis]]'')
*[[Solèr's theorem]] (''[[Mathematical logic|mathematical logic]]'')
*Tikhonov fixed-point theorem (''[[Functional analysis|functional analysis]]'')
*[[Trudinger's theorem]] (''[[Functional analysis|functional analysis]]'')

==Operator theory==

*Aronszajn–Smith theorem (''[[Functional analysis|functional analysis]]'')
*[[Atiyah–Singer index theorem]] (''elliptic differential operators'', ''[[Harmonic analysis|harmonic analysis]]'')
*[[Atkinson's theorem]] (''[[Operator theory|operator theory]]'')
*[[Babuška–Lax–Milgram theorem]] (''[[Partial differential equation|partial differential equation]]s'')
*[[Banach–Stone theorem]] (''[[Operator theory|operator theory]]'')
*[[Bauer–Fike theorem]] (''[[Spectral theory|spectral theory]]'')
*[[Bounded inverse theorem]] (''[[Operator theory|operator theory]]'')
*[[Browder–Minty theorem]] (''[[Operator theory|operator theory]]'')
*[[Choi's theorem on completely positive maps]] (''[[Operator theory|operator theory]]'')
*[[Commutation theorem]] (''[[Von Neumann algebra|von Neumann algebra]]'')
*[[Fuglede's theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Gelfand–Mazur theorem]] (''[[Banach algebra]]'')
*[[Gelfand–Naimark theorem]] (''[[Functional analysis|functional analysis]]'')
*Hardy–Littlewood maximal theorem (''[[Real analysis|real analysis]]'')
*Hellinger&ndash;Toeplitz theorem (''[[Functional analysis|functional analysis]]'')
*[[Hilbert–Schmidt theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Hille–Yosida theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Kaplansky density theorem]] (''[[Von Neumann algebra|von Neumann algebra]]'')
*[[Kuiper's theorem]] (''[[Operator theory|operator theory]]'', ''[[Topology|topology]]'')
*[[Lax–Milgram theorem]] (''partial differential equations'')
*[[Lions–Lax–Milgram theorem]] (''partial differential equations'')
*[[Lumer–Phillips theorem]] (''semigroup theory'')
*Marcinkiewicz theorem (''[[Functional analysis|functional analysis]]'')
*[[Mazur–Ulam theorem]] (''[[Normed space|normed space]]s'')
*[[Mercer's theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Min-max theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Moreau's theorem]] (''[[Convex analysis|convex analysis]]'')
*[[Nash–Moser theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Open mapping theorem (functional analysis)|Open mapping theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Peetre theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Riesz–Thorin theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Ryll-Nardzewski fixed-point theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Sazonov's theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Schröder–Bernstein theorems for operator algebras]] (''[[Operator algebra|operator algebra]]s'')
*[[Stinespring factorization theorem]] (''[[Operator theory|operator theory]]'')
*[[Stone's theorem on one-parameter unitary groups]] (''[[Functional analysis|functional analysis]]'')
*[[Sz.-Nagy's dilation theorem]] (''[[Operator theory|operator theory]]'')
*Tomita's theorem (''[[Operator algebra|operator algebra]]s'')
*[[Von Neumann bicommutant theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Von Neumann's theorem]] (''[[Operator theory|operator theory]]'')

==Calculus of variations and optimal control; optimization==

*[[Caristi fixed-point theorem]] (''[[Fixed point (mathematics)|fixed points]]'')
*[[Envelope theorem]] (''[[Calculus of variations|calculus of variations]]'')
*Isoperimetric theorem (''[[Curve|curve]]s'', ''[[Calculus of variations|calculus of variations]]'')
*[[Minimax theorem]] (''[[Game theory|game theory]]'')
*[[Mountain pass theorem]] (''[[Calculus of variations|calculus of variations]]'')
*[[Physics:Noether's second theorem|Noether's second theorem]] (''[[Calculus of variations|calculus of variations]]'', ''[[HandWiki:Physics|physics]]'')
*[[Parthasarathy's theorem]] (''[[Game theory|game theory]]'')
*[[Sion's minimax theorem]] (''[[Game theory|game theory]]'')
*[[Tonelli's theorem (functional analysis)|Tonelli's theorem]] (''[[Functional analysis|functional analysis]]'')

