List of theorems

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

• List of algebras
• List of algorithms
• List of axioms
• List of conjectures
• List of data structures
• List of derivatives and integrals in alternative calculi
• List of equations
• List of fundamental theorems
• List of hypotheses
• List of inequalities
• Lists of integrals
• List of laws
• List of lemmas
• List of limits
• List of logarithmic identities
• List of mathematical functions
• List of mathematical identities
• List of mathematical proofs
• List of misnamed theorems
• List of scientific laws
• List of theories

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

Logics and foundations

• Ax–Grothendieck theorem (model theory)
• Barwise compactness theorem (mathematical logic)
• Borel determinacy theorem (set theory)
• Büchi-Elgot-Trakhtenbrot theorem (mathematical logic)
• Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers)
• Cantor's theorem (set theory, Cantor's diagonal argument)
• Church–Rosser theorem (lambda calculus)
• Compactness theorem (mathematical logic)
• Conservativity theorem (mathematical logic)
• Craig's theorem (mathematical logic)
• Craig's interpolation theorem (mathematical logic)
• Cut-elimination theorem (proof theory)
• Deduction theorem (logic)
• Diaconescu's theorem (mathematical logic)
• Easton's theorem (set theory)
• Erdős–Dushnik–Miller theorem (set theory)
• Erdős–Rado theorem (set theory)
• Feferman–Vaught theorem (model theory)
• Friedberg–Muchnik theorem (mathematical logic)
• Fundamental theorem of equivalence relations (set theory)
• Glivenko's theorem (mathematical logic)
• Gödel's completeness theorem (mathematical logic)
• Gödel's incompleteness theorem (mathematical logic)
• Goodstein's theorem (mathematical logic)
• Herbrand's theorem (logic)
• Independence of the axiom of choice (mathematical logic)
• Independence of the continuum hypothesis (mathematical logic)
• Kanamori–McAloon theorem (mathematical logic)
• Kirby–Paris theorem (proof theory)
• Kleene's recursion theorem (recursion theory)
• König's theorem (set theory, mathematical logic)
• Lindström's theorem (mathematical logic)
• Löb's theorem (mathematical logic)
• Łoś' theorem (model theory)
• Löwenheim–Skolem theorem (mathematical logic)
• Matiyasevich's theorem (mathematical logic)
• Morley's categoricity theorem (model theory)
• Paris–Harrington theorem (mathematical logic)
• Post's theorem (mathematical logic)
• Richardson's theorem (mathematical logic)
• Robinson's joint consistency theorem (mathematical logic)
• Sahlqvist correspondence theorem (modal logic)
• Soundness theorem (mathematical logic)
• Tarski's indefinability theorem (mathematical logic)
• Tennenbaum's theorem (model theory)
• Uncountability of the continuum (set theory)
• Well-ordering theorem (mathematical logic)
• Wilkie's theorem (model theory)
• Zorn's lemma (set theory)

