# List of theorems

### From Wikipedia, the free encyclopedia

This is a **list of theorems**, by Wikipedia page. See also

- list of fundamental theorems
- list of lemmas
- list of conjectures
- list of inequalities
- list of mathematical proofs
- list of misnamed theorems
- Existence theorem
- Classification of finite simple groups

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

Contents |
Top · 0–9 · A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |

## [edit] 0–9

## [edit] A

- AF+BG theorem (
*algebraic geometry*) - ATS theorem (
*number theory*) - Abel's binomial theorem (
*combinatorics*) - Abel's curve theorem (
*mathematical analysis*) - Abel's theorem (
*mathematical analysis*) - Abelian and tauberian theorems (
*mathematical analysis*) - Abel-Ruffini theorem (
*theory of equations*,*Galois theory*) - Abhyankar–Moh theorem (
*algebraic geometry*) - Abouabdillah's theorem (
*geometry*,*number theory*) - Absolute convergence theorem (
*mathematical series*) - Acyclic models theorem (
*algebraic topology*) - Addition theorem (
*algebraic geometry*) - Adiabatic theorem (
*physics*) - Ado's theorem (
*Lie algebra*) - Alperin-Brauer-Gorenstein theorem (
*finite groups*) - Analytic Fredholm theorem (
*functional analysis*) - Anderson's theorem (
*real analysis*) - Angle bisector theorem (
*Euclidean geometry*) - Ankeny-Artin-Chowla theorem (
*number theory*) - Apéry's theorem (
*number theory*) - Apollonius' theorem (
*plane geometry*) - Area theorem (conformal mapping) (
*complex analysis*) - Arithmetic Riemann–Roch theorem (
*algebraic geometry*) - Aronszajn-Smith theorem (
*functional analysis*) - Arrival theorem (
*queueing theory*) - Arrow's impossibility theorem (
*game theory*) - Artin approximation theorem (
*commutative algebra*) - Artin-Schreier theorem (
*real closed fields*) - Artin-Wedderburn theorem (
*abstract algebra*) - Artin-Zorn theorem (
*algebra*) - Arzelà-Ascoli theorem (
*functional analysis*) - Atiyah–Bott fixed-point theorem (
*differential topology*) - Atiyah-Segal completion theorem (
*homotopy theory*) - Atiyah-Singer index theorem (
*elliptic differential operators*,*harmonic analysis*) - Atkinson's theorem (
*operator theory*) - Autonomous convergence theorem (
*dynamical systems*) - Ax-Grothendieck theorem (
*model theory*) - Ax–Kochen theorem (
*number theory*)

## [edit] B

- Babuška-Lax-Milgram theorem (
*partial differential equations*) - Baily-Borel theorem (
*algebraic geometry*) - Baire category theorem (
*topology*,*metric spaces*) - Balian-Low theorem (
*Fourier analysis*) - Banach-Alaoglu theorem (
*functional analysis*) - Banach fixed point theorem (
*metric spaces, differential equations*) - Banach-Steinhaus theorem (
*functional analysis*) - Barbier's theorem (
*geometry*) - Bapat-Beg theorem (
*statistics*) - Bass's theorem (
*group theory*) - Bayes' theorem (
*probability*) - Beatty's theorem (
*diophantine approximation*) - Beauville–Laszlo theorem (
*vector bundles*) - Beck's monadicity theorem (
*category theory*) - Beck's theorem (
*incidence geometry*) - Bell's theorem (
*quantum theory - physics*) - Belyi's theorem (
*algebraic curves*) - Bendixson-Dulac theorem (
*dynamical systems*) - Berger–Kazdan comparison theorem (
*Riemannian geometry*) - Bernstein's theorem (
*functional analysis*) - Berry-Esséen theorem (
*probability theory*) - Bertrand's ballot theorem (
*probability theory*,*combinatorics*) - Bertrand's postulate (
*prime numbers*) - Beurling–Lax theorem (
*Hardy spaces*) - Bézout's theorem (
*algebraic curves*) - Bing metrization theorem(
*general topology*) - Binomial inverse theorem (
*matrix theory*) - Binomial theorem (
*algebra, combinatorics*) - Birch's theorem (
*Diophantine equation*) - Birkhoff-Grothendieck theorem (
*vector bundles*) - Birkhoff's representation theorem (
*lattice theory*) - Birkhoff's theorem (
*ergodic theory*) - Birkhoff's theorem (relativity) (
*physics*) - Blaschke selection theorem (
*geometric topology*) - Bloch's theorem (
*complex analysis*) - Blum's speedup theorem (
*computational complexity theory*) - Bôcher's theorem (
*complex analysis*) - Bohr-Mollerup theorem (
*gamma function*) - Bolyai-Gerwien theorem (
*geometry*) - Bolzano's theorem (
*real analysis, calculus*) - Bolzano-Weierstrass theorem (
*real analysis, calculus*) - Bombieri's theorem (
*number theory*) - Bombieri–Friedlander–Iwaniec theorem (
*number theory*) - Bondy-Chvátal theorem (
*graph theory*) - Bonnet theorem (
*differential geometry*) - Boolean prime ideal theorem (
*mathematical logic*) - Borel-Bott-Weil theorem (
*representation theory*) - Borel–Carathéodory theorem (
*complex analysis*) - Borel-Weil theorem (
*representation theory*) - Borel fixed-point theorem (
*algebraic geometry*) - Borsuk-Ulam theorem (
*topology*) - Bott-Duffin theorem (
*network theory*) - Bott periodicity theorem (
*homotopy theory*) - Bounded inverse theorem (
*operator theory*) - Bourbaki–Witt theorem (
*order theory*) - Brahmagupta theorem (
*Euclidean geometry*) - Branching theorem (
*complex manifold*) - Brauer–Nesbitt theorem (
*representation theory of finite groups*) - Brauer-Siegel theorem (
*number theory*) - Brauer–Suzuki theorem (
*finite groups*) - Brauer's theorem (
*number theory*) - Brauer's theorem on induced characters (
*representation theory of finite groups*) - Brauer's three main theorems (
*finite groups*) - Brauer–Cartan–Hua theorem (
*ring theory*) - Brianchon's theorem (
*conics*) - Brooks’ theorem (
*graph theory*) - Brouwer fixed point theorem (
*topology*) - Browder-Minty theorem (
*operator theory*) - Brown's representability theorem (
*homotopy theory*) - Bruck-Chowla-Ryser theorem (
*combinatorics*) - Brun's theorem (
*number theory*) - Brun-Titchmarsh theorem (
*number theory*) - Brunn-Minkowski theorem (
*Riemannian geometry*) - Buckingham π theorem (
*dimensional analysis*) - Busemann's theorem (
*Euclidean geometry*) - Butterfly theorem (
*Euclidean geometry*)

