Editing 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]]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]], but some are from [[theoretical physics]], [[economics]], and other [[applied mathematics|applied]] fields.

{{TOC left|limit=2}}

==Logics and foundations==

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

==Combinatorics==

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

==Order, lattices, ordered algebraic structures==

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

==General algebraic systems==

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

==Number theory==

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

==Field theory and polynomials==

*[[Abel–Ruffini theorem]] (''[[theory of equations]]'', ''[[Galois theory]]'')
*[[Artin–Schreier theorem]] (''[[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]]'')
*[[Hilbert's theorem 90]] (''[[number theory]]'')
*[[Isomorphism extension theorem]] (''[[abstract algebra]]'')
*[[Joubert's theorem]] (''[[algebra]]'')
*[[Lagrange's theorem (number theory)|Lagrange's theorem]] (''[[number theory]]'')
*[[Mason–Stothers theorem]] (''[[polynomials]]'')
*[[Little Bézout's theorem|Polynomial remainder theorem]] (''[[polynomials]]'')
*[[Primitive element theorem]] (''[[field theory (mathematics)|field theory]]'')
*[[Rational root theorem]] (''[[algebra]], [[polynomials]]'')
*[[Cubic equation|Solutions of a general cubic equation]] (''[[algebra]]'')
*[[Quartic equation|Solutions of a general quartic equation]] (''[[algebra]]'')
*[[Strassmann's theorem]] (''[[field theory (mathematics)|field theory]]'')
*[[Sturm's theorem]] (''[[theory of equations]]'')
*[[Vieta's formulas]] (''[[quadratics]]'')

==Commutative algebra==

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

==Algebraic geometry==

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

==Linear and multilinear algebra; matrix theory==

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

==Associative rings and algebras==

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

==Nonassociative rings and algebras==

*[[Ado's theorem]] (''[[Lie algebra]]'')
*[[Goddard–Thorn theorem]] (''[[vertex algebra]]s'')
*[[Hurwitz's theorem (normed division algebras)|Hurwitz's theorem]] (''[[normed division algebra]]s'')
*[[Jacobson–Morozov theorem]] (''[[Lie algebra]]'')
*[[Levi's theorem]] (''[[Lie groups]]'')
*[[Lie's theorem]] (''[[Lie algebra]]'')
*[[Poincaré–Birkhoff–Witt theorem]] (''[[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]]'')
*[[Bruguières modularity theorem]] (''[[category theory]]'')
*[[Freyd's adjoint functor theorem]] (''[[category theory]]'')
*[[Golod–Shafarevich theorem]] (''[[group theory]]'')
*[[Lawvere's fixed-point theorem]] (''[[mathematical logic]]'')
*[[Mitchell's embedding theorem]] (''[[category theory]]'')
*[[Stone duality#The duality theorem|The duality theorem]] (''[[topology]]'')