Combinatorics

• 2-factor theorem (graph theory)
• Abel's binomial theorem (combinatorics)
• Alspach's theorem (graph theory)
• Aztec diamond theorem (combinatorics)
• BEST theorem (graph theory)
• Baranyai's theorem (combinatorics)
• Berge's theorem (graph theory)
• Binomial theorem (algebra, combinatorics)
• Bondy's theorem (graph theory, combinatorics)
• Bondy–Chvátal theorem (graph theory)
• Brooks's theorem (graph theory)
• Bruck–Chowla–Ryser theorem (combinatorics)
• Cameron–Erdős theorem (discrete mathematics)
• Corners theorem (arithmetic combinatorics)
• Courcelle's theorem (graph theory)
• De Bruijn–Erdős theorem (graph theory)
• Dirac's theorems (graph theory)
• Erdős–Gallai theorem (graph theory)
• Erdős–Ginzburg–Ziv theorem (number theory)
• Erdős–Ko–Rado theorem (combinatorics)
• Erdős–Pósa theorem (graph theory)
• Erdős–Stone theorem (graph theory)
• Euler's partition theorem (number theory)
• Fermat polygonal number theorem (number theory)
• Five color theorem (graph theory)
• Four color theorem (graph theory)
• Freiman's theorem (number theory)
• Friendship theorem (graph theory)
• Galvin's theorem (combinatorics)
• Gomory's theorem (combinatorics)
• Graph structure theorem (graph theory)
• Grinberg's theorem (graph theory)
• Grötzsch's theorem (graph theory)
• Hajnal–Szemerédi theorem (graph theory)
• Hales–Jewett theorem (combinatorics)
• Hall's marriage theorem (combinatorics)
• Halpern–Läuchli theorem (Ramsey theory)
• Hindman's theorem (Ramsey theory)
• Kirchhoff's theorem (graph theory)
• Kneser's theorem (combinatorics)
• Kőnig's theorem (bipartite graphs)
• Kövari–Sós–Turán theorem (graph theory)
• Kruskal–Katona theorem (combinatorics)
• Kuratowski's theorem (graph theory)
• Lambek–Moser theorem (combinatorics)
• MacMahon Master theorem (enumerative combinatorics)
• Menger's theorem (graph theory)
• Milliken–Taylor theorem (Ramsey theory)
• Milliken's tree theorem (Ramsey theory)
• Multinomial theorem (algebra, combinatorics)
• Mycielski's theorem (graph theory)
• Nicomachus's theorem (number theory)
• Ore's theorem (graph theory)
• Paley's theorem (algebra)
• Perfect graph theorem (graph theory)
• Perlis theorem (graph theory)
• Planar separator theorem (graph theory)
• Pólya enumeration theorem (combinatorics)
• Ramsey's theorem (graph theory, combinatorics)
• Ringel–Youngs theorem (graph theory)
• Robbins' theorem (graph theory)
• Robertson–Seymour theorem (graph theory)
• Schnyder's theorem (graph theory)
• Schur's theorem (Ramsey theory)
• Schwenk's theorem (graph theory)
• Sensitivity theorem (computational complexity theory)
• Sperner's theorem (combinatorics)
• Stanley's reciprocity theorem (combinatorics)
• Star of David theorem (combinatorics)
• Stirling's theorem (mathematical analysis)
• Strong perfect graph theorem (graph theory)
• Symmetric hypergraph theorem (graph theory)
• Szemerédi's theorem (combinatorics)
• Theorem on friends and strangers (Ramsey theory)
• Tutte theorem (graph theory)
• Turán's theorem (graph theory)
• Van der Waerden's theorem (combinatorics)
• Wagner's theorem (graph theory)
• Zeilberger–Bressoud theorem (combinatorics)

Order, lattices, ordered algebraic structures

• Birkhoff's representation theorem (lattice theory)
• Boolean prime ideal theorem (mathematical logic)
• Bourbaki–Witt theorem (order theory)
• Cantor's isomorphism theorem (order theory)
• Dilworth's theorem (combinatorics, order theory)
• Four functions theorem (combinatorics)
• Hahn embedding theorem (ordered groups)
• Hausdorff maximality theorem (set theory)
• Kleene fixed-point theorem (order theory)
• Knaster–Tarski theorem (order theory)
• Kruskal's tree theorem (order theory)
• Shannon's expansion theorem (Boolean algebra)
• Stone's representation theorem for Boolean algebras (mathematical logic)
• Szpilrajn extension theorem (axiom of choice)

General algebraic systems

• Fundamental theorem on homomorphisms (abstract algebra)
• Isomorphism theorem (abstract algebra)
• Lattice theorem (abstract algebra)

