# List of theorems

﻿
List of theorems

*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.

__NOTOC__

0–9

*15 and 290 theorems ("number theory")
*2π theorem ("Riemannian geometry")

A

*AF+BG theorem ("algebraic geometry")
*Abel's binomial theorem ("combinatorics")
*Abel's theorem ("mathematical analysis")
*Abelian and tauberian theorems ("mathematical analysis")
*Abel-Ruffini theorem ("theory of equations", "Galois theory")
*Abouabdillah's theorem ("geometry","number theory")
*Alperin-Brauer-Gorenstein theorem ("finite groups")
*Analytic Fredholm theorem ("functional analysis")
*Anderson's theorem ("real analysis")
*Ankeny-Artin-Chowla theorem ("number theory")
*Apéry's theorem ("number theory")
*Apollonius' theorem ("plane geometry")
*Aronszajn-Smith theorem ("functional analysis")
*Arrow's impossibility theorem ("game theory")
*Artin-Schreier theorem ("real closed fields")
*Artin-Wedderburn theorem ("abstract 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")

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 theorem ("incidence geometry")
*Bell's theorem ("quantum theory - physics")
*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 theorem ("algebra, combinatorics")
*Birkhoff-Grothendieck theorem ("vector bundles")
*Birkhoff's theorem ("ergodic theory")
*Blaschke selection theorem ("geometric topology")
*Bloch's theorem ("complex analysis")
*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-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")
*Branching theorem ("complex manifold")
*Brauer–Suzuki theorem ("finite groups")
*Brauer's three main theorems ("finite groups")
*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")

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")
*Carmichael's theorem ("Fibonacci numbers")
*Carnot's theorem ("geometry")
*Carnot's theorem ("thermodynamics")
*Cartan–Kähler theorem ("partial differential equations")
*Cartan's theorem ("Lie group")
*Cartan's theorems A and B ("several complex variables")
*Castigliano's first and second theorems ("structural analysis")
*Cauchy integral theorem ("Complex analysis")
*Cauchy-Kowalevski theorem ("partial differential equations")
*Cayley-Hamilton theorem ("Linear algebra")
*Cayley's theorem ("group theory")
*Central limit theorem ("probability")
*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")
*Chinese remainder theorem ("number theory")
*Choi's theorem on completely positive maps ("operator theory")
*Chowla-Mordell theorem ("number theory")
*Church-Rosser theorem ("lambda calculus")
*Clark-Ocone theorem ("stochastic processes")
*Classification of finite simple groups ("group theory")
*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")
*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")
*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")

D

*Dandelin's theorem ("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")
*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")

E

*Earnshaw's theorem ("electrostatics")
*Easton's theorem ("set 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-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

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 polygonal number theorem ("number theory")
*Fieller's theorem ("statistics")
*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")
*Four color theorem ("graph theory")
*Fourier inversion theorem ("harmonic analysis")
*Fourier theorem ("harmonic analysis")
*Freudenthal suspension theorem ("homotopy theory")
*Freyd's adjoint functor theorem ("category theory")
*Frobenius reciprocity theorem ("group representations")
*Frobenius theorem ("foliations")
*Frobenius theorem ("abstract algebras")
*Fubini's theorem ("integration")
*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")

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")
*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")
*Going-up and going-down theorems ("commutative algebra")
*Goldie's theorem ("ring theory")
*Goodstein's theorem ("mathematical logic")
*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's connectedness theorem ("algebraic geometry")
*Grushko theorem ("group theory")

H

*H-theorem ("thermodynamics")
*Haag's theorem ("quantum field theory")
*Haboush's theorem ("algebraic groups", "representation theory", "invariant 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")
*Ham sandwich theorem ("topology")
*Hardy–Littlewood maximal theorem ("real analysis")
*Hardy–Ramanujan theorem ("number theory")
*Harish-Chandra's regularity theorem ("representation theory")
*Harnack's theorem ("complex analysis")
*Hartogs' theorem ("complex analysis")
*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")
*Helly's theorem ("convex sets")
*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 theorem (differential geometry)
*Hille–Yosida theorem ("functional analysis")
*Hindman's theorem ("Ramsey theory")
*Hinge theorem ("geometry")
*Hironaka theorem ("algebraic geometry")
*Hirzebruch–Riemann–Roch theorem ("complex manifolds")
*Holland's schema theorem ("genetic algorithm")
*Hopf-Rinow theorem ("differential geometry")
*Hurewicz theorem ("algebraic topology")
*Hurwitz's automorphisms theorem ("algebraic curves")

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")

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")

K

*Kachurovskii's theorem ("convex analysis")
*Kantorovich theorem ("functional analysis")
*Kaplansky density theorem ("von Neumann algebra")
*Khinchin's theorem ("probability")
*Kirchhoff's theorem ("graph theory")
*Kirszbraun theorem ("Lipschitz continuity")
*Kleene's recursion theorem ("recursion theory")
*Knaster-Tarski theorem ("order theory")
*Kneser theorem ("differential equations")
*Kodaira embedding theorem ("algebraic geometry")
*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")
*Kronecker's theorem ("diophantine approximation")
*Kronecker-Weber theorem ("number theory")
*Krull's principal ideal theorem ("commutative algebra")
*Krull-Schmidt theorem ("group theory")
*Kruskal's tree theorem ("order theory")
*Krylov-Bogolyubov theorem ("dynamical systems")
*Künneth theorem ("algebraic topology")
*Kurosh subgroup theorem ("group theory")