## [edit] C

- Cameron–Martin theorem (
*measure theory*) - Cantor–Bernstein–Schroeder theorem (
*Set theory*,*cardinal numbers*) - Cantor's theorem (
*Set theory*,*Cantor's diagonal argument*) - Carathéodory-Jacobi-Lie theorem (
*symplectic topology*) - Carathéodory's theorem (
*conformal mapping*) - Carathéodory's theorem (
*convex hull*) - Carathéodory's theorem (
*measure theory*) - Carathéodory's extension theorem (
*measure theory*) - Caristi fixed point theorem (
*fixed points*) - Carlson's theorem (
*Complex analysis*) - Carmichael's theorem (
*Fibonacci numbers*) - Carnot's theorem (
*geometry*) - Carnot's theorem (
*thermodynamics*) - Cartan–Hadamard theorem (
*Riemannian geometry*) - Cartan–Kähler theorem (
*partial differential equations*) - Cartan's theorem (
*Lie group*) - Cartan's theorems A and B (
*several complex variables*) - Casey's theorem (
*Euclidean geometry*) - Castigliano's first and second theorems (
*structural analysis*) - Cauchy integral theorem (
*Complex analysis*) - Cauchy-Hadamard theorem (
*Complex analysis*) - Cauchy-Kowalevski theorem (
*partial differential equations*) - Cayley-Hamilton theorem (
*Linear algebra*) - Cayley's theorem (
*group theory*) - Central limit theorem (
*probability*) - Cesaro's theorem (
*real analysis*) - Ceva's theorem (
*geometry*) - Chebotarev's density theorem (
*number theory*) - Chen's theorem (
*number theory*) - Chern-Gauss-Bonnet theorem (
*differential geometry*) - Chevalley–Shephard–Todd theorem (
*finite group*) - Chevalley-Warning theorem (
*field theory*) - Chinese remainder theorem (
*number theory*) - Choi's theorem on completely positive maps (
*operator theory*) - Chomsky-Schützenberger theorem (
*linguistics*) - Chowla-Mordell theorem (
*number theory*) - Church-Rosser theorem (
*lambda calculus*) - Clairaut's theorem (
*physics*) - Clark-Ocone theorem (
*stochastic processes*) - Classification of finite simple groups (
*group theory*) - Clifford's theorem (
*algebraic curves*) - Closed graph theorem (
*functional analysis*) - Cluster decomposition theorem (
*quantum field theory*) - Coase theorem (
*economics*) - Cochran's theorem (
*statistics*) - Codd's theorem (
*relational model*) - Cohn's irreducibility criterion (
*polynomials*) - Coleman-Mandula theorem (
*quantum field theory*) - Commutation theorem (
*von Neumann algebra*) - Compactness theorem (
*mathematical logic*) - Conservativity theorem (
*mathematical logic*) - Convolution theorem (
*Fourier transforms*) - Cook's theorem (
*computational complexity theory*) - Corona theorem (
*Complex analysis*) - Cox's theorem (
*probability foundations*) - Craig's theorem (
*mathematical logic*) - Critical line theorem (
*number theory*) - Crystallographic restriction theorem (
*group theory*,*crystallography*) - Curtis–Hedlund–Lyndon theorem (
*cellular automata*) - Cut-elimination theorem (
*proof theory*) - Cybenko theorem (
*neural networks*)