==K-theory==

*[[Atiyah–Segal completion theorem]] (''[[homotopy theory]]'')
*[[Snaith's theorem]] (''[[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]]'')
*[[Bass–Serre_theory#Fundamental_theorem_of_Bass–Serre_theory|Bass-Serre theorem]] (''[[group theory]]'')
*[[Borel–Bott–Weil theorem]] (''[[representation theory]]'')
*[[Borel–Weil theorem]] (''[[representation theory]]'')
*[[Brauer–Nesbitt theorem]] (''[[representation theory of finite groups]]'')
*[[Brauer–Suzuki theorem]] (''[[finite groups]]'')
*[[Brauer–Suzuki–Wall theorem]] (''[[group theory]]'')
*[[Brauer's main theorem|Brauer's theorem]] (''[[number theory]]'')
*[[Brauer's theorem on induced characters]] (''[[representation theory of finite groups]]'')
*[[Burnside's theorem]] (''[[group theory]]'')
*[[Cartan–Dieudonné theorem]] (''[[group theory]]'')
*[[Cauchy's theorem (group theory)|Cauchy's theorem]] (''[[finite groups]]'')
*[[Cayley's theorem]] (''[[group theory]]'')
*[[Chevalley–Shephard–Todd theorem]] (''[[finite group]]'')
*[[Classification of finite simple groups]] (''[[group theory]]'')
*[[Feit–Thompson theorem]] (''[[finite group]]s'')
*[[Fitting's theorem]] (''[[group theory]]'')
*[[Preissmann's_theorem#Flat_torus_theorem|Flat torus theorem]] (''[[geometric group theory]]'')
*[[Focal subgroup theorem]] (''[[abstract algebra]]'')
*[[Frobenius determinant theorem]] (''[[group theory]]'')
*[[Frobenius reciprocity theorem]] (''[[group representation]]s'')
*[[Frucht's theorem]] (''[[graph theory]]'')
*[[Great orthogonality theorem]] (''[[group theory]]'')
*[[Gromov's theorem on groups of polynomial growth]] (''[[geometric group theory]]'')
*[[Grushko theorem]] (''[[group theory]]'')
*[[Higman's embedding theorem]] (''[[group theory]]'')
*[[Dehn_function#Known_results|Isoperimetric gap]] (''[[geometric group theory]]'', ''[[metric geometry]]'')
*[[Jordan–Hölder theorem]] (''[[group theory]]'')
*[[Jordan–Schur theorem]] (''[[group theory]]'')
*[[Jordan's theorem (multiply transitive groups)]] (''[[group theory]]'')
*[[Krull–Schmidt theorem]] (''[[group theory]]'')
*[[Kurosh subgroup theorem]] (''[[group theory]]'')
*[[L-balance theorem]] (''[[finite groups]]'')
*[[Lagrange's theorem (group theory)|Lagrange's theorem]] (''[[group theory]]'')
*[[Lie–Kolchin theorem]] (''[[algebraic group]]s'', ''[[representation theory]]'')
*[[Maschke's theorem]] (''[[group representation]]s'')
*[[Moufang_loop#Associativity|Moufang's theorem]] (''[[loop theory]]'')
*[[Nielsen–Schreier theorem]] (''[[free group]]s'')
*[[Orbit-stabilizer theorem]] (''[[group theory]]'')
*[[Schreier refinement theorem]] (''[[group theory]]'')
*[[Schur's lemma]] (''[[representation theory]]'')
*[[Schur–Zassenhaus theorem]] (''[[group theory]]'')
*[[Zlil Sela#Mathematical contributions|Sela's theorem]] (''[[hyperbolic group]]s'')
*[[Stallings theorem about ends of groups]] (''[[group theory]]'')
*[[Superrigidity theorem]] (''[[algebraic groups]]'')
*[[Švarc–Milnor_lemma|Švarc-Milnor lemma]] (''[[geometric group theory]]'')
*[[Sylow theorems]] (''[[group theory]]'')
*[[Thompson transitivity theorem]] (''[[finite groups]]'')
*[[Thompson uniqueness theorem]] (''[[finite groups]]'')
*[[Tits alternative]] (''[[geometric group theory]]'')
*[[Trichotomy theorem]] (''[[finite groups]]'')
*[[Walter theorem]] (''[[finite groups]]'')
*[[Z* theorem]] (''[[finite groups]]'')
*[[ZJ theorem]] (''[[finite groups]]'')

==Topological groups, Lie groups==

*[[Closed subgroup theorem|Cartan's theorem]] (''[[Lie group]]'')
*[[Discrete series representation|Harish–Chandra theorem]] (''[[representation theory]]'')
*[[Harish–Chandra's regularity theorem]] (''[[representation theory]]'')
*[[Iwasawa decomposition]] (''[[Lie theory]]'')
*[[Kempf–Ness theorem]] (''[[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]]'')
*[[Trombi–Varadarajan theorem]] (''[[Lie group]]'')

==Real functions==

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

==Measure and integration==

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

==Several complex variables and analytic spaces==

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

==Special functions==

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

==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]]'')
*[[Kneser's theorem (differential equations)|Kneser's theorem]] (''[[differential equations]]'')
*[[Liénard's theorem]] (''[[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]]s'')
*[[Sturm–Picone comparison theorem]] (''[[differential equations]]'')

