List of theorems

This is a list of notable theorems. 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 fields.

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 numbers )
• 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 )
• 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 )
• 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, 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 )
• 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 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 theorem ( discrete mathematics )
• Corners theorem ( arithmetic combinatorics )
• Courcelle's theorem ( graph theory )
• De Bruijn–Erdős theorem (graph theory)
• 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 )
• 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 )
• 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 )
• Kőnig's theorem ( bipartite graphs )
• 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 groups )
• 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 ( algebras )
• Ankeny–Artin–Chowla theorem ( number theory )
• Apéry's theorem ( number theory )
• 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 )
• 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 numbers )
• 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 )
• Ford's theorem ( number theory )
• 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 fields )
• Hilbert–Speiser theorem ( cyclotomic fields )
• Hilbert–Waring theorem ( number theory )
• Hilbert's irreducibility 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 ( 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 representations )
• Nagell–Lutz theorem ( elliptic curves )
• 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 curves )
• 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 )
• Solutions to Pell's equation ( number theory )
• Sophie Germain's theorem ( number theory )
• Sphere packing theorems in dimensions 8 and 24 ( geometry , modular forms )
• Stark–Heegner theorem ( number theory )
• Subspace theorem ( Diophantine approximation )
• Sylvester's theorem ( number theory )
• Takagi existence theorem ( number theory )
• Thabit ibn Qurra's theorem ( amicable numbers )
• Thue's theorem ( Diophantine equation )
• Thue–Siegel–Roth theorem ( Diophantine approximation )
• Tijdeman's theorem ( Diophantine equations )
• Tunnell's theorem ( number theory )
• 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 fields )
• Chevalley–Warning theorem ( field theory )
• Diller–Dress theorem ( 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 )
• Mason–Stothers theorem ( polynomials )
• Polynomial remainder theorem ( polynomials )
• Primitive element theorem ( field theory )
• Rational root theorem ( algebra, polynomials )
• Solutions of a general cubic equation ( algebra )
• Solutions of a general quartic equation ( algebra )
• Strassmann's theorem ( field theory )
• Sturm's theorem ( theory of equations )
• Vieta's formulas ( quadratics )

Commutative algebra

• Artin approximation theorem ( commutative algebra )
• 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 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 )
• 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 surfaces )
• 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 groups , 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 surfaces )
• Katz–Lang finiteness theorem ( number theory )
• Lefschetz hyperplane theorem ( algebraic topology )
• Leray's theorem ( algebraic geometry )
• Manin–Drinfeld theorem ( number theory )
• 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 surfaces )
• Proper base change theorem ( algebraic geometry )
• Puiseux's theorem ( algebraic geometry )
• Ramanujam vanishing theorem ( algebraic geometry )
• Reider's theorem ( algebraic surfaces )
• Riemann–Roch theorem for surfaces ( algebraic surfaces )
• 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 )
• 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 spaces, 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 forms )

Associative rings and algebras

• Artin–Wedderburn theorem ( abstract algebra )
• Artin–Zorn theorem ( algebra )
• Brauer–Cartan–Hua theorem ( ring theory )
• Frobenius theorem ( abstract algebras )
• 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 algebras )
• Wedderburn's little theorem ( ring theory )
• Wedderburn's theorem ( abstract algebra )

Nonassociative rings and algebras

• Ado's theorem ( Lie algebra )
• Goddard–Thorn theorem ( vertex 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 algebras )
• Shirshov–Cohn theorem ( Jordan algebras )
• Shirshov–Witt theorem ( Lie algebras )

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 )
• 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 )
• Bass-Guirvarc'h formula ( group 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 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 ( finite groups )
• Cayley's theorem ( group theory )
• Chevalley–Shephard–Todd theorem ( finite group )
• Classification of finite simple groups ( group theory )
• Feit–Thompson theorem ( finite groups )
• Fitting's theorem ( group theory )
• Flat torus theorem ( geometric group theory )
• Focal subgroup theorem ( abstract algebra )
• Frobenius determinant theorem ( group theory )
• Frobenius reciprocity theorem ( group representations )
• 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 )
• 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 )
• Lie–Kolchin theorem ( algebraic groups , representation theory )
• Maschke's theorem ( group representations )
• Moufang's theorem ( loop theory )
• Nielsen–Schreier theorem ( free groups )
• Orbit-stabilizer theorem ( group theory )
• Schreier refinement theorem ( group theory )
• Schur's lemma ( representation theory )
• Schur–Zassenhaus theorem ( group theory )
• Sela's theorem ( hyperbolic groups )
• Stallings theorem about ends of groups ( group theory )
• Superrigidity theorem ( algebraic groups )
• 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