## [edit] D

- Dandelin's theorem (
*solid geometry*) - Danskin's theorem (
*convex analysis*) - Darboux's theorem (
*real analysis*) - Darboux's theorem (
*symplectic topology*) - Davenport–Schmidt theorem (
*number theory*,*Diophantine approximations*) - De Branges' theorem (
*complex analysis*) - De Finetti's theorem (
*probability*) - De Gua's theorem (
*geometry*) - De Moivre's theorem (
*complex analysis*) - De Rham's theorem (
*differential topology*) - Deduction theorem (
*logic*) - Desargues' theorem (
*geometry*) - Descartes' theorem (
*geometry*) - Dilworth's theorem (
*combinatorics*,*order theory*) - Dimension theorem for vector spaces (
*vector spaces, linear algebra*) - Dini's theorem (
*analysis*) - Dirac's theorems (
*graph theory*) - Dirichlet's approximation theorem (
*Diophantine approximations*) - Dirichlet's theorem on arithmetic progressions (
*number theory*) - Dirichlet's unit theorem (
*algebraic number theory*) - Divergence theorem (
*vector calculus*) - Dominated convergence theorem (
*Lebesgue integration*) - Donaldson's theorem (
*differential topology*) - Donsker's theorem (
*probability theory*) - Duggan-Schwartz theorem (
*voting theory*) - Dunford-Schwartz theorem (
*functional analysis*)

## [edit] E

- Earnshaw's theorem (
*electrostatics*) - Easton's theorem (
*set theory*) - Edge-of-the-wedge theorem (
*complex analysis*) - Egorov's theorem (
*measure theory*) - Ehresmann's theorem (
*differential topology*) - Eilenberg–Zilber theorem (
*algebraic topology*) - Envelope theorem (
*calculus of variations*) - Equal incircles theorem (
*Euclidean geometry*) - Equidistribution theorem (
*ergodic theory*) - Equipartition theorem (
*ergodic theory*) - Erdős–Anning theorem (
*discrete geometry*) - Erdos-Dushnik-Miller theorem (
*set theory*) - Erdős-Kac theorem (
*number theory*) - Erdős-Ko-Rado theorem (
*combinatorics*) - Erdős–Pósa theorem (
*graph theory*) - Erdős-Stone theorem (
*graph theory*) - Euclid's theorem (
*number theory*) - Euclid-Euler Theorem (
*number theory*) - Euler's rotation theorem (
*geometry*) - Euler's theorem (
*number theory*) - Euler's theorem on homogeneous functions (
*multivariate calculus*) - Extreme value theorem

## [edit] F

- Faltings' theorem (
*diophantine geometry*) - Fáry's theorem (
*graph theory*) - Fary-Milnor theorem (
*knot theory*) - Fatou's theorem (
*complex analysis*) - Fatou-Lebesgue theorem (
*real analysis*) - Feit-Thompson theorem (
*finite groups*) - Fermat's last theorem (
*number theory*) - Fermat's little theorem (
*number theory*) - Fermat's theorem (stationary points) (
*real analysis*) - Fermat polygonal number theorem (
*number theory*) - Fieller's theorem (
*statistics*) - Final value theorem (
*mathematical analysis*) - Fisher separation theorem (
*economics*) - Fitting's theorem (
*group theory*) - Five color theorem (
*graph theory*) - Fixed point theorems in infinite-dimensional spaces
- Fluctuation dissipation theorem (
*physics*) - Fluctuation theorem (
*statistical mechanics*) - Ford's theorem (
*number theory*) - Four color theorem (
*graph theory*) - Fourier inversion theorem (
*harmonic analysis*) - Fourier theorem (
*harmonic analysis*) - Franel-Landau theorem (
*number theory*) - Freidlin-Wentzell theorem (
*stochastic processes*) - Freiman's theorem (
*number theory*) - Freudenthal suspension theorem (
*homotopy theory*) - Freyd's adjoint functor theorem (
*category theory*) - Frobenius reciprocity theorem (
*group representations*) - Frobenius theorem (
*foliations*) - Frobenius theorem (
*abstract algebras*) - Froda's theorem (
*mathematical analysis*) - Fubini's theorem (
*integration*) - Fuchs's theorem (
*differential equations*) - Fuglede's theorem (
*functional analysis*) - Fulton-Hansen connectedness theorem (
*algebraic geometry*) - Fundamental theorem of algebra (
*complex analysis*) - Fundamental theorem of arbitrage-free pricing (
*financial mathematics*) - Fundamental theorem of arithmetic (
*number theory*) - Fundamental theorem of calculus (
*calculus*) - Fundamental theorem on homomorphisms (
*abstract algebra*)