==Geometry==

*Alternate Interior Angles Theorem (''[[Geometry|geometry]]'')
*Alternate segment theorem (''[[Geometry|geometry]]'')
*[[Angle bisector theorem]] (''[[Euclidean geometry]]'')
*[[Anne's theorem]] (''[[Geometry|geometry]]'')
*[[Apollonius's theorem]] (''plane geometry'')
*[[Barbier's theorem]] (''[[Geometry|geometry]]'')
*[[Beck's theorem (geometry)|Beck's theorem]] (''[[Incidence geometry|incidence geometry]]'')
*[[Beckman–Quarles theorem]] (''[[Euclidean geometry]]'')
*[[Beer's theorem]] (''metric geometry'')
*[[Brahmagupta theorem]] (''[[Euclidean geometry]]'')
*[[Brianchon's theorem]] (''[[Conic|conic]]s'')
*[[British flag theorem]] (''[[Euclidean geometry]]'')
*[[Butterfly theorem]] (''[[Euclidean geometry]]'')
*CPCTC (''triangle geometry'')
*[[Carnot's theorem (inradius, circumradius)|Carnot's theorem]] (''[[Geometry|geometry]]'')
*[[Casey's theorem]] (''[[Euclidean geometry]]'')
*[[Cayley–Bacharach theorem]] (''[[Projective geometry|projective geometry]]'')
*[[Ceva's theorem]] (''[[Geometry|geometry]]'')
*[[Clifford's circle theorems]] (''Euclidean plane geometry'')
*[[Commandino's theorem]] (''[[Geometry|geometry]]'')
*[[Constant chord theorem]] (''[[Geometry|geometry]]'')
*Conway circle theorem (''Euclidean plane geometry'')
*[[Crossbar theorem]] (''Euclidean plane geometry'')
*Dandelin's theorem (''[[Solid geometry|solid geometry]]'')
*[[De Bruijn–Erdős theorem (incidence geometry)]]
*[[De Gua's theorem]] (''[[Geometry|geometry]]'')
*[[Desargues's theorem]] (''[[Projective geometry|projective geometry]]'')
*Descartes's theorem (''plane geometry'')
*[[Dinostratus' theorem]] (''[[Geometry|geometry]]'', ''[[Mathematical analysis|analysis]]'')
*[[Equal incircles theorem]] (''[[Euclidean geometry]]'')
*[[Euler's quadrilateral theorem]] (''[[Geometry|geometry]]'')
*[[Euler's theorem in geometry]] (''triangle geometry'')
*[[Exterior angle theorem]] (''triangle geometry'')
*Feuerbach's theorem (''[[Geometry|geometry]]'')
*[[Finsler–Hadwiger theorem]] (''[[Geometry|geometry]]'')
*[[Five circles theorem]] (''[[Circle|circle]]s'')
*Gauss–Wantzel theorem (''[[Geometry|geometry]]'')
*[[Geometric mean theorem]] (''[[Geometry|geometry]]'')
*[[Hinge theorem]] (''[[Geometry|geometry]]'')
*[[Hjelmslev's theorem]] (''[[Geometry|geometry]]'')
*[[Angle trisection#Proof of impossibility|Impossibility of angle trisection]] (''[[Geometry|geometry]]'')
*[[Parallel postulate#History|Independence of the parallel postulate]] (''[[Geometry|geometry]]'')
*[[Inscribed angle#Theorem|Inscribed angle theorem]] (''[[Geometry|geometry]]'')
*[[Intercept theorem]] (''[[Euclidean geometry]]'')
*[[Intersecting chords theorem]] (''[[Euclidean geometry]]'')
*[[Intersecting secants theorem]] (''[[Euclidean geometry]]'')
*[[Intersection theorem]] (''[[Projective geometry|projective geometry]]'')
*Japanese theorem for concyclic polygons (''[[Euclidean geometry]]'')
*Japanese theorem for concyclic quadrilaterals (''[[Euclidean geometry]]'')
*[[Kawasaki's theorem]] (''[[Mathematics of paper folding|mathematics of paper folding]]'')
*[[Lester's theorem]] (''Euclidean plane geometry'')
*[[Lexell's theorem]] (''[[Spherical geometry|spherical geometry]]'')
*[[Menelaus's theorem]] (''[[Geometry|geometry]]'')
*[[Miquel's theorem]] (''[[Geometry|geometry]]'')
*[[Mohr–Mascheroni theorem]] (''[[Geometry|geometry]]'')
*[[Monge's theorem]] (''[[Geometry|geometry]]'')
*[[Morley's trisector theorem]] (''[[Geometry|geometry]]'')
*[[Napoleon's theorem]] (''triangle geometry'')
*[[Newton's theorem about ovals]] (''[[Curve|curve]]s'')
*[[Newton's theorem (quadrilateral)]] (''[[Geometry|geometry]]'')
*[[Pappus's area theorem]] (''[[Geometry|geometry]]'')
*[[Pappus's centroid theorem]] (''[[Geometry|geometry]]'')
*[[Pappus's hexagon theorem]] (''[[Geometry|geometry]]'')
*[[Pascal's theorem]] (''[[Conic|conic]]s'')
*[[Pasch's theorem]] (''[[Order theory|order theory]]'')
*[[Pitot theorem]] (''plane geometry'')
*Pivot theorem (''[[Circle|circle]]s'')
*[[Pompeiu's theorem]] (''[[Euclidean geometry]]'')
*[[Poncelet's closure theorem]] (''[[Conic|conic]]s'')
*[[Poncelet–Steiner theorem]] (''[[Geometry|geometry]]'')
*[[Ptolemy's theorem]] (''[[Geometry|geometry]]'')
*[[Pythagorean theorem]] (''[[Geometry|geometry]]'')
*[[Reuschle's theorem]] (''[[Euclidean geometry]]'')
*[[Routh's theorem]] (''triangle geometry'')
*[[Saccheri–Legendre theorem]] (''[[Absolute geometry|absolute geometry]]'')
*[[Six circles theorem]] (''[[Circle|circle]]s'')
*[[Steiner–Lehmus theorem]] (''triangle geometry'')
*[[Altitude (triangle)|Symphonic theorem]] (''triangle geometry'')
*[[Tangent-secant theorem]] (''[[Geometry|geometry]]'')
*[[Thales's theorem]] (''[[Geometry|geometry]]'')
*[[Thébault's theorem]] (''[[Geometry|geometry]]'')
*[[Theorem of the gnomon]] (''[[Geometry|geometry]]'')
*[[Thomsen's theorem]] (''[[Geometry|geometry]]'')
*[[Van Aubel's theorem]] (''quadrilaterals'')
*[[Van Schooten's theorem]]  (''[[Euclidean geometry]]'')
*[[Varignon's theorem]] (''[[Euclidean geometry]]'')
*[[Viviani's theorem]] (''[[Euclidean geometry]]'')