==Partial differential equations==

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

==Dynamical systems and ergodic theory==

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

==Difference and functional equations==

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

==Sequence, series, summability==

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

==Approximations and expansions==

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

==Harmonic analysis on Euclidean spaces==

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

==Abstract harmonic analysis==

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

==Integral transforms, operational calculus==

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

==Integral equations==

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

==Functional analysis==

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

==Operator theory==

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

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

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

==Geometry==

*[[Alternate Interior Angles Theorem]] (''[[geometry]]'')
*[[Circumcircle#Angles|Alternate segment theorem]] (''[[geometry]]'')
*[[Angle bisector theorem]] (''[[Euclidean geometry]]'')
*[[Anne's theorem]] (''[[geometry]]'')
*[[Apollonius's theorem]] (''[[plane geometry]]'')
*[[Barbier's theorem]] (''[[geometry]]'')
*[[Beck's theorem (geometry)|Beck's theorem]] (''[[incidence geometry]]'')
*[[Beckman–Quarles theorem]] (''[[Euclidean geometry]]'')
*[[Beer's theorem]] (''[[metric geometry]]'')
*[[Brahmagupta theorem]] (''[[Euclidean geometry]]'')
*[[Brianchon's theorem]] (''[[conic]]s'')
*[[British flag theorem]] (''[[Euclidean geometry]]'')
*[[Butterfly theorem]] (''[[Euclidean geometry]]'')
*[[CPCTC]] (''[[triangle geometry]]'')
*[[Carnot's theorem (inradius, circumradius)|Carnot's theorem]] (''[[geometry]]'')
*[[Casey's theorem]] (''[[Euclidean geometry]]'')
*[[Cayley–Bacharach theorem]] (''[[projective geometry]]'')
*[[Ceva's theorem]] (''[[geometry]]'')
*[[Clifford's circle theorems]] (''[[Euclidean plane geometry]]'')
*[[Commandino's theorem]] (''[[geometry]]'')
*[[Constant chord theorem]] (''[[geometry]]'')
*[[Conway circle theorem]] (''[[Euclidean plane geometry]]'')
*[[Crossbar theorem]] (''[[Euclidean plane geometry]]'')
*[[Dandelin's theorem]] (''[[solid geometry]]'')
*[[De Bruijn–Erdős theorem (incidence geometry)]]
*[[De Gua's theorem]] (''[[geometry]]'')
*[[Desargues's theorem]] (''[[projective geometry]]'')
*[[Descartes's theorem]] (''[[plane geometry]]'')
*[[Dinostratus' theorem]] (''[[geometry]]'', ''[[Mathematical analysis|analysis]]'')
*[[Equal incircles theorem]] (''[[Euclidean geometry]]'')
*[[Euler's quadrilateral theorem]] (''[[geometry]]'')
*[[Euler's theorem in geometry]] (''[[triangle geometry]]'')
*[[Exterior angle theorem]] (''[[triangle geometry]]'')
*[[Feuerbach's theorem]] (''[[geometry]]'')
*[[Finsler–Hadwiger theorem]] (''[[geometry]]'')
*[[Five circles theorem]] (''[[circle]]s'')
*[[Gauss–Wantzel theorem]] (''[[geometry]]'')
*[[Geometric mean theorem]] (''[[geometry]]'')
*[[Hinge theorem]] (''[[geometry]]'')
*[[Hjelmslev's theorem]] (''[[geometry]]'')
*[[Angle trisection#Proof of impossibility|Impossibility of angle trisection]] (''[[geometry]]'')
*[[Parallel postulate#History|Independence of the parallel postulate]] (''[[geometry]]'')
*[[Inscribed angle#Theorem|Inscribed angle theorem]] (''[[geometry]]'')
*[[Intercept theorem]] (''[[Euclidean geometry]]'')
*[[Intersecting chords theorem]] (''[[Euclidean geometry]]'')
*[[Intersecting secants theorem]] (''[[Euclidean geometry]]'')
*[[Intersection theorem]] (''[[projective geometry]]'')
*[[Japanese theorem for concyclic polygons]] (''[[Euclidean geometry]]'')
*[[Japanese theorem for concyclic quadrilaterals]] (''[[Euclidean geometry]]'')
*[[Kawasaki's theorem]] (''[[mathematics of paper folding]]'')
