List of theorems

Last updated February 15, 2025

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This is a list of notable theorems. Lists of theorems and similar statements include:

Contents

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
Z

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

0–9

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–Jacobi theorem ( algebraic geometry )
Abel–Ruffini theorem ( theory of equations , Galois theory )
Abhyankar–Moh theorem ( algebraic geometry )
Absolute convergence theorem ( mathematical series )
Acyclic models theorem ( algebraic topology )
Addition theorem ( algebraic geometry )
Adiabatic theorem ( physics )
Ado's theorem ( Lie algebra )
Akhiezer's theorem ( complex analysis )
Akra–Bazzi theorem ( computer science )
Alternate Interior Angles Theorem ( geometry )
Alternate segment theorem ( geometry )
Albert–Brauer–Hasse–Noether theorem ( algebras )
Alchian–Allen theorem ( economics )
Alexandrov's uniqueness theorem ( discrete geometry )
Alperin–Brauer–Gorenstein theorem ( finite groups )
Alspach's theorem ( graph theory )
Amitsur–Levitzki theorem ( linear algebra )
Analyst's traveling salesman theorem ( discrete mathematics )
Analytic Fredholm theorem ( functional analysis )
Anderson's theorem ( real analysis )
Andreotti–Frankel theorem ( algebraic geometry )
Angle bisector theorem ( Euclidean geometry )
Ankeny–Artin–Chowla theorem ( number theory )
Anne's theorem ( geometry )
Apéry's theorem ( number theory )
Apollonius's theorem ( plane geometry )
Appell–Humbert theorem ( complex manifold )
Arakelyan's theorem ( complex analysis )
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 )
Arrow-Lind theorem ( welfare economics )
Art gallery theorem ( geometry )
Artin approximation theorem ( commutative algebra )
Artin–Schreier theorem ( real closed fields )
Artin–Verdier duality theorem ( number theory )
Artin–Wedderburn theorem ( abstract algebra )
Artin–Zorn theorem ( algebra )
Artstein's theorem ( control theory )
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 )
Aumann's agreement theorem ( statistics )
Autonomous convergence theorem ( dynamical systems )
Auxiliary polynomial theorem ( Diophantine approximation )
Ax–Grothendieck theorem ( model theory )
Ax–Kochen theorem ( number theory )
Aztec diamond theorem ( combinatorics )

B

BBD decomposition theorem ( algebraic geometry )
BEST theorem ( graph theory )
Babuška–Lax–Milgram theorem ( partial differential equations )
Baily–Borel theorem ( algebraic geometry )
Baire category theorem ( topology , metric spaces )
Baker's theorem ( number theory )
Balian–Low theorem ( Fourier analysis )
Balinski's theorem ( combinatorics )
Banach–Alaoglu theorem ( functional analysis )
Banach–Mazur theorem ( functional analysis )
Banach fixed-point theorem ( metric spaces, differential equations )
Banach–Steinhaus theorem ( functional analysis )
Banach–Stone theorem ( operator theory )
Banach–Tarski theorem ( measure theory )
Bang's theorem ( geometry )
Barban–Davenport–Halberstam theorem ( analytic number theory )
Barbier's theorem ( geometry )
Bapat–Beg theorem ( statistics )
Baranyai's theorem ( combinatorics )
Barwise compactness theorem ( mathematical logic )
Base change theorems ( algebraic geometry )
Basel problem ( mathematical analysis )
Bass-Guirvarc'h formula ( group theory )
Bass-Serre theorem ( group theory )
Basu's theorem ( statistics )
Bauer–Fike theorem ( spectral 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 )
Beckman–Quarles theorem ( Euclidean geometry )
Beer's theorem ( metric geometry )
Behnke–Stein theorem ( several complex variables )
Behrend's theorem ( number theory )
Bell's theorem ( quantum mechanics )
Beltrami's theorem ( Riemannian geometry )
Belyi's theorem ( algebraic geometry )
Bendixson–Dulac theorem ( dynamical systems )
Berge's theorem ( graph theory )
Berger–Kazdan comparison theorem ( Riemannian geometry )
Bernstein's theorem ( approximation theory )
Bernstein's theorem ( functional analysis )
Berry–Esséen theorem ( probability theory )
Bertini's theorem ( algebraic geometry )
Bertrand–Diquet–Puiseux theorem ( differential geometry )
Bertrand's ballot theorem ( probability theory , combinatorics )
Bertrand's postulate ( number theory )
Besicovitch covering theorem ( mathematical analysis )
Betti's theorem ( physics )
Beurling–Lax theorem ( Hardy spaces )
Bézout's identity ( number theory )
Bézout's theorem ( algebraic geometry )
Bing metrization theorem ( general topology )
Bing's recognition theorem ( geometric topology )
Binomial inverse theorem ( linear algebra )
Binomial theorem ( algebra, combinatorics )
Birch's theorem ( algebraic number theory )
Birkhoff–Grothendieck theorem ( complex geometry )
Birkhoff–Von Neumann theorem ( linear algebra )
Birkhoff's representation theorem ( lattice theory )
Birkhoff's theorem ( ergodic theory )
Birkhoff's theorem ( general relativity )
Birman short exact sequence ( geometric topology )
Bishop–Cannings theorem ( economics )
Bishop-Gromov inequality ( riemannian geometry )
Blakers–Massey theorem ( homotopy theory )
Blaschke selection theorem ( geometric topology )
Bloch's theorem ( complex analysis )
Blondel's theorem ( electric power ) ( physics )
Blum's speedup theorem ( computational complexity theory )
Bôcher's theorem ( complex analysis )
Bochner's tube theorem ( complex analysis )
Bogoliubov–Parasyuk theorem ( quantum field theory )
Bohr–Mollerup theorem ( gamma function )
Bohr–van Leeuwen theorem ( physics )
Bolyai–Gerwien theorem ( discrete geometry )
Bolzano's theorem ( real analysis, calculus )
Bolzano–Weierstrass theorem ( real analysis, calculus )
Bombieri's theorem ( number theory )
Bombieri–Friedlander–Iwaniec theorem ( number theory )
Bondareva–Shapley theorem ( economics )
Bondy's theorem ( graph theory , combinatorics )
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 determinacy theorem ( set theory )
Borel fixed-point theorem ( algebraic geometry )
Borsuk–Ulam theorem ( topology )
Bott periodicity theorem ( homotopy theory )
Bounded convergence theorem ( measure 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–Suzuki–Wall theorem ( group theory )
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 )
Bregman–Minc inequality ( discrete mathematics )
Brianchon's theorem ( conics )
British flag theorem ( Euclidean geometry )
Brooks's 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 )
Büchi-Elgot-Trakhtenbrot theorem ( mathematical logic )
Buckingham π theorem ( dimensional analysis )
Burke's theorem ( probability theory , queueing theory )
Burnside's theorem ( group theory )
Busemann's theorem ( Euclidean geometry )
Butterfly theorem ( Euclidean geometry )
Byers–Yang theorem ( quantum mechanics )