==Convex and discrete geometry==

*[[Alexandrov's uniqueness theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Balinski's theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Tarski's plank problem|Bang's theorem]] (''[[Geometry|geometry]]'')
*[[Besicovitch covering theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Blaschke selection theorem]] (''[[Geometric topology|geometric topology]]'')
*Bolyai–Gerwien theorem (''[[Discrete geometry|discrete geometry]]'')
*[[Busemann's theorem]] (''[[Euclidean geometry]]'')
*[[Carathéodory's theorem (convex hull)|Carathéodory's theorem]] (''[[Convex geometry|convex geometry]]'')
*[[Cauchy's theorem (geometry)|Cauchy's theorem]] (''[[Geometry|geometry]]'')
*[[Platonic solid#Classification|Classification of Platonic solids]] (''[[Geometry|geometry]]'')
*[[De Bruijn's theorem|de Bruijn's theorem]] (''[[Discrete geometry|discrete geometry]]'')
*Descartes's theorem on total angular defect (''polyhedra'')
*[[Erdős–Anning theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Erdős–Nagy theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Erdős–Szekeres theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Fáry's theorem]] (''[[Graph theory|graph theory]]'')
*[[Fenchel's duality theorem]] (''[[Convex analysis|convex analysis]]'')
*[[Fenchel–Moreau theorem]] (''[[Mathematical analysis|mathematical analysis]]'')
*[[Hadwiger's theorem]] (''[[Geometry|geometry]]'', ''measure theory'')
*[[Helly's theorem]] (''[[Convex set|convex set]]s'')
*[[Holditch's theorem]] (''plane geometry'')
*[[John ellipsoid]] (''[[Geometry|geometry]]'')
*[[Jung's theorem]] (''[[Geometry|geometry]]'')
*[[Kepler conjecture]] (''[[Discrete geometry|discrete geometry]]'')
*[[Kirchberger's theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Krein–Milman theorem]] (''[[Mathematical analysis|mathematical analysis]], [[Discrete geometry|discrete geometry]]'')
*[[Minkowski's theorem]] (''[[Geometry of numbers|geometry of numbers]]'')
*[[Minkowski's second theorem]] (''[[Geometry of numbers|geometry of numbers]]'')
*[[Minkowski–Hlawka theorem]] (''[[Geometry of numbers|geometry of numbers]]'')
*[[Monsky's theorem]] (''[[Discrete geometry|discrete geometry]]'')
*[[Pick's theorem]] (''[[Geometry|geometry]]'')
*[[Pizza theorem]] (''[[Geometry|geometry]]'')
*[[Radon's theorem]] (''[[Convex set|convex set]]s'')
*Separating axis theorem (''[[Convex geometry|convex geometry]]'')
*[[Steinitz theorem]] (''[[Graph theory|graph theory]]'')
*[[Stewart's theorem]] (''plane geometry'')
*Supporting hyperplane theorem (''[[Convex geometry|convex geometry]]'')
*[[Sylvester–Gallai theorem]] (''plane geometry'')
*[[Szemerédi–Trotter theorem]] (''[[Combinatorics|combinatorics]]'')
*[[Tverberg's theorem]] (''[[Discrete geometry|discrete geometry]]'')
*Vitali covering theorem (''measure theory'')
*[[Wallace–Bolyai–Gerwien theorem]] (''[[Discrete geometry|discrete geometry]]'')

==Differential geometry==

*[[2π theorem|2π theorem]] (''[[Riemannian geometry]]'')
*[[Abel–Jacobi map#The Abel–Jacobi map of a Riemannian manifold|Abel's curve theorem]] (''[[Riemannian geometry|riemannian geometry]]'')
*[[Beltrami's theorem]] (''[[Riemannian geometry]]'')
*[[Berger–Kazdan comparison theorem]] (''[[Riemannian geometry]]'')
*Bertrand–Diquet–Puiseux theorem (''[[Differential geometry|differential geometry]]'')
*Bishop-Gromov inequality (''[[Riemannian geometry|riemannian geometry]]'')
*[[Bonnet theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Carathéodory–Jacobi–Lie theorem]] (''symplectic topology'')
*[[Cartan–Hadamard theorem]] (''[[Riemannian geometry]]'')
*[[Cheng's eigenvalue comparison theorem]] (''[[Riemannian geometry]]'')
*[[Chern–Gauss–Bonnet theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Symmetric space#Classification of Riemannian symmetric spaces|Classification of symmetric spaces]] (''[[Lie theory]]'')
*[[Darboux's theorem]] (''symplectic topology'')
*[[Euler's theorem (differential geometry)|Euler's theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Four-vertex theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Frobenius theorem (differential topology)|Frobenius theorem]] (''[[Foliation|foliation]]s'')
*[[Gauss's lemma (Riemannian geometry)|Gauss's lemma]] (''[[Riemannian geometry|riemannian geometry]]'')
*Gauss's Theorema Egregium (''[[Differential geometry|differential geometry]]'')
*[[Gauss–Bonnet theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Geroch's splitting theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Gromov's compactness theorem (geometry)|Gromov's compactness theorem]] (''[[Riemannian geometry]]'')
*[[Gromov's compactness theorem (topology)|Gromov's compactness theorem]] (''symplectic topology'')
*Gromov–Ruh theorem (''[[Differential geometry|differential geometry]]'')
*[[Hilbert's theorem (differential geometry)|Hilbert's theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Hopf–Rinow theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Killing–Hopf theorem]] (''[[Riemannian geometry]]'')
*[[Lee Hwa Chung theorem]] (''symplectic topology'')
*[[Lie–Palais theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Meusnier's theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Mostow rigidity theorem]] (''[[Differential geometry|differential geometry]]'')
*Myers theorem (''[[Differential geometry|differential geometry]]'')
*[[Myers–Steenrod theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Nash embedding theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Non-squeezing theorem]] (''[[Symplectic geometry|symplectic geometry]]'')
*[[Orbit (control theory)#Corollary (Rashevsky–Chow theorem)|Rashevsky–Chow theorem]] (''[[Control theory|control theory]]'')
*[[Rauch comparison theorem]] (''[[Riemannian geometry]]'')
*[[Schwarz–Ahlfors–Pick theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Soul theorem]] (''[[Riemannian geometry]]'')
*[[Sphere theorem]] (''[[Riemannian geometry]]'')
*[[Synge's theorem]] (''[[Riemannian geometry]]'')
*[[Toponogov's theorem]] (''[[Riemannian geometry]]'')