L

*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")
*Laurent expansion theorem ("complex 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 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")
*Lie's third theorem ("Lie algebra")
*Lindemann-Weierstrass theorem ("transcendence theory")
*Lie-Kolchin theorem ("algebraic groups", "representation theory")
*Liénard's theorem ("dynamical systems")
*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")

M

*Mahler's compactness theorem ("geometry of numbers")
*Malgrange–Ehrenpreis theorem ("differential equations")
*Marcinkiewicz theorem ("functional analysis")
*Marden's theorem ("polynomials")
*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")
*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")
*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")
*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")
*Mountain pass theorem ("calculus of variations")
*Multinomial theorem ("algebra", "combinatorics")
*Myers theorem ("differential geometry")
*Myhill-Nerode theorem ("formal languages")

N

*Nachbin's theorem("complex analysis")
*Nagata-Smirnov metrization theorem("general topology")
*Nagell-Lutz theorem ("elliptic curves")
*Nash embedding theorem ("differential geometry")
*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")

O

*Open mapping theorem ("functional analysis")
*Ornstein theorem ("ergodic theory")
*Oseledec theorem ("ergodic theory")
*Ostrowski's theorem ("number theory")

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")
*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")
*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")

Q

*Quillen–Suslin theorem ("abstract algebra")

R

*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")
*Rédei's theorem ("group theory")
*Reeh-Schlieder theorem ("local quantum field theory")
*Residue theorem ("complex analysis")
*Reynolds transport theorem ("fluid dynamics")
*Rice's theorem ("recursion theory, computer science")
*Rice-Shapiro theorem ("computer science")
*Riemann mapping theorem ("complex analysis")
*Riemann-Roch theorem ("Riemann surfaces", "algebraic curves")
*Riesz representation theorem ("functional analysis,Hilbert space")
*Riesz-Thorin theorem ("functional analysis")
*Robertson-Seymour theorem ("graph 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")

*Sahlqvist correspondence theorem ("modal logic")
*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")
*Schur's lemma ("representation theory")
*Schur's theorem ("Ramsey 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")
*Siegel–Walfisz theorem ("analytic number theory")
*Silverman–Toeplitz theorem ("mathematical analysis")
*Simplicial approximation theorem ("algebraic topology")
*Sklar's theorem ("statistics")
*Skoda-El Mir theorem ("complex geometry")
*Skolem-Noether theorem ("simple algebras")
*Slutsky's theorem ("probability theory")
*Sokhatsky-Weierstrass theorem ("complex analysis")
*Soundness theorem ("mathematical logic")
*Space hierarchy theorem ("computational complexity theory")
*Spectral theorem ("functional analysis")
*Speedup theorem ("computational complexity theory")
*Sperner's theorem ("combinatorics")
*Spin-statistics theorem ("physics")
*Sprague-Grundy theorem ("combinatorial game theory")
*Squeeze theorem ("mathematical analysis")
*Stallings-Zeeman theorem ("algebraic topology")
*Stanley's reciprocity theorem ("combinatorics")
*Stark-Heegner theorem ("number 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")
*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")

T

*Takagi existence theorem ("number theory")
*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
*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")
*Tits alternative ("geometric group theory")
*Tonelli's theorem ("functional analysis")
*Tsen's theorem ("algebraic geometry")
*Tunnell's theorem ("number theory")
*Tutte theorem ("graph theory")
*Turán's theorem ("graph theory")
*Tychonoff's theorem ("general topology")

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")

V

*Van der Waerden's theorem ("combinatorics")
*Vantieghems theorem ("number theory")
*Varignon's theorem ("Euclidean geometry")
*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")

W

*Wedderburn's theorem ("abstract algebra")
*Weierstrass-Casorati theorem ("complex analysis")
*Weierstrass preparation theorem ("several complex variables","commutative algebra")
*Well-ordering theorem ("mathematical logic")
*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")
*Wilson's theorem ("number theory")

Z

*Z* theorem ("finite groups")
*ZJ theorem ("finite groups")
*Zariski's main theorem ("algebraic geometry")
*Zeckendorf's theorem ("number theory")

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• List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

• List of conjectures — This is an incomplete list of mathematical conjectures. They are divided into four sections, according to their status in 2007. See also: * Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators * Unsolved problems in… …   Wikipedia

• List of mathematical proofs — A list of articles with mathematical proofs:Theorems of which articles are primarily devoted to proving them: See also: *Bertrand s postulate and a proof *Estimation of covariance matrices *Fermat s little theorem and some proofs *Gödel s… …   Wikipedia

• List of misnamed theorems — This is a list of misnamed theorems in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object) that are well known in mathematics, but which are not named for the originator. That is, these… …   Wikipedia

• List of lemmas — This following is a list of lemmas (or, lemmata , i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures. 0 to 9 *0/1 Sorting Lemma ( comparison… …   Wikipedia

• List of theories — This is a list of topics commonly referred to as theory .This is not a list of theorems or theories (e.g., Theory of relativity, String theory) but branches of knowledge with theory in their name.*Atomic theory *Automata theory *Axiomatic set… …   Wikipedia

• List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5. This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

• List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia

• List of Russian people — The Millennium of Russia monument in Veliky Novgorod, featuring the statues and reliefs of the most celebrated people in the first 1000 years of Russian history …   Wikipedia

• List of trigonometric identities — Cosines and sines around the unit circle …   Wikipedia