C

C-theorem ( physics )
CAP theorem ( theoretical computer science )
CPCTC ( triangle geometry )
Cameron–Erdős theorem ( discrete mathematics )
Cameron–Martin theorem ( measure theory )
Cantor–Bernstein–Schröder theorem ( set theory , cardinal numbers )
Cantor's intersection theorem ( real analysis )
Cantor's isomorphism theorem ( order theory )
Cantor's theorem ( set theory , Cantor's diagonal argument )
Carathéodory–Jacobi–Lie theorem ( symplectic topology )
Carathéodory's existence theorem ( ordinary differential equations )
Carathéodory's theorem ( complex analysis )
Carathéodory's theorem ( convex geometry )
Carathéodory's theorem ( measure theory )
Carathéodory's extension theorem ( measure theory )
Caristi fixed-point theorem ( fixed points )
Carleson–Jacobs theorem ( complex analysis )
Carleson's theorem ( harmonic analysis )
Carlson's theorem ( complex analysis )
Carmichael's theorem ( Fibonacci numbers )
Carnot's theorem ( geometry )
Carnot's theorem ( thermodynamics )
Cartan–Dieudonné theorem ( group theory )
Cartan–Hadamard theorem ( Riemannian geometry )
Cartan–Kähler theorem ( partial differential equations )
Cartan–Kuranishi prolongation theorem ( partial differential equations )
Cartan's theorem ( Lie group )
Cartan's theorems A and B ( several complex variables )
Casey's theorem ( Euclidean geometry )
Castelnuovo theorem ( algebraic geometry )
Castelnuovo–de Franchis theorem ( algebraic geometry )
Castigliano's first and second theorems ( structural analysis )
Cauchy integral theorem ( complex analysis )
Cauchy-Binet formula ( linear algebra )
Cauchy–Hadamard theorem ( complex analysis )
Cauchy–Kowalevski theorem ( partial differential equations )
Cauchy's theorem ( geometry )
Cauchy's theorem ( finite groups )
Cayley–Bacharach theorem ( projective geometry )
Cayley–Hamilton theorem ( Linear algebra )
Cayley–Salmon theorem ( algebraic surfaces )
Cayley's theorem ( group theory )
Cellular approximation theorem ( algebraic topology )
Central limit theorem ( probability )
Cesàro's theorem ( real analysis )
Ceva's theorem ( geometry )

Chasles' theorem, ( kinematics )
Chasles' theorem ( gravity )
Chasles' theorem ( algebraic geometry )
Chebotarev's density theorem ( number theory )
Chen's theorem ( number theory )
Cheng's eigenvalue comparison theorem ( Riemannian geometry )
Chern–Gauss–Bonnet theorem ( differential geometry )
Chevalley's structure theorem ( algebraic 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 enumeration theorem ( formal language theory )
Chomsky–Schützenberger representation theorem ( formal language theory )
Choquet–Bishop–de Leeuw theorem ( functional analysis )
Chow's theorem ( algebraic geometry )
Chowla–Mordell theorem ( number theory )
Church–Rosser theorem ( lambda calculus )
Clairaut's theorem ( physics )
Clapeyron's theorem ( physics )
Clark–Ocone theorem ( stochastic processes )
Classification of compact surfaces ( Topology )
Classification of finite simple groups ( group theory )
Classification of Platonic solids ( geometry )
Classification of symmetric spaces ( Lie theory )
Clausius theorem ( physics )
Clifford's circle theorems ( Euclidean plane geometry )
Clifford's theorem on special divisors ( algebraic curves )
Closed graph theorem ( functional analysis )
Closed range theorem ( functional analysis )
Cluster decomposition theorem ( quantum field theory )
Coase theorem ( economics )
Cochran's theorem ( statistics )
Codd's theorem ( relational model )
Cohen structure theorem ( commutative algebra )
Cohn's irreducibility criterion ( polynomials )
Coleman–Mandula theorem ( quantum field theory )
Commandino's theorem ( geometry )
Commutation theorem ( von Neumann algebra )
Compactness theorem ( mathematical logic )
Compression theorem ( computational complexity theory , structural complexity theory )
Conley–Zehnder theorem ( dynamical systems )
Conservativity theorem ( mathematical logic )
Constant chord theorem ( geometry )
Constant rank theorem ( multivariate calculus )
Continuous mapping theorem ( probability theory )
Convolution theorem ( Fourier transforms )
Conway circle theorem ( Euclidean plane geometry )
Cook's theorem ( computational complexity theory )
Corners theorem ( arithmetic combinatorics )
Corona theorem ( complex analysis )
Courcelle's theorem ( graph theory )
Cousin's lemma ( real analysis )
Cox's theorem ( probability )
Craig's theorem ( mathematical logic )
Craig's interpolation theorem ( mathematical logic )
Cramér’s decomposition theorem ( statistics )
Cramér's theorem (large deviations) ( probability )
Cramer's theorem (algebraic curves) ( analytic geometry )
Cramér–Wold theorem ( measure theory )
Critical line theorem ( number theory )
Crooks fluctuation theorem ( physics )
Crossbar theorem ( Euclidean plane geometry )
Crystallographic restriction theorem ( group theory , crystallography )
Curtis–Hedlund–Lyndon theorem ( cellular automata )
Cut-elimination theorem ( proof theory )