• Cartan's theorem ( Lie group )
• 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 )
• 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 ( functional analysis )
• Bohr–Mollerup theorem ( gamma function )
• Bolzano's theorem ( real analysis, calculus )
• Constant rank theorem ( multivariate calculus )
• Cousin's lemma ( real analysis )
• Danskin's theorem ( convex analysis )
• Darboux's theorem ( real analysis )
• Denjoy–Carleman theorem ( functional analysis )
• Denjoy-Young-Saks theorem ( real analysis )
• Dini's theorem ( 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 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 ( 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 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 spaces )
• Bloch's theorem ( complex analysis )
• Bôcher's theorem ( complex analysis )
• Borel–Carathéodory theorem ( complex analysis )
• Branching theorem ( complex manifold )
• 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 curves )
• 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 curves )
• 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, entire functions )
• Liouville's theorem ( conformal mappings )
• Looman–Menchoff theorem ( complex analysis )
• Marden's theorem ( polynomials )
• Mergelyan's theorem ( complex analysis )
• 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 )
• 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 surfaces , algebraic curves )
• 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 )
• 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 )
• 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 theorem ( complex analysis )
• Hölder's theorem ( mathematical analysis )
• Multiplication theorem ( special functions )

Ordinary differential equations

• Carathéodory's existence theorem ( ordinary differential equations )
• Floquet's theorem ( differential equations )
• Fuchs's theorem ( differential equations )
• Kharitonov's theorem ( control theory )
• Kneser's theorem ( differential equations )
• Liénard's theorem ( dynamical systems )
• Markus−Yamabe theorem ( dynamical systems )
• Peano existence theorem ( ordinary differential equations )
• Picard–Lindelöf theorem ( ordinary differential equations )
• Shift theorem ( differential operators )
• Sturm–Picone comparison theorem ( differential equations )

Partial differential equations

• Cartan–Kähler theorem ( partial differential equations )
• Cartan–Kuranishi prolongation theorem ( partial differential equations )
• Cauchy–Kowalevski theorem ( partial differential equations )
• Malgrange–Ehrenpreis theorem ( differential equations )

Dynamical systems and ergodic theory

• Autonomous convergence theorem ( dynamical systems )
• Banach fixed-point theorem ( metric spaces, differential equations )
• Bendixson–Dulac theorem ( dynamical systems )
• Birkhoff's theorem ( ergodic theory )
• Conley–Zehnder theorem ( dynamical systems )
• Curtis–Hedlund–Lyndon theorem ( cellular automata )
• Hartman–Grobman theorem ( dynamical systems )
• 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 groups , calculus of variations , differential invariants , physics )
• Ornstein theorem ( ergodic theory )
• Oseledec theorem ( ergodic theory )
• Peixoto's theorem ( dynamical systems )
• Poincaré–Bendixson theorem ( dynamical systems )
• Poincaré recurrence theorem ( dynamical systems )
• Ratner's theorems ( ergodic theory )
• Sarkovskii's theorem ( dynamical systems )
• Takens's theorem ( dynamical systems )

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'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 )
• Carleson's theorem ( harmonic analysis )
• Convolution theorem ( Fourier transforms )
• Denjoy theorem ( dynamical systems )
• Fourier inversion theorem ( harmonic analysis )
• Fourier theorem ( harmonic analysis )
• Hausdorff-Young inequality ( Fourier analysis )
• Lauricella's theorem ( functional analysis )
• Paley–Wiener theorem ( Fourier transforms )
• 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 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 )
• 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 functions )
• 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 operators , harmonic analysis )
• Atkinson's theorem ( operator theory )
• Babuška–Lax–Milgram theorem ( partial differential equations )
• 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–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 spaces )
• 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 )
• 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 algebras )
• 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 algebras )
• Von Neumann bicommutant theorem ( functional analysis )
• Von Neumann's theorem ( operator theory )

Calculus of variations and optimal control; optimization

• Caristi fixed-point theorem ( fixed points )
• Envelope theorem ( calculus of variations )
• Isoperimetric theorem ( curves , 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 )

