# 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 thermodynamics, 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)