## [edit] G

- Gauss theorem (
*vector calculus*) - Gauss's Theorema Egregium (
*differential geometry*) - Gauss-Bonnet theorem (
*differential geometry*) - Gauss-Lucas theorem (
*complex analysis*) - Gauss-Markov theorem (
*statistics*) - Gauss-Wantzel theorem (
*geometry*) - Gelfand–Naimark theorem (
*functional analysis*) - Gelfond–Schneider theorem (
*transcendence theory*) - Gershgorin circle theorem (
*matrix theory*) - Gibbard-Satterthwaite theorem (
*voting methods*) - Girsanov's theorem (
*stochastic processes*) - Glaisher's theorem (
*number theory*) - Gleason's theorem (
*Hilbert space*) - Glivenko's theorem (
*mathematical logic*) - Goddard-Thorn theorem (
*vertex algebras*) - Gödel's completeness theorem (
*mathematical logic*) - Gödel's incompleteness theorem (
*mathematical logic*) - Godunov's theorem (
*numerical analysis*) - Going-up and going-down theorems (
*commutative algebra*) - Goldie's theorem (
*ring theory*) - Goodstein's theorem (
*mathematical logic*) - Gordon–Newell theorem (
*queueing theory*) - Gradient theorem (
*vector calculus*) - Graph structure theorem (
*graph theory*) - Great orthogonality theorem (
*group theory*) - Green-Tao theorem (
*number theory*) - Green's theorem (
*vector calculus*) - Gromov's compactness theorem (
*Riemannian geometry*) - Gromov's theorem (
*group theory*) - Gromov-Ruh theorem (
*differential geometry*) - Gross-Zagier theorem (
*number theory*) - Grothendieck–Hirzebruch–Riemann–Roch theorem (
*algebraic geometry*) - Grothendieck's connectedness theorem (
*algebraic geometry*) - Grunwald-Wang theorem (
*algebraic number theory*) - Grushko theorem (
*group theory*)

## [edit] H

- H-theorem (
*thermodynamics*) - Haag's theorem (
*quantum field theory*) - Haboush's theorem (
*algebraic groups*,*representation theory*,*invariant theory*) - Hadamard three-circle theorem (
*complex analysis*) - Hadwiger's theorem (
*geometry*,*measure theory*) - Hahn embedding theorem (
*ordered groups*) - Hairy ball theorem (
*algebraic topology*) - Hahn-Banach theorem (
*functional analysis*) - Hahn–Kolmogorov theorem (
*measure theory*) - Hales-Jewett theorem (
*combinatorics*) - Halpern-Lauchli theorem (
*Ramsey theory*) - Ham sandwich theorem (
*topology*) - Hardy–Littlewood maximal theorem (
*real analysis*) - Hardy–Ramanujan theorem (
*number theory*) - Harish-Chandra's regularity theorem (
*representation theory*) - Harnack's curve theorem (
*real algebraic geometry*) - Harnack's theorem (
*complex analysis*) - Hartogs' theorem (
*complex analysis*) - Hasse norm theorem (
*number theory*) - Hasse's theorem on elliptic curves (
*number theory*) - Hasse–Minkowski theorem (
*number theory*) - Heine-Borel theorem (
*real analysis*) - Heine–Cantor theorem (
*metric geometry*) - Hellinger-Toeplitz theorem (
*functional analysis*) - Hellmann–Feynman theorem (
*physics*) - Helly's theorem (
*convex sets*) - Helmholtz theorem (classical mechanics) (
*physics*) - Herbrand's theorem (
*logic*) - Herbrand–Ribet theorem (
*cyclotomic fields*) - Higman's embedding theorem (
*group theory*) - Hilbert's basis theorem (
*commutative algebra*,*invariant theory*) - Hilbert's Nullstellensatz (theorem of zeroes) (
*commutative algebra*,*algebraic geometry*) - Hilbert-Schmidt theorem (
*functional analysis*) - Hilbert-Speiser theorem (
*cyclotomic fields*) - Hilbert's irreducibility theorem (
*number theory*) - Hilbert's syzygy theorem (
*commutative algebra*) - Hilbert's theorem (
*differential geometry*) - Hilbert's theorem 90 (
*number theory*) - Hilbert projection theorem (
*convex analysis*) - Hille–Yosida theorem (
*functional analysis*) - Hindman's theorem (
*Ramsey theory*) - Hinge theorem (
*geometry*) - Hironaka theorem (
*algebraic geometry*) - Hirzebruch–Riemann–Roch theorem (
*complex manifolds*) - Hjelmslev's theorem (
*geometry*) - Hobby–Rice theorem (
*mathematical analysis*) - Hölder's theorem (
*mathematical analysis*) - Holland's schema theorem (
*genetic algorithm*) - Holmström's theorem (
*economics*) - Hopf-Rinow theorem (
*differential geometry*) - Hurewicz theorem (
*algebraic topology*) - Hurwitz's automorphisms theorem (
*algebraic curves*)

## [edit] I

- Identity theorem for Riemann surfaces (
*Riemann surfaces*) - Implicit function theorem (
*vector calculus*) - Increment theorem (
*mathematical analysis*) - Infinite monkey theorem (
*probability*) - Integral root theorem (
*algebra, polynomials*) - Integral representation theorem for classical Wiener space (
*measure theory*) - Intermediate value theorem (
*calculus*) - Intersection theorem (
*projective geometry*) - Inverse function theorem (
*vector calculus*) - Isomorphism extension theorem (
*abstract algebra*) - Isomorphism theorem (
*abstract algebra*) - Isoperimetric theorem (
*curves*,*calculus of variations*)