*[[Lester's theorem]] (''[[Euclidean plane geometry]]'')
*[[Lexell's theorem]] (''[[spherical geometry]]'')
*[[Menelaus's theorem]] (''[[geometry]]'')
*[[Miquel's theorem]] (''[[geometry]]'')
*[[Mohr–Mascheroni theorem]] (''[[geometry]]'')
*[[Monge's theorem]] (''[[geometry]]'')
*[[Morley's trisector theorem]] (''[[geometry]]'')
*[[Napoleon's theorem]] (''[[triangle geometry]]'')
*[[Newton's theorem about ovals]] (''[[curve]]s'')
*[[Newton's theorem (quadrilateral)]] (''[[geometry]]'')
*[[Pappus's area theorem]] (''[[geometry]]'')
*[[Pappus's centroid theorem]] (''[[geometry]]'')
*[[Pappus's hexagon theorem]] (''[[geometry]]'')
*[[Pascal's theorem]] (''[[conic]]s'')
*[[Pasch's theorem]] (''[[order theory]]'')
*[[Pitot theorem]] (''[[plane geometry]]'')
*[[Pivot theorem]] (''[[circle]]s'')
*[[Pompeiu's theorem]] (''[[Euclidean geometry]]'')
*[[Poncelet's closure theorem]] (''[[conic]]s'')
*[[Poncelet–Steiner theorem]] (''[[geometry]]'')
*[[Ptolemy's theorem]] (''[[geometry]]'')
*[[Pythagorean theorem]] (''[[geometry]]'')
*[[Reuschle's theorem]] (''[[Euclidean geometry]]'')
*[[Routh's theorem]] (''[[triangle geometry]]'')
*[[Saccheri–Legendre theorem]] (''[[absolute geometry]]'')
*[[Six circles theorem]] (''[[circle]]s'')
*[[Steiner–Lehmus theorem]] (''[[triangle geometry]]'')
*[[Altitude (triangle)|Symphonic theorem]] (''[[triangle geometry]]'')
*[[Tangent-secant theorem]] (''[[geometry]]'')
*[[Thales's theorem]] (''[[geometry]]'')
*[[Thébault's theorem]] (''[[geometry]]'')
*[[Theorem of the gnomon]] (''[[geometry]]'')
*[[Thomsen's theorem]] (''[[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]]'')
*[[Balinski's theorem]] (''[[combinatorics]]'')
*[[Tarski's plank problem|Bang's theorem]] (''[[geometry]]'')
*[[Besicovitch covering theorem]] (''[[mathematical analysis]]'')
*[[Blaschke selection theorem]] (''[[geometric topology]]'')
*[[Bolyai–Gerwien theorem]] (''[[discrete geometry]]'')
*[[Busemann's theorem]] (''[[Euclidean geometry]]'')
*[[Carathéodory's theorem (convex hull)|Carathéodory's theorem]] (''[[convex geometry]]'')
*[[Cauchy's theorem (geometry)|Cauchy's theorem]] (''[[geometry]]'')
*[[Platonic solid#Classification|Classification of Platonic solids]] (''[[geometry]]'')
*[[de Bruijn's theorem]] (''[[discrete geometry]]'')
*[[Defect (geometry)#Descartes.27s theorem|Descartes's theorem on total angular defect]] (''[[polyhedra]]'')
*[[Erdős–Anning theorem]] (''[[discrete geometry]]'')
*[[Erdős–Nagy theorem]] (''[[discrete geometry]]'')
*[[Erdős–Szekeres theorem]] (''[[discrete geometry]]'')
*[[Fáry's theorem]] (''[[graph theory]]'')
*[[Fenchel's duality theorem]] (''[[convex analysis]]'')
*[[Fenchel–Moreau theorem]] (''[[mathematical analysis]]'')
*[[Hadwiger's theorem]] (''[[geometry]]'', ''[[measure theory]]'')
*[[Helly's theorem]] (''[[convex set]]s'')
*[[Holditch's theorem]] (''[[plane geometry]]'')
*[[John ellipsoid]] (''[[geometry]]'')
*[[Jung's theorem]] (''[[geometry]]'')
*[[Kepler conjecture]] (''[[discrete geometry]]'')
*[[Kirchberger's theorem]] (''[[discrete geometry]]'')
*[[Krein–Milman theorem]] (''[[mathematical analysis]], [[discrete geometry]]'')
*[[Minkowski's theorem]] (''[[geometry of numbers]]'')
*[[Minkowski's second theorem]] (''[[geometry of numbers]]'')
*[[Minkowski–Hlawka theorem]] (''[[geometry of numbers]]'')
*[[Monsky's theorem]] (''[[discrete geometry]]'')
*[[Pick's theorem]] (''[[geometry]]'')
*[[Pizza theorem]] (''[[geometry]]'')
*[[Radon's theorem]] (''[[convex set]]s'')
*[[Separating axis theorem]] (''[[convex geometry]]'')
*[[Steinitz theorem]] (''[[graph theory]]'')
*[[Stewart's theorem]] (''[[plane geometry]]'')
*[[Supporting hyperplane theorem]] (''[[convex geometry]]'')
*[[Sylvester–Gallai theorem]] (''[[plane geometry]]'')
*[[Szemerédi–Trotter theorem]] (''[[combinatorics]]'')
*[[Tverberg's theorem]] (''[[discrete geometry]]'')
*[[Vitali covering theorem]] (''[[measure theory]]'')
*[[Wallace–Bolyai–Gerwien theorem]] (''[[discrete geometry]]'')