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 )
Dawson–Gärtner theorem ( asymptotic analysis )
de Branges's theorem ( complex analysis )
de Bruijn's theorem ( discrete geometry )
De Bruijn–Erdős theorem (incidence geometry)
De Bruijn–Erdős theorem (graph theory)
De Finetti's theorem ( probability )
De Franchis theorem ( Riemann surfaces )
De Gua's theorem ( geometry )
De Moivre's theorem ( complex analysis )
De Rham's theorem ( differential topology )
Deduction theorem ( logic )
Dehn-Nielsen-Baer theorem ( geometric topology )
Denjoy theorem ( dynamical systems )
Denjoy–Carleman theorem ( functional analysis )
Denjoy-Young-Saks theorem ( real analysis )
Desargues's theorem ( projective geometry )
Descartes's theorem ( plane geometry )
Descartes's theorem on total angular defect ( polyhedra )
Diaconescu's theorem ( mathematical logic )
Diller–Dress theorem ( field theory )
Dilworth's theorem ( combinatorics , order theory )
Dinostratus' theorem ( geometry , analysis )
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 )
Disintegration theorem ( measure theory )
Divergence theorem ( vector calculus )
Dold–Thom theorem ( algebraic topology )
Dominated convergence theorem ( Lebesgue integration )
Donaldson's theorem ( differential topology )
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 )
Duggan–Schwartz theorem ( voting theory )
Dunford–Pettis theorem ( probability theory )
Dunford–Schwartz theorem ( functional analysis )

E

Earnshaw's theorem ( electrostatics )
Easton's theorem ( set theory )
Eberlein–Šmulian theorem ( functional analysis )
Edge-of-the-wedge theorem ( complex analysis )
Edgeworth's limit theorem ( economics )
Egorov's theorem ( measure theory )
Ehresmann's theorem ( differential topology )
Eilenberg–Ganea theorem ( homological algebra , algebraic topology )
Eilenberg–Zilber theorem ( algebraic topology )
Elitzur's theorem ( quantum field theory, statistical field theory )
Envelope theorem ( calculus of variations )
Equal incircles theorem ( Euclidean geometry )
Equidistribution theorem ( ergodic theory )
Equipartition theorem ( ergodic theory )
Erdős–Anning theorem ( discrete geometry )
Erdős–Dushnik–Miller theorem ( set theory )
Erdős–Gallai theorem ( graph theory )
Erdős–Ginzburg–Ziv theorem ( number theory )
Erdős–Kac theorem ( number theory )
Erdős–Ko–Rado theorem ( combinatorics )
Erdős–Nagy theorem ( discrete geometry )
Erdős–Pósa theorem ( graph theory )
Erdős–Rado theorem ( set theory )
Erdős–Stone theorem ( graph theory )
Erdős–Szekeres theorem ( discrete geometry )
Euclid's theorem ( number theory )
Euclid–Euler theorem ( number theory )
Euler's partition theorem ( number theory )
Euler's polyhedron theorem ( polyhedra )
Euler's quadrilateral theorem ( geometry )
Euler's rotation theorem ( geometry )
Euler's theorem ( differential geometry )
Euler's theorem ( number theory )
Euler's theorem in geometry ( triangle geometry )
Euler's theorem on homogeneous functions ( multivariate calculus )
Exchange theorem ( linear algebra )
Excision theorem ( homology theory )
Exterior angle theorem ( triangle geometry )
Extreme value theorem ( calculus )

F

F. and M. Riesz theorem ( measure theory )
FWL theorem ( economics )
Factor theorem ( polynomials )
Fagin's theorem ( computational complexity theory )
Faltings's theorem ( Diophantine geometry )
Farrell–Markushevich theorem ( complex analysis )
Fáry's theorem ( graph theory )
Fáry–Milnor theorem ( knot theory )
Fatou's theorem ( complex analysis )
Fatou–Lebesgue theorem ( real analysis )
Faustman–Ohlin theorem ( economics )
Feferman–Vaught theorem ( model theory )
Feit–Thompson theorem ( finite groups )
Fenchel's duality theorem ( convex analysis )
Fenchel's theorem ( differential geometry )
Fenchel–Moreau theorem ( mathematical analysis )
Fermat's Last Theorem ( number theory )
Fermat's little theorem ( number theory )
Fermat's theorem on sums of two squares ( number theory )
Fermat's theorem (stationary points) ( real analysis )
Fermat polygonal number theorem ( number theory )
Fernique's theorem ( measure theory )
Ferrero–Washington theorem ( algebraic number theory )
Feuerbach's theorem ( geometry )
Fieller's theorem ( statistics )
Final value theorem ( mathematical analysis )
Finsler–Hadwiger theorem ( geometry )
Fisher separation theorem ( economics )
Fisher–Tippett–Gnedenko theorem ( statistics )
Fitting's theorem ( group theory )
Five circles theorem ( circles )
Five color theorem ( graph theory )
Fixed-point theorems in infinite-dimensional spaces
Flat torus theorem ( geometric group theory )
Floquet's theorem ( differential equations )
Fluctuation dissipation theorem ( physics )
Fluctuation theorem ( statistical mechanics )
Ford's theorem ( number theory )
Focal subgroup theorem ( abstract algebra )
Folk theorem ( game theory )
Foster's theorem ( statistics )
Four color theorem ( graph theory )
Four functions theorem ( combinatorics )
Four-vertex theorem ( differential geometry )
Fourier inversion theorem ( harmonic analysis )
Fourier theorem ( harmonic analysis )
Franel–Landau theorem ( number theory )
Fraňková–Helly selection theorem ( mathematical analysis )
Fredholm's theorem ( linear algebra )
Freidlin–Wentzell theorem ( stochastic processes )
Freiman's theorem ( number theory )
Freudenthal suspension theorem ( homotopy theory )
Freyd's adjoint functor theorem ( category theory )
Friedberg–Muchnik theorem ( mathematical logic )
Friendship theorem ( graph theory )
Frobenius determinant theorem ( group theory )
Frobenius reciprocity theorem ( group representations )
Frobenius theorem ( foliations )
Frobenius theorem ( abstract algebras )
Froda's theorem ( mathematical analysis )
Frucht's theorem ( graph theory )
Fubini's theorem ( integration )
Fubini's theorem on differentiation ( real analysis )
Fuchs's theorem ( differential equations )
Fuglede's theorem ( functional analysis )
Full employment theorem ( theoretical computer science )
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 of equivalence relations ( set theory )
Fundamental theorem of Galois theory ( Galois theory )
Fundamental theorem on homomorphisms ( abstract algebra )
Fundamental theorems of welfare economics ( economics )
Furry's theorem ( quantum field theory )