## [edit] J

- Jackson's theorem (
*queueing theory*) - Jacobson density theorem (
*ring theory*) - Japanese theorem (
*geometry*) - Japanese theorem for concyclic polygons (
*Euclidean geometry*) - Jordan curve theorem (
*topology*) - Jordan-Hölder theorem (
*group theory*) - Jordan-Schönflies theorem (
*geometric topology*) - Jung's theorem (
*geometry*) - Jurkat–Richert theorem (
*analytic number theory*)

## [edit] K

- Kachurovskii's theorem (
*convex analysis*) - Kantorovich theorem (
*functional analysis*) - Kaplansky density theorem (
*von Neumann algebra*) - Kaplansky's theorem on quadratic forms (
*quadratic forms*) - Karhunen-Loève theorem (
*stochastic processes*) - Khinchin's theorem (
*probability*) - Kirby-Paris theorem (
*proof theory*) - Kirchhoff's theorem (
*graph theory*) - Kirszbraun theorem (
*Lipschitz continuity*) - Kleene's recursion theorem (
*recursion theory*) - Kleene fixed-point theorem (
*order theory*) - Knaster-Tarski theorem (
*order theory*) - Kneser theorem (
*differential equations*) - Kodaira embedding theorem (
*algebraic geometry*) - Kodaira vanishing theorem (
*complex manifold*) - Koebe 1/4 theorem (
*complex analysis*) - Kolmogorov-Arnold-Moser theorem (
*dynamical systems*) - Kolmogorov extension theorem (
*stochastic processes*) - König's theorem (
*mathematical logic*) - König's theorem (graph theory) (
*bipartite graphs*) - König's theorem (set theory) (
*cardinal numbers*) - Krein–Milman theorem (
*mathematical analysis, discrete geometry*) - Kronecker's theorem (
*diophantine approximation*) - Kronecker-Weber theorem (
*number theory*) - Krull's principal ideal theorem (
*commutative algebra*) - Krull-Schmidt theorem (
*group theory*) - Kruskal–Katona theorem (
*combinatorics*) - Kruskal's tree theorem (
*order theory*) - Krylov-Bogolyubov theorem (
*dynamical systems*) - Künneth theorem (
*algebraic topology*) - Kurosh subgroup theorem (
*group theory*)

## [edit] L

- Ladner's theorem (
*computational complexity theory*) - Lagrange's theorem (
*group theory*) - Lagrange's theorem (
*number theory*) - Lagrange's four-square theorem (
*number theory*) - Lagrange inversion theorem (
*mathematical analysis*,*combinatorics*) - Lagrange reversion theorem (
*mathematical analysis*,*combinatorics*) - Lambek-Moser theorem (
*combinatorics*) - Lami's theorem (
*statics*) - Landau prime ideal theorem (
*number theory*) - Lasker–Noether theorem (
*commutative algebra*) - Laurent expansion theorem (
*complex analysis*) - Lauricella's theorem (
*functional analysis*) - Lax–Milgram theorem (
*partial differential equations*) - Lax-Richtmyer theorem (
*numerical analysis*) - Lebesgue covering dimension (
*dimension theory*) - Lebesgue's decomposition theorem (
*dimension theory*) - Lebesgue's density theorem (
*dimension theory*) - Lee Hwa Chung theorem (
*symplectic topology*) - Lebesgue differentiation theorem (
*real analysis*) - Le Cam's theorem (
*probability theory*) - Lee–Yang theorem (
*statistical mechanics*) - Lefschetz-Hopf theorem (
*topology*) - Lefschetz fixed point theorem (
*algebraic topology*) - Lefschetz hyperplane theorem (
*algebraic topology*) - Lehmann-Scheffé theorem (
*statistics*) - Lester's theorem (
*Euclidean plane geometry*) - Levi's theorem (
*Lie groups*) - Lickorish–Wallace theorem (
*3-manifolds*) - Lie's third theorem (
*Lie algebra*) - Lindemann-Weierstrass theorem (
*transcendence theory*) - Lie-Kolchin theorem (
*algebraic groups*,*representation theory*) - Liénard's theorem (
*dynamical systems*) - Lindelöf's theorem (
*complex analysis*) - Linear congruence theorem (
*number theory*,*modular arithmetic*) - Linear speedup theorem (
*computational complexity theory*) - Linnik's theorem (
*number theory*) - Lions-Lax-Milgram theorem (
*partial differential equations*) - Liouville's theorem (complex analysis) (
*entire functions*) - Liouville's theorem (conformal mappings) (
*conformal mappings*) - Liouville's theorem (Hamiltonian) (
*Hamiltonian mechanics*) - Löb's theorem (
*mathematical logic*) - Lochs' theorem (
*number theory*) - Looman–Menchoff theorem (
*complex analysis*) - Löwenheim-Skolem theorem (
*mathematical logic*) - Lucas' theorem (
*number theory*) - Lumer-Phillips theorem (
*semigroup theory*) - Luzin's theorem (
*real analysis*) - Lyapunov's central limit theorem (
*probability theory*)