==Differential geometry==

*[[2π theorem]] (''[[Riemannian geometry]]'')
*[[Abel–Jacobi_map#The_Abel–Jacobi_map_of_a_Riemannian_manifold|Abel's curve theorem]] (''[[riemannian geometry]]'')
*[[Beltrami's theorem]] (''[[Riemannian geometry]]'')
*[[Berger–Kazdan comparison theorem]] (''[[Riemannian geometry]]'')
*[[Bertrand–Diquet–Puiseux theorem]] (''[[differential geometry]]'')
*[[Bishop-Gromov inequality]] (''[[riemannian geometry]]'')
*[[Bonnet theorem]] (''[[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]]'')
*[[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]]'')
*[[Four-vertex theorem]] (''[[differential geometry]]'')
*[[Frobenius theorem (differential topology)|Frobenius theorem]] (''[[foliation]]s'')
*[[Gauss's_lemma_(Riemannian_geometry)|Gauss's lemma]] (''[[riemannian geometry]]'')
*[[Gauss's Theorema Egregium]] (''[[differential geometry]]'')
*[[Gauss–Bonnet theorem]] (''[[differential geometry]]'')
*[[Geroch's splitting theorem]] (''[[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]]'')
*[[Hilbert's theorem (differential geometry)|Hilbert's theorem]] (''[[differential geometry]]'')
*[[Hopf–Rinow theorem]] (''[[differential geometry]]'')
*[[Killing–Hopf theorem]] (''[[Riemannian geometry]]'')
*[[Lee Hwa Chung theorem]] (''[[symplectic topology]]'')
*[[Lie–Palais theorem]] (''[[differential geometry]]'')
*[[Meusnier's theorem]] (''[[differential geometry]]'')
*[[Mostow rigidity theorem]] (''[[differential geometry]]'')
*[[Myers theorem]] (''[[differential geometry]]'')
*[[Myers-Steenrod theorem]] (''[[differential geometry]]'')
*[[Nash embedding theorem]] (''[[differential geometry]]'')
*[[Non-squeezing theorem]] (''[[symplectic geometry]]'')
*[[Orbit (control theory)#Corollary (Rashevsky–Chow theorem)|Rashevsky–Chow theorem]] (''[[control theory]]'')
*[[Rauch comparison theorem]] (''[[Riemannian geometry]]'')
*[[Schwarz–Ahlfors–Pick theorem]] (''[[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]]'')
*[[Baire category theorem]] (''[[topology]]'', ''[[metric space]]s'')
*[[Bing metrization theorem]] (''[[general topology]]'')
*[[Bolzano–Weierstrass theorem]] (''[[real analysis]], [[calculus]]'')
*[[Borsuk–Ulam theorem]] (''[[topology]]'')
*[[Brouwer fixed-point theorem]] (''[[topology]]'')
*[[Cantor's intersection theorem]] (''[[real analysis]]'')
*[[Closed graph theorem]] (''[[functional analysis]]'')
*[[Extreme value theorem]] (''[[calculus]]'')
*[[Fixed-point theorems in infinite-dimensional spaces]]
*[[Hairy ball theorem]] (''[[algebraic topology]]'')
*[[Hahn–Mazurkiewicz theorem]] (''[[continuum theory]]'')
*[[Heine–Borel theorem]] (''[[real analysis]]'')
*[[Heine–Cantor theorem]] (''[[metric geometry]]'')
*[[Jordan curve theorem]] (''[[topology]]'')
*[[Kuratowski's closure-complement problem]] (''[[topology]]'')
*[[Lebesgue covering dimension]] (''[[dimension theory]]'')
*[[Metrization theorems]] (''[[topological space]]s'')
*[[Nagata–Smirnov metrization theorem]](''[[general topology]]'')
*[[Netto's theorem]] (''[[topology]]'')
*[[Parovicenko's theorem]] (''[[topology]]'')
*[[Tietze extension theorem]] (''[[general topology]]'')
*[[Tychonoff's theorem]] (''[[general topology]]'')