==General topology==

*[[Arzelà–Ascoli theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Baire category theorem]] (''[[Topology|topology]]'', ''[[Metric space|metric space]]s'')
*[[Bing metrization theorem]] (''[[General topology|general topology]]'')
*[[Bolzano–Weierstrass theorem]] (''[[Real analysis|real analysis]], [[Calculus|calculus]]'')
*[[Borsuk–Ulam theorem]] (''[[Topology|topology]]'')
*[[Brouwer fixed-point theorem]] (''[[Topology|topology]]'')
*[[Cantor's intersection theorem]] (''[[Real analysis|real analysis]]'')
*[[Closed graph theorem]] (''[[Functional analysis|functional analysis]]'')
*[[Extreme value theorem]] (''[[Calculus|calculus]]'')
*[[Fixed-point theorems in infinite-dimensional spaces]]
*[[Hairy ball theorem]] (''[[Algebraic topology|algebraic topology]]'')
*Hahn–Mazurkiewicz theorem (''continuum theory'')
*[[Heine–Borel theorem]] (''[[Real analysis|real analysis]]'')
*[[Heine–Cantor theorem]] (''metric geometry'')
*[[Jordan curve theorem]] (''[[Topology|topology]]'')
*[[Kuratowski's closure-complement problem]] (''[[Topology|topology]]'')
*[[Lebesgue covering dimension]] (''[[Dimension theory|dimension theory]]'')
*Metrization theorems (''[[Topological space|topological space]]s'')
*[[Nagata–Smirnov metrization theorem]](''[[General topology|general topology]]'')
*[[Netto's theorem]] (''[[Topology|topology]]'')
*Parovicenko's theorem (''[[Topology|topology]]'')
*[[Tietze extension theorem]] (''[[General topology|general topology]]'')
*[[Tychonoff's theorem]] (''[[General topology|general topology]]'')

==Algebraic topology==

*Acyclic models theorem (''[[Algebraic topology|algebraic topology]]'')
*[[Blakers–Massey theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Bott periodicity theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Brown's representability theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Cellular approximation theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Dold–Thom theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Eilenberg–Ganea theorem]] (''[[Homological algebra|homological algebra]]'', ''[[Algebraic topology|algebraic topology]]'')
*[[Eilenberg–Zilber theorem]] (''[[Algebraic topology|algebraic topology]]'')
*Euler's polyhedron theorem (''polyhedra'')
*[[Excision theorem]] (''[[Homology theory|homology theory]]'')
*[[Freudenthal suspension theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Hilton's theorem|Hilton–Milnor theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Homotopy excision theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Hopf theorem]] (''[[Differential topology|differential topology]]'')
*[[Hurewicz theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Künneth theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Invariance of domain]] (''[[Algebraic topology|algebraic topology]]'')
*[[Landweber exact functor theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Lefschetz fixed-point theorem]] (''[[Fixed point (mathematics)|fixed points]]'', ''[[Algebraic topology|algebraic topology]]'')
*Lefschetz–Hopf theorem (''[[Topology|topology]]'')
*[[Leray–Hirsch theorem]] (''[[Algebraic topology|algebraic topology]]'')
*Nielsen fixed-point theorem (''[[Fixed point (mathematics)|fixed points]]'')
*[[Nilpotence theorem]] (''[[Algebraic topology|algebraic topology]]'')
*Poincaré duality theorem (''[[Algebraic topology|algebraic topology]] of [[Manifold|manifold]]s'')
*[[Seifert–van Kampen theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Simplicial approximation theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Stallings–Zeeman theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Sullivan conjecture]] (''[[Homotopy theory|homotopy theory]]'')
*[[Universal coefficient theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Vietoris–Begle mapping theorem]] (''[[Algebraic topology|algebraic topology]]'')
*[[Whitehead theorem]] (''[[Homotopy theory|homotopy theory]]'')
*[[Regular homotopy|Whitney–Graustein Theorem]] (''[[Algebraic topology|algebraic topology]]'')