G

Galvin's theorem ( combinatorics )
Gamas's Theorem ( multilinear algebra )
Gap theorem ( computational complexity theory )
Gauss's lemma ( riemannian geometry )
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–Mazur theorem ( Banach algebra )
Gelfand–Naimark theorem ( functional analysis )
Gelfond–Schneider theorem ( transcendental number theory )
Gell-Mann and Low theorem ( quantum field theory )
Geometric mean theorem ( geometry )
Geroch's splitting theorem ( differential geometry )
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 )
Glivenko's theorem ( probability )
Glivenko–Cantelli theorem ( probability )
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 )
Goldberg–Sachs theorem ( physics )
Goldie's theorem ( ring theory )
Goldstine theorem ( functional analysis )
Goldstone's theorem ( physics )
Golod–Shafarevich theorem ( group theory )
Gomory's theorem ( mathematical logic )
Goodstein's theorem ( mathematical logic )
Gordon–Newell theorem ( queueing theory )
Gottesman–Knill theorem ( quantum computation )
Gradient theorem ( vector calculus )
Graph structure theorem ( graph theory )
Grauert–Riemenschneider vanishing theorem ( algebraic geometry )
Great orthogonality theorem ( group theory )
Green–Tao theorem ( number theory )
Green's theorem ( vector calculus )
Grinberg's theorem ( graph theory )
Gromov's compactness theorem ( Riemannian geometry )
Gromov's compactness theorem ( symplectic topology )
Gromov's theorem on groups of polynomial growth ( geometric 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 )
Grötzsch's theorem ( graph theory )
Grunsky's theorem ( complex analysis )
Grunwald–Wang theorem ( algebraic number theory )
Grushko theorem ( group theory )

H

H-cobordism theorem ( differential topology )
H-theorem ( thermodynamics )
Haag's theorem ( quantum field theory )
Haag–Łopuszański–Sohnius theorem ( physics )
Haboush's theorem ( algebraic groups , representation theory , invariant theory )
Hadamard three-circle theorem ( complex analysis )
Hadamard three-lines theorem ( complex analysis )
Hadwiger's theorem ( geometry , measure theory )
Hahn decomposition theorem ( measure theory )
Hahn embedding theorem ( ordered groups )
Hairy ball theorem ( algebraic topology )
Hahn–Banach theorem ( functional analysis )
Hahn–Kolmogorov theorem ( measure theory )
Hahn–Mazurkiewicz theorem ( continuum theory )
Hajnal–Szemerédi theorem ( graph theory )
Hales–Jewett theorem ( combinatorics )
Hall's marriage theorem ( combinatorics )
Halpern–Läuchli theorem ( Ramsey theory )
Ham sandwich theorem ( topology )
Hammersley–Clifford theorem ( probability )
Hardy's theorem ( complex analysis )
Hardy–Littlewood maximal theorem ( real analysis )
Hardy–Littlewood tauberian theorem ( mathematical analysis )
Hardy–Ramanujan theorem ( number theory )
Harish–Chandra theorem ( representation theory )
Harish–Chandra's regularity theorem ( representation theory )
Harnack's curve theorem ( real algebraic geometry )
Harnack's theorem ( complex analysis )
Hartman–Grobman theorem ( dynamical systems )
Hartogs–Rosenthal theorem ( complex analysis )
Hartogs's theorem ( complex analysis )
Hartogs's extension theorem ( several complex variables )
Hasse norm theorem ( number theory )
Hasse's theorem on elliptic curves ( number theory )
Hasse–Arf theorem ( local class field theory )
Hasse–Minkowski theorem ( number theory )
Hausdorff maximality theorem ( set theory )
Heckscher–Ohlin theorem ( economics )
Heine–Borel theorem ( real analysis )
Heine–Cantor theorem ( metric geometry )
Hellinger–Toeplitz theorem ( functional analysis )
Hellmann–Feynman theorem ( physics )
Helly–Bray theorem ( probability theory )
Helly's selection theorem ( mathematical analysis )
Helly's theorem ( convex sets )
Helmholtz theorem (classical mechanics) ( physics )
Helmholtz's theorems ( 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–Waring theorem ( number theory )
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 )
Hilton–Milnor theorem ( algebraic topology )
Hindman's theorem ( Ramsey theory )
Hinge theorem ( geometry )
Hironaka theorem ( algebraic geometry )
Hirzebruch signature theorem ( topology , algebraic geometry )
Hirzebruch–Riemann–Roch theorem ( complex manifolds )
Hjelmslev's theorem ( geometry )
Hobby–Rice theorem ( mathematical analysis )
Hodge index theorem ( algebraic surfaces )
Hohenberg–Kohn theorems ( density functional theory )
Hölder's theorem ( mathematical analysis )
Holditch's theorem ( plane geometry )
Holland's schema theorem ( genetic algorithm )
Holmström's theorem ( economics )
Homotopy excision theorem ( algebraic topology )
Hopf theorem ( differential topology )
Hopf–Rinow theorem ( differential geometry )
Hurewicz theorem ( algebraic topology )
Hurwitz's automorphisms theorem ( algebraic curves )
Hurwitz's theorem ( complex analysis )
Hurwitz's theorem ( normed division algebras )
Hurwitz's theorem ( number theory )