Geometry

• Alternate Interior Angles Theorem ( geometry )
• 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 ( incidence geometry )
• Beckman–Quarles theorem ( Euclidean geometry )
• Beer's theorem ( metric geometry )
• Brahmagupta theorem ( Euclidean geometry )
• Brianchon's theorem ( conics )
• British flag theorem ( Euclidean geometry )
• Butterfly theorem ( Euclidean geometry )
• CPCTC ( triangle geometry )
• 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 , 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 ( circles )
• Gauss–Wantzel theorem ( geometry )
• Geometric mean theorem ( geometry )
• Hinge theorem ( geometry )
• Hjelmslev's theorem ( geometry )
• Impossibility of angle trisection ( geometry )
• Independence of the parallel postulate ( geometry )
• 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 ( curves )
• Newton's theorem (quadrilateral) ( geometry )
• Pappus's area theorem ( geometry )
• Pappus's centroid theorem ( geometry )
• Pappus's hexagon theorem ( geometry )
• Pascal's theorem ( conics )
• Pasch's theorem ( order theory )
• Pitot theorem ( plane geometry )
• Pivot theorem ( circles )
• Pompeiu's theorem ( Euclidean geometry )
• Poncelet's closure theorem ( conics )
• 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 ( circles )
• Steiner–Lehmus theorem ( triangle geometry )
• 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 )
• 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 geometry )
• Cauchy's theorem ( geometry )
• Classification of Platonic solids ( geometry )
• de Bruijn's theorem ( discrete geometry )
• 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 sets )
• 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 sets )
• 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'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 )
• Classification of symmetric spaces ( Lie theory )
• Darboux's theorem ( symplectic topology )
• Euler's theorem ( differential geometry )
• Four-vertex theorem ( differential geometry )
• Frobenius theorem ( foliations )
• 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 ( Riemannian geometry )
• Gromov's compactness theorem ( symplectic topology )
• Gromov–Ruh 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 )
• 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 spaces )
• 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 spaces )
• 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–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 points , algebraic topology )
• Lefschetz–Hopf theorem ( topology )
• Leray–Hirsch theorem ( algebraic topology )
• Nielsen fixed-point theorem ( fixed points )
• Nilpotence theorem ( algebraic topology )
• Poincaré duality theorem ( algebraic topology of manifolds )
• 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 )
• Whitney–Graustein Theorem ( algebraic topology )

Manifolds and cell complexes

• Atiyah–Bott fixed-point theorem ( differential topology )
• Bing's recognition theorem ( geometric topology )
• Birman short exact sequence ( geometric topology )
• Classification of compact surfaces ( Topology )
• De Rham's theorem ( differential topology )
• 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 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 ( foliations )
• Perelman's Geometrization theorem ( 3-manifolds )
• Poincaré–Hopf theorem ( differential topology )
• Poincaré conjecture ( topology )
• Preimage theorem ( differential topology )
• Reeb sphere theorem ( foliations )
• Reidemeister–Singer Theorem ( geometric topology )
• Riemann–Roch theorem for smooth manifolds ( differential topology )
• Rokhlin's theorem ( geometric topology )
• 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 )
• Thurston's geometrization theorem ( 3-manifolds )
• Waldhausen's theorem ( geometric topology )
• Whitney embedding theorem ( differential manifolds )
• Whitney immersion theorem ( differential topology )

Global analysis, analysis on manifolds

• 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 processes )
• 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 )
• 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–Koopman–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–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 )
• Lamé’s theorem ( computational complexity theory )
• Linear speedup theorem ( computational complexity theory )
• Master theorem (analysis of algorithms) ( recurrence relations , asymptotic analysis )
• Max/min_CSP/Ones_classification_theorems ( computational complexity theory )
• Myhill–Nerode theorem ( formal languages )
• 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 ( gravity )
• Helmholtz theorem (classical mechanics) ( physics )
• König's theorem ( physics )
• Lami's theorem ( statics )
• 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 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 circuits )
• Norton's theorem ( electrical networks )
• Optical theorem ( physics )
• Poynting's theorem ( physics )
• Thévenin's theorem ( electrical circuits )

Classical theormodynamics, heat transfer

• 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 ( 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 )
• 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 theorem ( welfare economics )
• Bishop–Cannings theorem ( economics )
• Bondareva–Shapley theorem ( economics )
• Coase theorem ( economics )
• Duggan–Schwartz theorem ( voting theory )
• Edgeworth's limit theorem ( economics )
• Faustman–Ohlin theorem ( economics )
• Fisher separation theorem ( economics )
• Folk theorem ( game theory )
• Fundamental theorem of arbitrage-free pricing ( financial mathematics )
• Fundamental theorems of welfare economics ( economics )
• Gibbard–Satterthwaite theorem ( voting methods )
• 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–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–Malkin theorem ( stability theory )
• 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 )