==Manifolds and cell complexes==

*[[Alexander's theorem]] (''[[Knot theory|knot theory]]'')
*[[Atiyah–Bott fixed-point theorem]] (''[[Differential topology|differential topology]]'')
*[[Bing's recognition theorem]] (''[[Geometric topology|geometric topology]]'')
*[[Mapping class group of a surface#The Birman exact sequence|Birman short exact sequence]] (''[[Geometric topology|geometric topology]]'')
*[[Surface (topology)#Classification of closed surfaces|Classification of compact surfaces]] (''[[Topology]]'')
*[[De Rham's theorem]] (''[[Differential topology|differential topology]]'')
*[[Mapping class group of a surface#The Dehn–Nielsen–Baer theorem|Dehn-Nielsen-Baer theorem]] (''[[Geometric topology|geometric topology]]'')
*[[Donaldson's theorem]] (''[[Differential topology|differential topology]]'')
*Ehresmann's theorem (''[[Differential topology|differential topology]]'')
*[[Fáry–Milnor theorem]] (''[[Knot theory|knot theory]]'')
*[[Fenchel's theorem]] (''[[Differential geometry|differential geometry]]'')
*H-cobordism theorem (''[[Differential topology|differential topology]]'')
*[[Hirzebruch signature theorem]] (''[[Topology|topology]]'', ''[[Algebraic geometry|algebraic geometry]]'')
*Jordan–Schönflies theorem (''[[Geometric topology|geometric topology]]'')
*[[JSJ decomposition|JSJ theorem]] (''3-manifolds'')
*Lickorish twist theorem (''[[Geometric topology|geometric topology]]'')
*[[Lickorish–Wallace theorem]] (''3-manifolds'')
*[[Nielsen realization problem]] (''[[Geometric topology|geometric topology]]'')
*Nielsen-Thurston classification (''[[Low-dimensional topology|low-dimensional topology]]'')
*[[Novikov's compact leaf theorem]] (''[[Foliation|foliation]]s'')
*[[Geometrization conjecture|Perelman's Geometrization theorem]] (''3-manifolds'')
*[[Poincaré–Hopf theorem]] (''[[Differential topology|differential topology]]'')
*[[Poincaré conjecture]] (''[[Topology|topology]]'')
*[[Preimage theorem]] (''[[Differential topology|differential topology]]'')
*[[Reeb sphere theorem]] (''[[Foliation|foliation]]s'')
*[[Heegaard splitting|Reidemeister–Singer Theorem]] (''[[Geometric topology|geometric topology]]'')
*[[Riemann–Roch theorem for smooth manifolds]] (''[[Differential topology|differential topology]]'')
*[[Rokhlin's theorem]] (''[[Geometric topology|geometric topology]]'')
*S–cobordism theorem (''[[Differential topology|differential topology]]'')
*[[Sard's theorem]] (''[[Differential geometry|differential geometry]]'')
*[[Scott core theorem]] (''3-manifolds'')
*Swan's theorem (''module theory'')
*[[Tameness theorem]] (''3-manifolds'')
*Thom transversality theorem (''[[Differential topology|differential topology]]'')
*[[Hyperbolization theorem|Thurston's geometrization theorem]] (''3-manifolds'')
*[[Heegaard splitting|Waldhausen's theorem]] (''[[Geometric topology|geometric topology]]'')
*[[Whitney embedding theorem]] (''differential manifolds'')
*[[Whitney immersion theorem]] (''[[Differential topology|differential topology]]'')

==Global analysis, analysis on manifolds==

*[[Radó's theorem (harmonic functions)|Radó's theorem]] (''[[Harmonic analysis|harmonic analysis]]'')

==Probability theory and stochastic processes==

*[[Bayes' theorem]] (''[[Probability|probability]]'')
*[[Bertrand's ballot theorem]] (''[[Probability theory|probability theory]]'', ''[[Combinatorics|combinatorics]]'')
*[[Burke's theorem]] (''[[Probability theory|probability theory]]'', ''[[Queueing theory|queueing theory]]'')
*[[Central limit theorem]] (''[[Probability|probability]]'')
*[[Clark–Ocone theorem]] (''stochastic processes'')
*[[Continuous mapping theorem]] (''[[Probability theory|probability theory]]'')
*[[Cramér's theorem (large deviations)]] (''[[Probability|probability]]'')
*[[Dawson–Gärtner theorem]] (''[[Asymptotic analysis|asymptotic analysis]]'')
*[[Donsker's theorem]] (''[[Probability theory|probability theory]]'')
*[[Doob decomposition theorem]] (''stochastic processes'')
*[[Doob's martingale convergence theorems]] (''stochastic processes'')
*[[Doob–Meyer decomposition theorem]] (''stochastic processes'')
*[[Dudley's theorem]] (''[[Probability|probability]]'')
*Dunford–Pettis theorem (''[[Probability theory|probability theory]]'')
*[[Fernique's theorem]] (''measure theory'')
*[[Foster's theorem]] (''[[Statistics|statistics]]'')
*[[Freidlin–Wentzell theorem]] (''stochastic processes'')
*Girsanov's theorem (''[[Stochastic process|stochastic process]]es'')
*[[Glivenko's theorem (probability theory)|Glivenko's theorem]] (''[[Probability|probability]]'')
*[[Gordon–Newell theorem]] (''[[Queueing theory|queueing theory]]'')
*[[Hammersley–Clifford theorem]] (''[[Probability|probability]]'')
*[[Helly–Bray theorem]] (''[[Probability theory|probability theory]]'')
*[[Integral representation theorem for classical Wiener space]] (''measure theory'')
*[[Ionescu-Tulcea theorem]] (''[[Probability theory|probability theory]]'')
*Jackson's theorem (''[[Queueing theory|queueing theory]]'')
*[[Karhunen–Loève theorem]] (''stochastic processes'')
*[[Kolmogorov extension theorem]] (''stochastic processes'')
*[[Kolmogorov's three-series theorem]] (''mathematical series'')
*[[Le Cam's theorem]] (''[[Probability theory|probability theory]]'')
*Lévy continuity theorem (''[[Probability|probability]]'')
*[[Lévy's modulus of continuity theorem]] (''[[Probability|probability]]'')
*[[Martingale representation theorem]] (''[[Probability theory|probability theory]]'')
*[[Maxwell's theorem]] (''[[Probability theory|probability theory]]'')
*[[Optional stopping theorem]] (''[[Probability theory|probability theory]]'')
*[[Poisson limit theorem]] (''[[Probability|probability]]'')
*[[Raikov's theorem]] (''[[Probability|probability]]'')
*[[Skorokhod's embedding theorem]] (''[[Statistics|statistics]]'')
*[[Skorokhod's representation theorem]] (''[[Statistics|statistics]]'')
*[[Slutsky's theorem]] (''[[Probability theory|probability theory]]'')
*Theorem of de Moivre–Laplace (''[[Probability theory|probability theory]]'')