I

Identity theorem ( complex analysis )
Identity theorem for Riemann surfaces ( Riemann surfaces )
Immerman–Szelepcsényi theorem ( computational complexity theory )
Implicit function theorem ( vector calculus )
Impossibility of angle trisection ( geometry )
Increment theorem ( mathematical analysis )
Independence of the axiom of choice ( mathematical logic )
Independence of the continuum hypothesis ( mathematical logic )
Independence of the parallel postulate ( geometry )
Infinite monkey theorem ( probability )
Integral root theorem ( algebra, polynomials )
Initial value theorem ( integral transform )
Inscribed angle theorem ( geometry )
Integral representation theorem for classical Wiener space ( measure theory )
Intermediate value theorem ( calculus )
Intercept theorem ( Euclidean geometry )
Intersecting chords theorem ( Euclidean geometry )
Intersecting secants theorem ( Euclidean geometry )
Intersection theorem ( projective geometry )
Inverse eigenvalues theorem ( linear algebra )
Inverse function theorem ( vector calculus )
Ionescu-Tulcea theorem ( probability theory )
Isomorphism extension theorem ( abstract algebra )
Isomorphism theorem ( abstract algebra )
Isoperimetric gap ( geometric group theory , metric geometry )
Isoperimetric theorem ( curves , calculus of variations )
Iwasawa decomposition ( Lie theory )

K

Kachurovskii's theorem ( convex analysis )
Kanamori–McAloon theorem ( mathematical logic )
Kantorovich theorem ( functional analysis )
Kaplansky density theorem ( von Neumann algebra )
Kaplansky's theorem on quadratic forms ( number theory )
Karhunen–Loève theorem ( stochastic processes )
Karp–Lipton theorem ( computational complexity theory )
Katz–Lang finiteness theorem ( number theory )
Kawamata–Viehweg vanishing theorem ( algebraic geometry )
Kawasaki's theorem ( mathematics of paper folding )
Kelvin's circulation theorem ( physics )
Kempf–Ness theorem ( algebraic geometry )
Kepler conjecture ( discrete geometry )
Kharitonov's theorem ( control theory )
Khinchin's theorem ( probability )
Killing–Hopf theorem ( Riemannian geometry )
Kinoshita–Lee–Nauenberg theorem ( quantum field theory )
Kirby–Paris theorem ( proof theory )
Kirchberger's theorem ( discrete geometry )
Kirchhoff's theorem ( graph theory )
Kirszbraun theorem ( Lipschitz continuity )
Kleene fixed-point theorem ( order theory )
Kleene's recursion theorem ( recursion theory )
Knaster–Tarski theorem ( order theory )
Kneser's theorem ( combinatorics )
Kneser's theorem ( differential equations )
Kochen–Specker theorem ( physics )
Kodaira embedding theorem ( algebraic geometry )
Kodaira vanishing theorem ( complex manifold )
Koebe 1/4 theorem ( complex analysis )
Kolmogorov extension theorem ( stochastic processes )
Kolmogorov's three-series theorem ( mathematical series )
Kolmogorov–Arnold representation theorem ( real analysis , approximation theory )
Kolmogorov–Arnold–Moser theorem ( dynamical systems )
Kőnig's theorem ( bipartite graphs )
König's theorem ( physics )
König's theorem ( set theory, mathematical logic )
Kövari–Sós–Turán theorem ( graph theory )
Kraft–McMillan theorem ( coding theory )
Kramers' theorem ( physics )
Krein–Milman theorem ( mathematical analysis, discrete geometry )
Krener's theorem ( control theory )
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 )
Kruskal–Katona theorem ( combinatorics )
Krylov–Bogolyubov theorem ( dynamical systems )
Kuhn's theorem ( game theory )
Kuiper's theorem ( operator theory , topology )
Künneth theorem ( algebraic topology )
Kuratowski's closure-complement problem ( topology )
Kuratowski's theorem ( graph theory )
Kurosh subgroup theorem ( group theory )
Kutta–Joukowski theorem ( physics )
Kōmura's theorem ( measure theory )

L

L-balance theorem ( finite groups )
Ladner's theorem ( computational complexity theory )
Lafforgue's theorem ( algebraic number 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 )
Lamé’s theorem ( computational complexity theory )
Lami's theorem ( statics )
Landau prime ideal theorem ( number theory )
Landweber exact functor theorem ( algebraic topology )
Lasker–Noether theorem ( commutative algebra )
Lattice theorem ( abstract algebra )
Laurent expansion theorem ( complex analysis )
Lauricella's theorem ( functional analysis )
Lawvere's fixed-point theorem ( mathematical logic )
Lax–Milgram theorem ( partial differential equations )
Lax–Richtmyer theorem ( numerical analysis )
Lax–Wendroff 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 ( fixed points , algebraic topology )
Lefschetz–Hopf theorem ( topology )
Lefschetz hyperplane theorem ( algebraic topology )
Lefschetz theorem on (1,1)-classes ( algebraic geometry )
Lehmann–Scheffé theorem ( statistics )
Leray's theorem ( algebraic geometry )
Leray–Hirsch theorem ( algebraic topology )
Lerner symmetry theorem ( economics )
Lester's theorem ( Euclidean plane geometry )
Levi's theorem ( Lie groups )
Levitzky's theorem ( ring theory )
Lévy continuity theorem ( probability )
Lévy's modulus of continuity theorem ( probability )
Lexell's theorem ( spherical geometry )
Lickorish twist theorem ( geometric topology )
Lickorish–Wallace theorem ( 3-manifolds )
Lie's theorem ( Lie algebra )
Lie's third theorem ( Lie group )
Lie–Palais theorem ( differential geometry )
Lindemann–Weierstrass theorem ( transcendental number theory )
Lie–Kolchin theorem ( algebraic groups , representation theory )
Liénard's theorem ( dynamical systems )
Lindelöf's theorem ( complex analysis )
Lindström's theorem ( mathematical logic )
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 )
Liouville's theorem ( Hamiltonian mechanics )
Löb's theorem ( mathematical logic )
Local invariant cycle theorem ( algebraic geometry )
Lochs's theorem ( number theory )
Looman–Menchoff theorem ( complex analysis )
Łoś' theorem ( model theory )
Lovelock's theorem ( physics )
Löwenheim–Skolem theorem ( mathematical logic )
Lucas's theorem ( number theory )
Lukacs's proportion-sum independence theorem ( probability )
Lumer–Phillips theorem ( semigroup theory )
Luzin's theorem ( real analysis )
Lyapunov–Malkin theorem ( stability theory )
Lyapunov's central limit theorem ( probability theory )