## [edit] M

- Mahler's compactness theorem (
*geometry of numbers*) - Mahler's theorem (
*p-adic analysis*) - Maier's theorem (
*analytic number theory*) - Malgrange–Ehrenpreis theorem (
*differential equations*) - Marcinkiewicz theorem (
*functional analysis*) - Marden's theorem (
*polynomials*) - Mergelyan's theorem (
*complex analysis*) - Marginal value theorem (
*biology*) - Marriage theorem (
*combinatorics*) - Martingale representation theorem (
*probability theory*) - Master theorem (
*recurrence relations*,*asymptotic analysis*) - Maschke's theorem (
*group representations*) - Matiyasevich's theorem (
*mathematical logic*) - Max flow min cut theorem (
*graph theory*) - Max Noether's theorem (
*algebraic geometry*) - Maximal ergodic theorem (
*ergodic theory*) - Maximum power theorem (
*electrical circuits*) - Maxwell's theorem (
*probability theory*) - May's theorem (
*game theory*) - Mazur's torsion theorem (
*algebraic geometry*) - Mean value theorem (
*calculus*) - Measurable Riemann mapping theorem (
*conformal mapping*) - Mellin inversion theorem (
*complex analysis*) - Menelaus' theorem (
*geometry*) - Menger's theorem (
*graph theory*) - Mercer's theorem (
*functional analysis*) - Mertens' theorems (
*number theory*) - Metrization theorems (
*topological spaces*) - Meusnier's theorem (
*differential geometry*) - Midy's theorem (
*number theory*) - Mihăilescu's theorem (
*number theory*) - Milliken-Taylor theorem (
*Ramsey theory*) - Milliken's tree theorem (
*Ramsey theory*) - Min-max theorem (
*functional analysis*) - Minimax theorem (
*game theory*) - Minkowski's theorem (
*geometry of numbers*) - Minkowski-Hlawka theorem (
*geometry of numbers*) - Minlos' theorem (
*functional analysis*) - Mitchell's embedding theorem (
*category theory*) - Mittag-Leffler's theorem (
*complex analysis*) - Modigliani-Miller theorem (
*finance theory*) - Modularity theorem (
*number theory*) - Mohr-Mascheroni theorem (
*geometry*) - Monge's theorem (
*geometry*) - Monodromy theorem (
*complex analysis*) - Monotone convergence theorem (
*mathematical analysis*) - Montel's theorem (
*complex analysis*) - Moore-Aronszajn theorem (
*Hilbert space*) - Mordell-Weil theorem (
*number theory*) - Moreau's theorem (
*convex analysis*) - Morera's theorem (
*complex analysis*) - Morley's categoricity theorem (
*model theory*) - Morley's trisector theorem (
*geometry*) - Morton's theorem (
*game theory*) - Mostow rigidity theorem (
*differential geometry*) - Mountain pass theorem (
*calculus of variations*) - Multinomial theorem (
*algebra*,*combinatorics*) - Multiplication theorem (
*special functions*) - Myers theorem (
*differential geometry*) - Myhill-Nerode theorem (
*formal languages*)

## [edit] N

- Nachbin's theorem(
*complex analysis*) - Nagata-Smirnov metrization theorem(
*general topology*) - Nagell-Lutz theorem (
*elliptic curves*) - Napoleon's theorem (
*triangle geometry*) - Nash embedding theorem (
*differential geometry*) - Nash-Moser theorem (
*mathematical analysis*) - Newlander-Niremberg theorem (
*differential geometry*) - Nicomachus's theorem (
*number theory*) - Nielsen-Schreier theorem (
*free groups*) - No cloning theorem (
*quantum computation*) - No wandering domain theorem (
*ergodic theory*) - Noether's theorem (
*Lie groups*,*calculus of variations*,*differential invariants*,*physics*) - No-ghost theorem (
*vertex algebras*) - Norton's theorem (
*electrical networks*) - Nyquist-Shannon sampling theorem (
*information theory*)

## [edit] O

- Open mapping theorem (
*complex analysis*) - Open mapping theorem (
*functional analysis*) - Optional stopping theorem (
*probability theory*) - Ore's theorem (
*graph theory*) - Ornstein theorem (
*ergodic theory*) - Ortsbogen theorem (
*Euclidean geometry*) - Oseledec theorem (
*ergodic theory*) - Ostrowski's theorem (
*number theory*) - Ostrowski-Hadamard gap theorem (
*complex analysis*)