==Statistics==

*[[Aumann's agreement theorem]] (''[[Statistics|statistics]]'')
*[[Bapat–Beg theorem]] (''[[Statistics|statistics]]'')
*[[Basu's theorem]] (''[[Statistics|statistics]]'')
*Berry–Esséen theorem (''[[Probability theory|probability theory]]'')
*[[Cochran's theorem]] (''[[Statistics|statistics]]'')
*[[Cox's theorem]] (''[[Probability|probability]]'')
*[[Cramér’s decomposition theorem]] (''[[Statistics|statistics]]'')
*[[De Finetti's theorem]] (''[[Probability|probability]]'')
*FWL theorem (''[[Finance:Economics|economics]]'')
*[[Fieller's theorem]] (''[[Statistics|statistics]]'')
*[[Fisher–Tippett–Gnedenko theorem]] (''[[Statistics|statistics]]'')
*[[Gauss–Markov theorem]] (''[[Statistics|statistics]]'')
*[[Glivenko–Cantelli theorem]] (''[[Probability|probability]]'')
*[[Infinite monkey theorem]] (''[[Probability|probability]]'')
*[[Lehmann–Scheffé theorem]] (''[[Statistics|statistics]]'')
*[[Lukacs's proportion-sum independence theorem]] (''[[Probability|probability]]'')
*[[Lyapunov's central limit theorem]] (''[[Probability theory|probability theory]]'')
*[[Pickands–Balkema–de Haan theorem]] (''[[Extreme value theory|extreme value theory]]'')
*Pitman&ndash;Koopman&ndash;Darmois theorem (''[[Statistics|statistics]]'')
*[[Rao–Blackwell theorem]] (''[[Statistics|statistics]]'')
*[[Sklar's theorem]] (''[[Statistics|statistics]]'')
*[[Wold's theorem]] (''[[Statistics|statistics]]'')

==Numerical analysis==

*[[Godunov's theorem]] (''[[Numerical analysis|numerical analysis]]'')
*[[Kantorovich theorem]] (''[[Functional analysis|functional analysis]]'')
*Lax&ndash;Richtmyer theorem (''[[Numerical analysis|numerical analysis]]'')
*[[Lax–Wendroff theorem]] (''[[Numerical analysis|numerical analysis]]'')
*[[Marsaglia's theorem]] (''[[Number theory|number theory]]'')

==Computer science==

*Akra–Bazzi theorem (''[[Computer science|computer science]]'')
*Art gallery theorem (''[[Geometry|geometry]]'')
*[[CAP theorem]] (''[[Theoretical computer science|theoretical computer science]]'')
*[[Chomsky–Schützenberger enumeration theorem]] (''formal language theory'')
*[[Chomsky–Schützenberger representation theorem]] (''formal language theory'')
*[[Codd's theorem]] (''[[Relational model|relational model]]'')
*[[Compression theorem]] (''[[Computational complexity theory|computational complexity theory]]'', ''[[Structural complexity theory|structural complexity theory]]'')
*Cook's theorem (''[[Computational complexity theory|computational complexity theory]]'')
*[[Fagin's theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Full employment theorem]] (''[[Theoretical computer science|theoretical computer science]]'')
*[[Gap theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Gottesman–Knill theorem]] (''quantum computation'')
*[[Holland's schema theorem]] (''[[Genetic algorithm|genetic algorithm]]'')
*[[Immerman–Szelepcsényi theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Karp–Lipton theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*Ladner's theorem (''[[Computational complexity theory|computational complexity theory]]'')
*[[Euclidean algorithm#Algorithmic efficiency|Lamé’s theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Linear speedup theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Master theorem (analysis of algorithms)]] (''[[Recurrence relation|recurrence relation]]s'', ''[[Asymptotic analysis|asymptotic analysis]]'')
*Max/min CSP/Ones classification theorems (''[[Computational complexity theory|computational complexity theory]]'')
*[[Myhill–Nerode theorem]] (''[[Formal language|formal language]]s'')
*[[No free lunch in search and optimization|No free lunch theorem (search and optimization)]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[PCP theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Pseudorandom generator theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Quantum threshold theorem]] (''[[Computer science|computer science]]'') (''[[Theoretical computer science|theoretical computer science]]'')
*[[Reversed compound agent theorem]] (''[[Probability|probability]]'')
*[[Rice's theorem]] (''recursion theory, [[Computer science|computer science]]'')
*[[Rice–Shapiro theorem]] (''[[Computer science|computer science]]'')
*[[Savitch's theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Schaefer's dichotomy theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Sipser–Lautemann theorem]] (''[[Probabilistic complexity theory|probabilistic complexity theory]]'') (''[[Structural complexity theory|structural complexity theory]]'')
*[[Smn theorem]] (''recursion theory, [[Computer science|computer science]]'')
*[[Space hierarchy theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Speedup theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Structured program theorem]] (''[[Computer science|computer science]]'')
*[[Time hierarchy theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Toda's theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*[[Universal approximation theorem]] (''artificial neural networks'')
*[[Valiant–Vazirani theorem]] (''[[Computational complexity theory|computational complexity theory]]'')

==Mechanics of particles and systems==

*[[Chasles' theorem (kinematics)|Chasles' theorem]] (''[[Physics:Kinematics|kinematics]]'')
*Chasles' theorem (''[[Company:Gravity|gravity]]'')
*[[Physics:Helmholtz theorem (classical mechanics)|Helmholtz theorem (classical mechanics)]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:König's theorem (kinetics)|König's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Lami's theorem|Lami's theorem]] (''[[Statics|statics]]'')
*[[Physics:Liouville's theorem (Hamiltonian)|Liouville's theorem]] (''[[Physics:Hamiltonian mechanics|Hamiltonian mechanics]]'')
*[[Physics:Parallel axis theorem|Parallel axis theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Perpendicular axis theorem|Perpendicular axis theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Virial theorem]] (''[[Physics:Classical mechanics|classical mechanics]]'')

==Mechanics of deformable solids==

*[[Betti's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Castigliano's method|Castigliano's first and second theorems]] (''[[Structural analysis|structural analysis]]'')
*Clapeyron's theorem (''[[HandWiki:Physics|physics]]'')
*[[Physics:Saint-Venant's theorem|Saint-Venant's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Theorem of three moments]] (''[[HandWiki:Physics|physics]]'')