M

M. Riesz extension theorem ( functional analysis )
MacMahon Master theorem ( enumerative combinatorics )
Maharam's theorem ( measure theory )
Mahler's compactness theorem ( geometry of numbers )
Mahler's theorem ( p-adic analysis )
Maier's theorem ( analytic number theory )
Malgrange preparation theorem ( singularity theory )
Malgrange–Ehrenpreis theorem ( differential equations )
Malgrange–Zerner theorem ( complex analysis )
Manin–Drinfeld theorem ( number theory )
Mann's theorem ( number theory )
Marcinkiewicz theorem ( functional analysis )
Marden's theorem ( polynomials )
Mazur's control theorem ( number theory )
Mergelyan's theorem ( complex analysis )
Marginal value theorem ( biology , optimization )
Markus−Yamabe theorem ( dynamical systems )
Martingale representation theorem ( probability theory )
Mason–Stothers theorem ( polynomials )
Master theorem (analysis of algorithms) ( recurrence relations , asymptotic analysis )
Maschke's theorem ( group representations )
Matiyasevich's theorem ( mathematical logic )
Max flow min cut theorem ( graph theory )
Max/min_CSP/Ones_classification_theorems ( computational complexity 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–Ulam theorem ( normed spaces )
Mazur's torsion theorem ( algebraic geometry )
Mean value theorem ( calculus )
Measurable Riemann mapping theorem ( conformal mapping )
Mellin inversion theorem ( complex analysis )
Menelaus's theorem ( geometry )
Menger's theorem ( graph theory )
Mercer's theorem ( functional analysis )
Mermin–Wagner theorem ( physics )
Mertens's 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 )
Milman–Pettis theorem ( Banach space )
Min-max theorem ( functional analysis )
Minimax theorem ( game theory )
Minkowski's theorem ( geometry of numbers )
Minkowski's second theorem ( geometry of numbers )
Minkowski–Hlawka theorem ( geometry of numbers )
Minlos's theorem ( functional analysis )
Miquel's theorem ( geometry )
Mirsky–Newman theorem ( group theory )
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 class theorem ( measure theory )
Monotone convergence theorem ( mathematical analysis )
Monsky's theorem ( discrete geometry )
Montel's theorem ( complex analysis )
Montgomery-Zippin-Gleason theorem ( Transformation groups )
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 )
Moufang's theorem ( loop theory )
Mountain pass theorem ( calculus of variations )
Moving equilibrium theorem ( economics )
Multinomial theorem ( algebra , combinatorics )
Multiplication theorem ( special functions )
Multiplicity-one theorem ( group representations )
Mumford vanishing theorem ( algebraic geometry )
Mutual fund separation theorem ( financial mathematics )
Müntz–Szász theorem ( functional analysis )
Mycielski's theorem ( graph theory )
Myers theorem ( differential geometry )
Myers-Steenrod theorem ( riemannian geometry )
Myhill–Nerode theorem ( formal languages )

N

Nachbin's theorem( complex analysis )
Nagata's compactification theorem ( algebraic geometry )
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 )
Netto's theorem ( topology )
Newlander–Niremberg theorem ( differential geometry )
Newton's theorem about ovals ( curves )
Newton's theorem (quadrilateral) ( geometry )
Nicomachus's theorem ( number theory )
Nielsen fixed-point theorem ( fixed points )
Nielsen–Ninomiya theorem ( quantum field theory )
Nielsen realization problem ( geometric topology )
Nielsen-Thurston classification ( geometric topology )
Nielsen–Schreier theorem ( free groups )
Nilpotence theorem ( algebraic topology )
Niven's theorem ( number theory )
No-broadcasting theorem ( quantum information theory )
No-cloning theorem ( quantum computation )
No-communication theorem ( quantum information theory )
No-deleting theorem ( quantum information theory )
No free lunch in search and optimization ( computational complexity theory )
No free lunch theorem ( philosophy of mathematics )
No-hair theorem ( physics )
No-trade theorem ( economics )
No wandering domain theorem ( ergodic theory )
Noether's theorem ( Lie groups , calculus of variations , differential invariants , physics )
Noether's second theorem ( calculus of variations , physics )
Noether's theorem on rationality for surfaces ( algebraic surfaces )
Non-squeezing theorem ( symplectic geometry )
Norton's theorem ( electrical networks )
Novikov's compact leaf theorem ( foliations )
Nyquist–Shannon sampling theorem ( information theory )

P

PCP theorem ( computational complexity theory )
Paley's theorem ( algebra )
Paley–Wiener theorem ( Fourier transforms )
Pandya theorem ( nuclear physics )
Pappus's area theorem ( geometry )
Pappus's centroid theorem ( geometry )
Pappus's hexagon theorem ( geometry )
Paris–Harrington theorem ( mathematical logic )
Parovicenko's theorem ( topology )
Parallel axis theorem ( physics )
Parseval's theorem ( Fourier analysis )
Parthasarathy's theorem ( game theory )
Pascal's theorem ( conics )
Pasch's theorem ( order theory )
Peano existence theorem ( ordinary differential equations )
Peeling theorem ( physics )
Peetre theorem ( functional analysis )
Peixoto's theorem ( dynamical systems )
Penrose–Hawking singularity theorems ( physics )
Pentagonal number theorem ( number theory )
Perelman's Geometrization theorem ( 3-manifolds )
Perfect graph theorem ( graph theory )
Perlis theorem ( graph theory )
Perpendicular axis theorem ( physics )
Perron–Frobenius theorem ( matrix theory )
Peter–Weyl theorem ( representation theory )
Phragmén–Lindelöf theorem ( complex analysis )
Picard theorem ( complex analysis )
Picard–Lindelöf theorem ( ordinary differential equations )
Pick's theorem ( geometry )
Pickands–Balkema–de Haan theorem ( extreme value theory )
Pitman–Koopman–Darmois theorem ( statistics )
Pitot theorem ( plane geometry )
Pizza theorem ( geometry )
Pivot theorem ( circles )
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–Hopf theorem ( differential topology )
Poincaré duality theorem ( algebraic topology of manifolds )
Poincaré conjecture ( topology )
Poincaré recurrence theorem ( dynamical systems )
Poisson limit theorem ( probability )
Pólya enumeration theorem ( combinatorics )
Polynomial remainder theorem ( polynomials )
Pomeranchuk's theorem ( physics )
Pompeiu's theorem ( Euclidean geometry )
Pontryagin duality theorem ( representation theory )
Poncelet's closure theorem ( conics )
Poncelet–Steiner theorem ( geometry )
Positive energy theorem ( physics )
Post's theorem ( mathematical logic )
Poynting's theorem ( physics )
Preimage theorem ( differential topology )
Price's theorem ( general relativity )
Prime number theorem ( number theory )
Primitive element theorem ( field theory )
Principal axis theorem ( linear algebra )
Principal ideal theorem ( algebraic number theory )
Prokhorov's theorem ( measure theory )
Proper base change theorem ( algebraic geometry )
Proth's theorem ( number theory )
Pseudorandom generator theorem ( computational complexity theory )
Ptolemy's theorem ( geometry )
Puiseux's theorem ( algebraic geometry )
Pythagorean theorem ( geometry )