## [edit] P

- Paley's theorem (
*algebra*) - Paley-Wiener theorem (
*Fourier transforms*) - Pappus's centroid theorem (
*geometry*) - Pappus's hexagon theorem (
*geometry*) - Paris–Harrington theorem (
*mathematical logic*) - Parovicenko's theorem (
*topology*) - Parseval's theorem (
*Fourier analysis*) - Pascal's theorem (
*conics*) - Pasch's theorem (
*order theory*) - Peano existence theorem (
*ordinary differential equations*) - Peetre theorem (
*functional analysis*) - Pentagonal number theorem (
*number theory*) - Perfect graph theorem (
*graph theory*) - Perron–Frobenius theorem (
*matrix theory*) - Peter-Weyl theorem (
*representation theory*) - Picard theorem (
*complex analysis*) - Picard-Lindelöf theorem (
*ordinary differential equations*) - Pick's theorem (
*geometry*) - Pitman-Koopman-Darmois theorem (
*statistics*) - Planar separator theorem (
*graph theory*) - Plancherel theorem (
*Fourier analysis*) - Plancherel theorem for spherical functions (
*representation theory*) - Poincaré-Bendixson theorem (
*dynamical systems*) - Poincaré-Birkhoff-Witt theorem (
*universal enveloping algebras*) - Poincaré duality theorem (
*algebraic topology of manifolds*) - Poisson limit theorem (
*probability*) - Pompeiu's theorem (
*Euclidean geometry*) - Poncelet-Steiner theorem (
*geometry*) - Post's theorem (
*mathematical logic*) - Preimage theorem (
*differential topology*) - Prime number theorem (
*number theory*) - Primitive element theorem (
*field theory*) - Principal axis theorem (
*linear algebra*) - Prokhorov's theorem (
*measure theory*) - Proth's theorem (
*number theory*) - Ptolemaios' theorem (
*geometry*) - Pythagorean theorem (
*geometry*)

## [edit] Q

## [edit] R

- Rademacher's theorem (
*mathematical analysis*) - Radon's theorem (
*convex sets*) - Radon-Nikodym theorem (
*measure theory*) - Ramanujan-Skolem's theorem (
*diophantine equations*) - Ramsey's theorem (
*graph theory,combinatorics*) - Rank-nullity theorem (
*linear algebra*) - Rao-Blackwell theorem (
*statistics*) - Rational root theorem (
*algebra,polynomials*) - Ratner's theorems (
*ergodic theory*) - Rauch comparison theorem (
*Riemannian geometry*) - Rédei's theorem (
*group theory*) - Reeh-Schlieder theorem (
*local quantum field theory*) - Residue theorem (
*complex analysis*) - Reynolds transport theorem (
*fluid dynamics*) - Ribet's theorem (
*elliptic curves*) - Rice's theorem (
*recursion theory, computer science*) - Rice-Shapiro theorem (
*computer science*) - Richardson's theorem (
*mathematical logic*) - Riemann mapping theorem (
*complex analysis*) - Riemann series theorem (
*mathematical series*) - Riemann's existence theorem (
*algebraic geometry*) - Riemann's theorem on removable singularities (
*complex analysis*) - Riemann-Roch theorem (
*Riemann surfaces*,*algebraic curves*) - Riemann–Roch theorem for smooth manifolds (
*differential topology*) - Riemann singularity theorem (
*algebraic geometry*) - Riesz representation theorem (
*functional analysis,Hilbert space*) - Riesz–Fischer theorem (
*real analysis*) - Riesz-Thorin theorem (
*functional analysis*) - Ringel–Youngs theorem (
*graph theory*) - Robertson-Seymour theorem (
*graph theory*) - Robin's theorem (
*number theory*) - Robinson's joint consistency theorem (
*mathematical logic*) - Rokhlin's theorem (
*geometric topology*) - Rolle's theorem (
*calculus*) - Rosser's theorem (
*number theory*) - Roth's theorem (
*diophantine approximation*) - Rouché's theorem (
*complex analysis*) - Routh's theorem (
*triangle geometry*) - Routh–Hurwitz theorem (
*polynomials*) - Runge's theorem (
*complex analysis*)

## [edit] S

- Sahlqvist correspondence theorem (
*modal logic*) - Sard's theorem (
*differential geometry*) - Sarkovskii's theorem (
*dynamical systems*) - Savitch's theorem (
*computational complexity theory*) - Sazonov's theorem (
*functional analysis*) - Schauder fixed point theorem (
*functional analysis*) - Schilder's theorem (
*stochastic processes*) - Schreier refinement theorem (
*group theory*) - Schroeder-Bernstein theorem for measurable spaces (
*measure theory*) - Schur's lemma (
*representation theory*) - Schur's theorem (
*Ramsey theory*) - Schwenk's theorem (
*graph theory*) - Scott core theorem (
*3-manifolds*) - Seifert-van Kampen theorem (
*algebraic topology*) - Separating axis theorem (
*convex geometry*) - Shannon's expansion theorem (
*Boolean algebra*) - Shannon's theorem (
*information theory*) - Shift theorem (
*differential operators*) - Siegel–Walfisz theorem (
*analytic number theory*) - Silverman–Toeplitz theorem (
*mathematical analysis*) - Simplicial approximation theorem (
*algebraic topology*) - Sion's minimax theorem (
*game theory*) - Six exponentials theorem (
*transcendence theory*) - Sklar's theorem (
*statistics*) - Skoda-El Mir theorem (
*complex geometry*) - Skolem-Noether theorem (
*simple algebras*) - Slutsky's theorem (
*probability theory*) - Smn theorem (
*recursion theory, computer science*) - Sokhatsky-Weierstrass theorem (
*complex analysis*) - Soul theorem (
*Riemannian geometry*) - Soundness theorem (
*mathematical logic*) - Space hierarchy theorem (
*computational complexity theory*) - Spectral theorem (
*functional analysis*) - Speedup theorem (
*computational complexity theory*) - Sperner's theorem (
*combinatorics*) - Sphere theorem (
*Riemannian geometry*) - Spin-statistics theorem (
*physics*) - Sprague-Grundy theorem (
*combinatorial game theory*) - Squeeze theorem (
*mathematical analysis*) - Stallings theorem about ends of groups (
*group theory*) - Stallings–Zeeman theorem (
*algebraic topology*) - Stanley's reciprocity theorem (
*combinatorics*) - Stark-Heegner theorem (
*number theory*) - Stein-Strömberg theorem (
*measure theory*) - Steiner-Lehmus theorem (
*triangle geometry*) - Stewart's theorem (
*plane geometry*) - Stirling's theorem (
*mathematical analysis*) - Stokes' theorem (
*vector calculus, differential topology*) - Stolper-Samuelson theorem (
*economics*) - Stolz-Cesàro theorem (
*calculus*) - Stone's representation theorem for Boolean algebras (
*mathematical logic*) - Stone's theorem on one-parameter unitary groups (
*functional analysis*) - Stone-Tukey theorem (
*topology*) - Stone-von Neumann theorem (
*functional analysis*,*representation theory*of the*Heisenberg group*,*quantum mechanics*) - Stone-Weierstrass theorem (
*functional analysis*) - Strassman's theorem (
*field theory*) - Structured program theorem (
*computer science*) - Sturm's theorem (
*theory of equations*) - Sturm-Picone comparison theorem (
*differential equations*) - Subspace theorem (
*Diophantine approximation*) - Supporting hyperplane theorem (
*convex geometry*) - Swan's theorem (
*module theory*) - Sylow theorems (
*group theory*) - Sylvester's determinant theorem (
*determinants*) - Sylvester's theorem (
*number theory*) - Sylvester-Gallai theorem (
*plane geometry*) - Sz.-Nagy's dilation theorem (
*operator theory*) - Szemerédi's theorem (
*combinatorics*) - Szemerédi-Trotter theorem (
*combinatorics*)