==Algebraic topology==

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

==Manifolds and cell complexes==

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

==Global analysis, analysis on manifolds==

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

==Probability theory and stochastic processes==

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

==Statistics==

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

==Numerical analysis==

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

==Computer science==

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

==Mechanics of particles and systems==

*[[Chasles' theorem (kinematics)|Chasles' theorem]], (''[[kinematics]]'')
*[[Chasles' theorem (gravity)|Chasles' theorem]] (''[[gravity]]'')
*[[Helmholtz theorem (classical mechanics)]] (''[[physics]]'')
*[[König's theorem (kinetics)|König's theorem]] (''[[physics]]'')
*[[Lami's theorem]] (''[[statics]]'')
*[[Liouville's theorem (Hamiltonian)|Liouville's theorem]] (''[[Hamiltonian mechanics]]'')
*[[Parallel axis theorem]] (''[[physics]]'')
*[[Perpendicular axis theorem]] (''[[physics]]'')
*[[Virial theorem]] (''[[classical mechanics]]'')

==Mechanics of deformable solids==

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

==Fluid mechanics==

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

==Optics, electromagnetic theory==

*[[Blondel's theorem]] (''[[electric power]]'') (''[[physics]]'')
*[[Earnshaw's theorem]] (''[[electrostatics]]'')
*[[Maximum power theorem]] (''[[electrical circuit]]s'')
*[[Norton's theorem]] (''[[electrical network]]s'')
*[[Optical theorem]] (''[[physics]]'')
*[[Poynting's theorem]] (''[[physics]]'')
*[[Thévenin's theorem]] (''[[electrical circuit]]s'')

==Classical thermodynamics, heat transfer==

*[[Carnot's theorem (thermodynamics)|Carnot's theorem]] (''[[thermodynamics]]'')
*[[Clausius theorem]] (''[[physics]]'')

==Quantum theory==

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

==Statistical mechanics, structure of matter==

*[[Bohr–van Leeuwen theorem]] (''[[physics]]'')
*[[Crooks fluctuation theorem]] (''[[physics]]'')
*[[Crystallographic restriction theorem]] (''[[group theory]]'', ''[[crystallography]]'')
*[[Equipartition theorem]] (''[[ergodic theory]]'')
*[[Fluctuation dissipation theorem]] (''[[physics]]'')
*[[Fluctuation theorem]] (''[[statistical mechanics]]'')
*[[H-theorem]] (''[[thermodynamics]]'')
*[[Hohenberg–Kohn theorems]] (''[[density functional theory]]'')
*[[Lee–Yang theorem]] (''[[statistical mechanics]]'')
*[[Mermin–Wagner theorem]] (''[[physics]]'')

==Relativity and gravitational theory==

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

==Astronomy and astrophysics==

*[[Clairaut's theorem]] (''[[physics]]'')
*[[Shell theorem]] (''[[physics]]'')

==Operations research, mathematical programming==

*[[Analyst's traveling salesman theorem]] (''[[discrete mathematics]]'')
*[[Arrival theorem]] (''[[queueing theory]]'')
*[[Blum's speedup theorem]] (''[[computational complexity theory]]'')
*[[Max flow min cut theorem]] (''[[graph theory]]'')
*[[No free lunch theorem]] (''[[philosophy of mathematics]]'')
*[[Topkis's theorem]] (''[[economics]]'')

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

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

==Biology and other natural sciences==

*[[Marginal value theorem]] (''[[biology]]'', ''[[optimization]]'')

==Systems theory; control==

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

==Information and communication, circuits==

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




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