Q

R

Rademacher's theorem ( mathematical analysis )
Radó's theorem ( harmonic analysis )
Radon's theorem ( convex sets )
Radon–Nikodym theorem ( measure theory )
Raikov's theorem ( probability )
Ramanujam vanishing theorem ( algebraic geometry )
Ramanujan–Skolem's theorem ( Diophantine equations )
Ramsey's theorem ( graph theory, combinatorics )
Rank–nullity theorem ( linear algebra )
Rao–Blackwell theorem ( statistics )
Rashevsky–Chow theorem ( control theory )
Rational root theorem ( algebra, polynomials )
Rationality theorem ( politics )
Ratner's theorems ( ergodic theory )
Rauch comparison theorem ( Riemannian geometry )
Rédei's theorem ( group theory )
Reeb sphere theorem ( foliations )
Reeh–Schlieder theorem ( local quantum field theory )
Reflection theorem ( algebraic number theory )
Regev's theorem ( ring theory )
Reidemeister–Singer Theorem ( geometric topology )
Reider's theorem ( algebraic surfaces )
Remmert–Stein theorem ( complex analysis )
Residue theorem ( complex analysis )
Reuschle's theorem ( Euclidean geometry )
Reversed compound agent theorem ( probability )
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–Roch theorem for surfaces ( algebraic surfaces )
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 )
Rising sun lemma ( real analysis )
Robbins 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 )
Rouché's theorem ( complex analysis )
Rouché–Capelli theorem ( Linear algebra )
Routh's theorem ( triangle geometry )
Routh–Hurwitz theorem ( polynomials )
Runge's theorem ( complex analysis )
Rybczynski theorem ( economics )
Ryll-Nardzewski fixed-point theorem ( functional analysis )

S

S–cobordism theorem ( differential topology )
Saccheri–Legendre theorem ( absolute geometry )
Sahlqvist correspondence theorem ( modal logic )
Saint-Venant's theorem ( physics )
Sard's theorem ( differential geometry )
Sarkovskii's theorem ( dynamical systems )
Savitch's theorem ( computational complexity theory )
Sazonov's theorem ( functional analysis )
Schaefer's dichotomy theorem ( computational complexity theory )
Schauder fixed-point theorem ( functional analysis )
Schilder's theorem ( stochastic processes )
Schnyder's theorem ( graph theory )
Schreier refinement theorem ( group theory )
Schröder–Bernstein theorems for operator algebras ( operator algebras )
Schröder–Bernstein theorem for measurable spaces ( measure theory )
Schur's lemma ( representation theory )
Schur's theorem ( Ramsey theory )
Schur–Zassenhaus theorem ( group theory )
Schwartz kernel theorem ( generalized functions )
Schwartz–Zippel theorem ( polynomials )
Schwarz–Ahlfors–Pick theorem ( differential geometry )
Schwenk's theorem ( graph theory )
Scott core theorem ( 3-manifolds )
Seifert–van Kampen theorem ( algebraic topology )
Sela's theorem ( hyperbolic groups )
Sensitivity theorem ( computational complexity theory )
Separating axis theorem ( convex geometry )
Shannon–Hartley theorem ( information theory )
Shannon's expansion theorem ( Boolean algebra )
Shannon's source coding theorem ( information theory )
Shell theorem ( physics )
Shirshov–Cohn theorem ( Jordan algebras )
Shirshov–Witt theorem ( Lie algebras )
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 )
Sinkhorn's theorem ( matrix theory )
Sion's minimax theorem ( game theory )
Sipser–Lautemann theorem ( probabilistic complexity theory ) ( structural complexity theory )
Siu's semicontinuity theorem ( complex analysis )
Six circles theorem ( circles )
Six exponentials theorem ( transcendental number theory )
Sklar's theorem ( statistics )
Skoda–El Mir theorem ( complex geometry )
Skolem–Mahler–Lech theorem ( number theory )
Skolem–Noether theorem ( simple algebras )
Skorokhod's embedding theorem ( statistics )
Skorokhod's representation theorem ( statistics )
Śleszyński–Pringsheim theorem ( continued fraction )
Slutsky's theorem ( probability theory )
Smn theorem ( recursion theory, computer science )
Snaith's theorem ( algebraic topology )
Sobolev embedding theorem ( mathematical analysis )
Sokhatsky–Weierstrass theorem ( complex analysis )
Solèr's theorem ( mathematical logic )
Solutions of a general cubic equation ( algebra )
Solutions of a general quartic equation ( algebra )
Solutions to Pell's equation ( number theory )
Sonnenschein–Mantel–Debreu Theorem ( economics )
Sophie Germain's theorem ( number theory )
Soul theorem ( Riemannian geometry )
Soundness theorem ( mathematical logic )
Space hierarchy theorem ( computational complexity theory )
Specht's theorem ( matrix theory )
Spectral theorem ( linear algebra , functional analysis )
Speedup theorem ( computational complexity theory )
Sperner's theorem ( combinatorics )
Sphere packing theorems in dimensions 8 and 24 ( geometry , modular forms )
Sphere theorem ( Riemannian geometry )
Spin–statistics theorem ( physics )
Sprague–Grundy theorem ( combinatorial game theory )
Squeeze theorem ( mathematical analysis )
Stahl's theorem ( matrix analysis )
Stallings theorem about ends of groups ( group theory )
Stallings–Zeeman theorem ( algebraic topology )
Stanley's reciprocity theorem ( combinatorics )
Star of David theorem ( combinatorics )
Stark–Heegner theorem ( number theory )
Stein–Strömberg theorem ( measure theory )
Steiner–Lehmus theorem ( triangle geometry )
Steinhaus theorem ( measure theory )
Steinitz theorem ( graph theory )
Stewart's theorem ( plane geometry )
Stinespring factorization theorem ( operator theory )
Stirling's theorem ( mathematical analysis )
Stokes's 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 )
Strassmann's theorem ( field theory )
Strong perfect graph theorem ( graph theory )
Structure theorem for finitely generated modules over a principal ideal domain ( abstract algebra )
Structure theorem for Gaussian measures ( measure theory )
Structured program theorem ( computer science )
Sturm's theorem ( theory of equations )
Sturm–Picone comparison theorem ( differential equations )
Subspace theorem ( Diophantine approximation )
Sullivan conjecture ( homotopy theory )
Superrigidity theorem ( algebraic groups )
Supersymmetry nonrenormalization theorems ( physics )
Supporting hyperplane theorem ( convex geometry )
Švarc-Milnor lemma ( geometric group theory )
Swan's theorem ( module theory )
Sylow theorems ( group theory )
Sylvester's determinant theorem ( determinants )
Sylvester's theorem ( number theory )
Sylvester pentahedral theorem ( invariant theory )
Sylvester's law of inertia ( quadratic forms )
Sylvester–Gallai theorem ( plane geometry )
Symmetric hypergraph theorem ( graph theory )
Symphonic theorem ( triangle geometry )
Synge's theorem ( Riemannian geometry )
Sz.-Nagy's dilation theorem ( operator theory )
Szegő limit theorems ( mathematical analysis )
Szemerédi's theorem ( combinatorics )
Szemerédi–Trotter theorem ( combinatorics )
Szpilrajn extension theorem ( axiom of choice )