## [edit] T

- Takagi existence theorem (
*number theory*) - Takens' theorem (
*dynamical systems*) - Tarski's indefinability theorem (
*mathematical logic*) - Taylor's theorem (
*calculus*) - Thales' theorem (
*geometry*) - Thébault's theorem (
*geometry*) - Theorem of de Moivre–Laplace (
*probability theory*) - Thevenin's theorem (
*electrical circuits*) - Thue's theorem (
*Diophantine equation*) - Thue-Siegel-Roth theorem (
*diophantine approximation*) - Tietze extension theorem (
*general topology*) - Tijdeman's theorem (
*diophantine equations*) - Tikhonov fixed point theorem (
*functional analysis*) - Time hierarchy theorem (
*computational complexity theory*) - Titchmarsh theorem (
*integral transform*) - Titchmarsh convolution theorem (
*complex analysis*) - Tits alternative (
*geometric group theory*) - Tonelli's theorem (
*functional analysis*) - Topkis's theorem (
*economics*) - Toponogov's theorem (
*Riemannian geometry*) - Torelli theorem (
*algebraic geometry*) - Tsen's theorem (
*algebraic geometry*) - Tunnell's theorem (
*number theory*) - Tutte theorem (
*graph theory*) - Turán's theorem (
*graph theory*) - Tychonoff's theorem (
*general topology*)

## [edit] U

- Ugly duckling theorem (
*computer science*) - Uniformization theorem (
*complex analysis*,*differential geometry*) - Universal approximation theorem (
*neural networks*) - Universal coefficient theorem (
*algebraic topology*) - Unmixedness theorem (
*algebraic geometry*)

## [edit] V

- Van Aubel's theorem (
*quadrilaterals*) - Van der Waerden's theorem (
*combinatorics*) - Vantieghems theorem (
*number theory*) - Varignon's theorem (
*Euclidean geometry*) - Vinogradov's theorem (
*number theory*) - Virial theorem (
*classical mechanics*) - Vitali convergence theorem (
*measure theory*) - Vitali theorem (
*measure theory*) - Vitali-Hahn-Saks theorem (
*measure theory*) - Viviani's theorem (
*Euclidean geometry*) - Von Neumann bicommutant theorem (
*functional analysis*) - Von Neumann's theorem (
*operator theory*)

## [edit] W

- Wedderburn's little theorem (
*ring theory*) - Wedderburn's theorem (
*abstract algebra*) - Weierstrass-Casorati theorem (
*complex analysis*) - Weierstrass factorization theorem (
*complex analysis*) - Weierstrass preparation theorem (
*several complex variables*,*commutative algebra*) - Weinberg–Witten theorem (
*quantum field theory*) - Well-ordering theorem (
*mathematical logic*) - Whitehead theorem (
*homotopy theory*) - Whitney embedding theorem (
*differential manifolds*) - Whitney extension theorem (
*mathematical analysis*) - Wiener's tauberian theorem (
*real analysis*) - Wiener-Ikehara theorem (
*number theory*) - Wigner-Eckart theorem (
*Clebsch-Gordan coefficients*) - Wilkie's theorem (
*model theory*) - Wilson's theorem (
*number theory*) - Wold's theorem (
*statistics*) - Wolstenholme's theorem (
*number theory*)