==Fluid mechanics==

*[[Buckingham π theorem]] (''[[Dimensional analysis|dimensional analysis]]'')
*[[Physics:Helmholtz's theorems|Helmholtz's theorems]] (''[[HandWiki:Physics|physics]]'')
*[[Kelvin's circulation theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Kutta–Joukowski theorem|Kutta–Joukowski theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Reynolds transport theorem]] (''[[Physics:Fluid dynamics|fluid dynamics]]'')
*[[Physics:Taylor–Proudman theorem|Taylor–Proudman theorem]] (''[[HandWiki:Physics|physics]]'')

==Optics, electromagnetic theory==

*[[Physics:Blondel's theorem|Blondel's theorem]] (''[[Physics:Electric power|electric power]]'') (''[[HandWiki:Physics|physics]]'')
*[[Physics:Earnshaw's theorem|Earnshaw's theorem]] (''[[Physics:Electrostatics|electrostatics]]'')
*Maximum power theorem (''[[Physics:Electrical circuit|electrical circuit]]s'')
*[[Engineering:Norton's theorem|Norton's theorem]] (''[[Physics:Electrical network|electrical network]]s'')
*[[Physics:Optical theorem|Optical theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Poynting's theorem|Poynting's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Engineering:Thévenin's theorem|Thévenin's theorem]] (''[[Physics:Electrical circuit|electrical circuit]]s'')

==Classical thermodynamics, heat transfer==

*[[Physics:Carnot's theorem (thermodynamics)|Carnot's theorem]] (''[[Physics:Thermodynamics|thermodynamics]]'')
*[[Physics:Clausius theorem|Clausius theorem]] (''[[HandWiki:Physics|physics]]'')

==Quantum theory==

*[[Physics:Adiabatic theorem|Adiabatic theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Bell's theorem]] (''[[Physics:Quantum mechanics|quantum mechanics]]'')
*[[Physics:Bogoliubov–Parasyuk theorem|Bogoliubov–Parasyuk theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Physics:Byers–Yang theorem|Byers–Yang theorem]] (''[[Physics:Quantum mechanics|quantum mechanics]]'')
*[[C-theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Cluster decomposition theorem|Cluster decomposition theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Physics:Coleman–Mandula theorem|Coleman–Mandula theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Elitzur's theorem]] (''[[Quantum field theory|quantum field theory]], [[Physics:Statistical field theory|statistical field theory]]'')
*[[Physics:Furry's theorem|Furry's theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Physics:Gell-Mann and Low theorem|Gell-Mann and Low theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Gleason's theorem]] (''[[Hilbert space]]'')
*[[Physics:Goldstone's theorem|Goldstone's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Haag's theorem|Haag's theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Physics:Haag–Łopuszański–Sohnius theorem|Haag–Łopuszański–Sohnius theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Hellmann–Feynman theorem|Hellmann–Feynman theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Kinoshita–Lee–Nauenberg theorem|Kinoshita–Lee–Nauenberg theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Kochen–Specker theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Kramers' theorem|Kramers' theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Nielsen–Ninomiya theorem|Nielsen–Ninomiya theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[No-broadcasting theorem]] (''[[Quantum information theory|quantum information theory]]'')
*[[No-cloning theorem]] (''quantum computation'')
*[[No-communication theorem]] (''[[Quantum information theory|quantum information theory]]'')
*[[No-deleting theorem]] (''[[Quantum information theory|quantum information theory]]'')
*[[Physics:Optical equivalence theorem|Optical equivalence theorem]] (''[[Physics:Quantum optics|quantum optics]]'')
*Osterwalder–Schrader theorem (''[[HandWiki:Physics|physics]]'')
*[[Physics:Pandya theorem|Pandya theorem]] (''[[Physics:Nuclear physics|nuclear physics]]'')
*[[Physics:Pomeranchuk's theorem|Pomeranchuk's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Reeh–Schlieder theorem|Reeh–Schlieder theorem]] (''[[Physics:Local quantum field theory|local quantum field theory]]'')
*[[Solovay–Kitaev theorem]] (''quantum computation'')
*[[Physics:Spin–statistics theorem|Spin–statistics theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Stone–von Neumann theorem]] (''[[Functional analysis|functional analysis]]'', ''[[Representation theory|representation theory]]'' of the ''[[Heisenberg group]]'', ''[[Physics:Quantum mechanics|quantum mechanics]]'')
*[[Physics:Supersymmetry nonrenormalization theorems|Supersymmetry nonrenormalization theorems]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Vafa–Witten theorem|Vafa–Witten theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Weinberg–Witten theorem|Weinberg–Witten theorem]] (''[[Quantum field theory|quantum field theory]]'')
*[[Physics:Wick's theorem|Wick's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Wigner–Eckart theorem]] (''[[Physics:Clebsch–Gordan coefficients|Clebsch–Gordan coefficients]]'')

==Statistical mechanics, structure of matter==

*[[Physics:Bohr–van Leeuwen theorem|Bohr–van Leeuwen theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Crooks fluctuation theorem|Crooks fluctuation theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Crystallographic restriction theorem]] (''[[Group theory|group theory]]'', ''[[Physics:Crystallography|crystallography]]'')
*[[Physics:Equipartition theorem|Equipartition theorem]] (''[[Ergodic theory|ergodic theory]]'')
*Fluctuation dissipation theorem (''[[HandWiki:Physics|physics]]'')
*[[Physics:Fluctuation theorem|Fluctuation theorem]] (''[[Physics:Statistical mechanics|statistical mechanics]]'')
*[[Physics:H-theorem|H-theorem]] (''[[Physics:Thermodynamics|thermodynamics]]'')
*Hohenberg–Kohn theorems (''[[Density functional theory|density functional theory]]'')
*[[Physics:Lee–Yang theorem|Lee–Yang theorem]] (''[[Physics:Statistical mechanics|statistical mechanics]]'')
*[[Physics:Mermin–Wagner theorem|Mermin–Wagner theorem]] (''[[HandWiki:Physics|physics]]'')