T

Takagi existence theorem ( number theory )
Takens's theorem ( dynamical systems )
Tameness theorem ( 3-manifolds )
Tangent-secant theorem ( geometry )
Tarski's indefinability theorem ( mathematical logic )
Taylor's theorem ( calculus )
Taylor–Proudman theorem ( physics )
Tennenbaum's theorem ( model theory )
Thabit ibn Qurra's theorem ( amicable numbers )
Thales's theorem ( geometry )
The duality theorem ( topology )
Thébault's theorem ( geometry )
Theorem of de Moivre–Laplace ( probability theory )
Theorem of the cube ( algebraic varieties )
Theorem of the gnomon ( geometry )
Theorem of three moments ( physics )
Theorem on friends and strangers ( Ramsey theory )
Thévenin's theorem ( electrical circuits )
Thom transversality theorem ( differential topology )
Thompson transitivity theorem ( finite groups )
Thompson uniqueness theorem ( finite groups )
Thomsen's theorem ( geometry )
Thue's theorem ( Diophantine equation )
Thue–Siegel–Roth theorem ( Diophantine approximation )
Thurston's geometrization theorem ( 3-manifolds )
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 )
Toda's theorem ( computational complexity theory )
Tomita's theorem ( operator algebras )
Tonelli's theorem ( functional analysis )
Topkis's theorem ( economics )
Toponogov's theorem ( Riemannian geometry )
Torelli theorem ( algebraic geometry )
Trichotomy theorem ( finite groups )
Trombi–Varadarajan theorem ( Lie group )
Trudinger's theorem ( functional analysis )
Tsen's theorem ( algebraic geometry )
Tunnell's theorem ( number theory )
Tutte theorem ( graph theory )
Turán's theorem ( graph theory )
Turán–Kubilius theorem ( number theory )
Tverberg's theorem ( discrete geometry )
Tychonoff's theorem ( general topology )

U

Ugly duckling theorem ( computer science )
Uncountability of the continuum ( set theory )
Uniformization theorem ( complex analysis , differential geometry )
Universal approximation theorem ( artificial neural networks )
Universal coefficient theorem ( algebraic topology )
Unmixedness theorem ( algebraic geometry )

V

Vafa–Witten theorem ( physics )
Valiant–Vazirani theorem ( computational complexity theory )
Van Aubel's theorem ( quadrilaterals )
Van der Waerden's theorem ( combinatorics )
Van Schooten's theorem ( Euclidean geometry )
Van Vleck's theorem ( mathematical analysis )
Vantieghems theorem ( number theory )
Varignon's theorem ( Euclidean geometry )
Vieta's formulas ( quadratics )
Vietoris–Begle mapping theorem ( algebraic topology )
Vinogradov's theorem ( number theory )
Virial theorem ( classical mechanics )
Vitali convergence theorem ( measure theory )
Vitali covering 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 )
Von Staudt–Clausen theorem ( number theory )

W

Wagner's theorem ( graph theory )
Waldhausen's theorem ( geometric topology )
Wallace–Bolyai–Gerwien theorem ( discrete geometry )
Walter theorem ( finite groups )
Weber's theorem ( algebraic curves )
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 )
Whitney immersion theorem ( differential topology )
Whitney–Graustein Theorem ( algebraic topology )
Wick's theorem ( physics )
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 )
Witt's theorem ( quadratic forms )
Wold's theorem ( statistics )
Wolstenholme's theorem ( number theory )

Z

Z* theorem ( finite groups )
ZJ theorem ( finite groups )
Zahorski theorem ( real analysis )
Zariski's connectedness theorem ( algebraic geometry )
Zariski's main theorem ( algebraic geometry )
Zeckendorf's theorem ( number theory )
Zeilberger–Bressoud theorem ( combinatorics )
Zorn's lemma ( set theory )
Zsigmondy's theorem ( number theory )

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