List of theorems

This is a list of notable theorems. Lists of theorems and similar statements include:
 * List of algebras
 * List of algorithms
 * List of axioms
 * List of conjectures
 * List of data structures
 * List of derivatives and integrals in alternative calculi
 * List of equations
 * List of fundamental theorems
 * List of hypotheses
 * List of inequalities
 * Lists of integrals
 * List of laws
 * List of lemmas
 * List of limits
 * List of logarithmic identities
 * List of mathematical functions
 * List of mathematical identities
 * List of mathematical proofs
 * List of misnamed theorems
 * List of scientific laws
 * List of theories

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

0–9

 * 2-factor theorem (graph theory)
 * 15 and 290 theorems (number theory)
 * 2π theorem (Riemannian geometry)

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)

• 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's 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 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)

• Bishop–Cannings theorem (economics)

• 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–Schroeder 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–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)

• Central limit theorem (probability)

• Cesàro's theorem (real analysis)

• Ceva's theorem (geometry)

• Chasles's theorems

• 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 finite simple groups (group theory)

• Classification of Platonic solids (geometry)

• 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)

• 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)

• Denjoy theorem (dynamical systems)

• Denjoy–Carleman theorem (functional analysis)

• Desargues's theorem (projective geometry)

• Descartes's theorem (plane geometry)

• Descartes's theorem on total angular defect (polyhedra)

• 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)

• 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–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)

• 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

• 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 on homomorphisms (abstract algebra)

• Fundamental theorems of welfare economics (economics)

• Furry's theorem (quantum field theory)

G
• Galvin's theorem (combinatorics)

• Gauss theorem (vector calculus)

• Gamas's Theorem (multilinear algebra)

• 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)

• 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)

• 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)

• 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)

• 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 theorem (curves, calculus of variations)

J
• Jackson's theorem (queueing theory)

• Jacobi's four-square theorem (number theory)

• Jacobson density theorem (ring theory)

• Jacobson–Bourbaki theorem (algebra)

• Jacobson–Morozov theorem (Lie algebra)

• Japanese theorem for concyclic polygons (Euclidean geometry)

• Japanese theorem for concyclic quadrilaterals (Euclidean geometry)

• John ellipsoid (geometry)

• Jordan curve theorem (topology)

• Jordan–Hölder theorem (group theory)

• Jordan–Schönflies theorem (geometric topology)

• Jordan–Schur theorem (group theory)

• Jordan's theorem (multiply transitive groups) (group theory)

• Joubert's theorem (algebra)

• Jung's theorem (geometry)

• Jurkat–Richert theorem (analytic number 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)

• 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)

• König'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)

• 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)

• Lasker–Noether theorem (commutative algebra)

• Lattice theorem (abstract algebra)

• Laurent expansion theorem (complex analysis)

• Lauricella's theorem (functional analysis)

• 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)

• 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)

• 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 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)

• 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)

• 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)

• 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–Schreier theorem (free groups)

• 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 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)

O
• Odd number theorem (physics)

• Open mapping theorem (complex analysis)

• Open mapping theorem (functional analysis)

• Optical equivalence theorem (quantum optics)

• Optical theorem (physics)

• Optional stopping theorem (probability theory)

• Orbit theorem (Nagano–Sussmann) (control theory)

• Orbit-stabilizer theorem (group theory)

• Ore's theorem (graph theory)

• Orlicz–Pettis theorem (functional analysis)

• Ornstein theorem (ergodic theory)

• Oseledec theorem (ergodic theory)

• Osterwalder–Schrader theorem (physics)

• Ostrowski's theorem (number theory)

• Ostrowski–Hadamard gap theorem (complex analysis)

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)

• 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 recurrence theorem (dynamical systems)

• Poisson limit theorem (probability)

• Pólya enumeration theorem (combinatorics)

• Pomeranchuk's theorem (physics)

• Pompeiu's theorem (Euclidean geometry)

• 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
• Quillen–Suslin theorem (abstract algebra)

• Quadratic reciprocity theorem

• Quantum threshold theorem (computer science) (theoretical computer science)

• Quotient of subspace theorem (functional analysis)

R
• Rademacher's theorem (mathematical analysis)

• Rado'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)

• 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)

• Schroeder–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)

• 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)

• 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 (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)

• 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)

• Supersymmetry nonrenormalization theorems (physics)

• 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 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)

• 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)

• 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)

• Zsigmondy's theorem (number theory)