==Relativity and gravitational theory==

*[[Physics:Birkhoff's theorem (relativity)|Birkhoff's theorem]] (''[[Physics:General relativity|general relativity]]'')
*[[Physics:Goldberg–Sachs theorem|Goldberg–Sachs theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Lovelock's theorem|Lovelock's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Astronomy:No-hair theorem|No-hair theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Odd number theorem|Odd number theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Peeling theorem|Peeling theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Penrose–Hawking singularity theorems|Penrose–Hawking singularity theorems]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Positive energy theorem|Positive energy theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Biography:Richard H. Price|Price's theorem]] (''[[Physics:General relativity|general relativity]]'')

==Astronomy and astrophysics==

*[[Physics:Clairaut's theorem|Clairaut's theorem]] (''[[HandWiki:Physics|physics]]'')
*[[Physics:Shell theorem|Shell theorem]] (''[[HandWiki:Physics|physics]]'')

==Operations research, mathematical programming==

*[[Analyst's traveling salesman theorem]] (''[[Discrete mathematics|discrete mathematics]]'')
*[[Arrival theorem]] (''[[Queueing theory|queueing theory]]'')
*[[Blum's speedup theorem]] (''[[Computational complexity theory|computational complexity theory]]'')
*Max flow min cut theorem (''[[Graph theory|graph theory]]'')
*[[No free lunch theorem]] (''[[Philosophy:Philosophy of mathematics|philosophy of mathematics]]'')
*[[Topkis's theorem]] (''[[Finance:Economics|economics]]'')

==Game theory, economics, social and behavioral sciences==

*Alchian–Allen theorem (''[[Finance:Economics|economics]]'')
*[[Arrow's impossibility theorem]] (''[[Game theory|game theory]]'')
*Arrow-Lind theorem (''[[Finance:Welfare economics|welfare economics]]'')
*[[Biology:Bishop–Cannings theorem|Bishop–Cannings theorem]] (''[[Finance:Economics|economics]]'')
*[[Bondareva–Shapley theorem]] (''[[Finance:Economics|economics]]'')
*[[Finance:Coase theorem|Coase theorem]] (''[[Finance:Economics|economics]]'')
*Duggan&ndash;Schwartz theorem (''voting theory'')
*[[Finance:Edgeworth's limit theorem|Edgeworth's limit theorem]] (''[[Finance:Economics|economics]]'')
*Faustman–Ohlin theorem (''[[Finance:Economics|economics]]'')
*[[Finance:Fisher separation theorem|Fisher separation theorem]] (''[[Finance:Economics|economics]]'')
*[[Software:Folk theorem (game theory)|Folk theorem]] (''[[Game theory|game theory]]'')
*Fundamental theorem of arbitrage-free pricing (''financial mathematics'')
*[[Finance:Fundamental theorems of welfare economics|Fundamental theorems of welfare economics]] (''[[Finance:Economics|economics]]'')
*[[Gibbard–Satterthwaite theorem]] (''voting methods'')
*[[Finance:Heckscher–Ohlin theorem|Heckscher–Ohlin theorem]] (''[[Finance:Economics|economics]]'')
*[[Finance:Holmström's theorem|Holmström's theorem]] (''[[Finance:Economics|economics]]'')
*[[Kuhn's theorem]] (''[[Game theory|game theory]]'')
*[[Finance:Lerner symmetry theorem|Lerner symmetry theorem]] (''[[Finance:Economics|economics]]'')
*[[May's theorem]] (''[[Game theory|game theory]]'')
*[[Finance:Modigliani–Miller theorem|Modigliani–Miller theorem]] (''finance theory'')
*Morton's theorem (''[[Game theory|game theory]]'')
*[[Finance:Moving equilibrium theorem|Moving equilibrium theorem]] (''[[Finance:Economics|economics]]'')
*[[Finance:Mutual fund separation theorem|Mutual fund separation theorem]] (''financial mathematics'')
*[[Finance:No-trade theorem|No-trade theorem]] (''[[Finance:Economics|economics]]'')
*Rationality theorem (''politics'')
*[[Finance:Rybczynski theorem|Rybczynski theorem]] (''[[Finance:Economics|economics]]'')
*Sonnenschein–Mantel–Debreu Theorem (''[[Finance:Economics|economics]]'')
*[[Sprague–Grundy theorem]] (''[[Combinatorial game theory|combinatorial game theory]]'')
*Stolper&ndash;Samuelson theorem (''[[Finance:Economics|economics]]'')

==Biology and other natural sciences==

*[[Biology:Marginal value theorem|Marginal value theorem]] (''[[Biology:Biology|biology]]'', ''[[Optimization|optimization]]'')

==Systems theory; control==

*[[Artstein's theorem]] (''[[Control theory|control theory]]'')
*[[Krener's theorem]] (''[[Control theory|control theory]]'')
*Lyapunov&ndash;Malkin theorem (''[[Stability theory|stability theory]]'')
*[[Orbit (control theory)#Orbit theorem (Nagano–Sussmann)|Orbit theorem (Nagano–Sussmann)]] (''[[Control theory|control theory]]'')

==Information and communication, circuits==

*Kraft–McMillan theorem (''[[Coding theory|coding theory]]'')
*[[Nyquist–Shannon sampling theorem]] (''[[Information theory|information theory]]'')
*[[Shannon–Hartley theorem]] (''[[Information theory|information theory]]'')
*[[Shannon's source coding theorem]] (''[[Information theory|information theory]]'')
*Shannon's theorem (''[[Information theory|information theory]]'')
*[[Ugly duckling theorem]] (''[[Computer science|computer science]]'')




[[Category:Mathematics-related lists|Theorems]]
[[Category:Theorems| ]]

{{Sourceattribution|List of theorems}}