Number theory

• 15 and 290 theorems (number theory)
• Albert–Brauer–Hasse–Noether theorem (algebras)
• Ankeny–Artin–Chowla theorem (number theory)
• Apéry's theorem (number theory)
• Artin–Verdier duality theorem (number theory)
• ATS theorem (number theory)
• Auxiliary polynomial theorem (Diophantine approximation)
• Ax–Kochen theorem (number theory)
• Baker's theorem (number theory)
• Barban–Davenport–Halberstam theorem (analytic number theory)
• Basel problem (mathematical analysis)
• Beatty's theorem (Diophantine approximation)
• Behrend's theorem (number theory)
• Bertrand's postulate (number theory)
• Birch's theorem (algebraic number theory)
• Bombieri's theorem (number theory)
• Bombieri–Friedlander–Iwaniec theorem (number theory)
• Brauer–Siegel theorem (number theory)
• Brun's theorem (number theory)
• Brun–Titchmarsh theorem (number theory)
• Carmichael's theorem (Fibonacci numbers)
• Chebotarev's density theorem (number theory)
• Chen's theorem (number theory)
• Chowla–Mordell theorem (number theory)
• Cohn's irreducibility criterion (polynomials)
• Critical line theorem (number theory)
• Davenport–Schmidt theorem (number theory, Diophantine approximations)
• Dirichlet's approximation theorem (Diophantine approximations)
• Dirichlet's theorem on arithmetic progressions (number theory)
• Dirichlet's unit theorem (algebraic number theory)
• Equidistribution theorem (ergodic theory)
• Erdős–Kac theorem (number theory)
• Euclid's theorem (number theory)
• Euclid–Euler theorem (number theory)
• Euler's theorem (number theory)
• Fermat's Last Theorem (number theory)
• Fermat's little theorem (number theory)
• Fermat's theorem on sums of two squares (number theory)
• Ferrero–Washington theorem (algebraic number theory)
• Ford's theorem (number theory)
• Franel–Landau theorem (number theory)
• Gelfond–Schneider theorem (transcendental number theory)
• Glaisher's theorem (number theory)
• Green–Tao theorem (number theory)
• Gross–Zagier theorem (number theory)
• Grunwald–Wang theorem (algebraic number theory)
• Hardy–Ramanujan theorem (number theory)
• Hasse norm theorem (number theory)
• Hasse–Minkowski theorem (number theory)
• Herbrand–Ribet theorem (cyclotomic fields)
• Hilbert–Speiser theorem (cyclotomic fields)
• Hilbert–Waring theorem (number theory)
• Hilbert's irreducibility theorem (number theory)
• Hurwitz's theorem (number theory)
• Jacobi's four-square theorem (number theory)
• Jurkat–Richert theorem (analytic number theory)
• Kaplansky's theorem on quadratic forms (number theory)
• Khinchin's theorem (probability)
• Kronecker's theorem (Diophantine approximation)
• Kronecker–Weber theorem (number theory)
• Lafforgue's theorem (algebraic number theory)
• Lagrange's four-square theorem (number theory)
• Landau prime ideal theorem (number theory)
• Lindemann–Weierstrass theorem (transcendental number theory)
• Linnik's theorem (number theory)
• Lochs's theorem (number theory)
• Lucas's theorem (number theory)
• Mahler's compactness theorem (geometry of numbers)
• Mahler's theorem (p-adic analysis)
• Maier's theorem (analytic number theory)
• Mann's theorem (number theory)
• Mazur's control theorem (number theory)
• Mertens's theorems (number theory)
• Midy's theorem (number theory)
• Mihăilescu's theorem (number theory)
• Mirsky–Newman theorem (group theory)
• Modularity theorem (number theory)
• Mordell–Weil theorem (number theory)
• Multiplicity-one theorem (group representations)
• Nagell–Lutz theorem (elliptic curves)
• Niven's theorem (number theory)
• Ostrowski's theorem (number theory)
• Pentagonal number theorem (number theory)
• Prime number theorem (number theory)
• Principal ideal theorem (algebraic number theory)
• Proth's theorem (number theory)
• Quadratic reciprocity theorem
• Ramanujan–Skolem's theorem (Diophantine equations)
• Reflection theorem (algebraic number theory)
• Ribet's theorem (elliptic curves)
• Robin's theorem (number theory)
• Rosser's theorem (number theory)
• Siegel–Walfisz theorem (analytic number theory)
• Six exponentials theorem (transcendental number theory)
• Skolem–Mahler–Lech theorem (number theory)
• Solutions to Pell's equation (number theory)
• Sophie Germain's theorem (number theory)
• Sphere packing theorems in dimensions 8 and 24 (geometry, modular forms)
• Stark–Heegner theorem (number theory)
• Subspace theorem (Diophantine approximation)
• Sylvester's theorem (number theory)
• Takagi existence theorem (number theory)
• Thabit ibn Qurra's theorem (amicable numbers)
• Thue's theorem (Diophantine equation)
• Thue–Siegel–Roth theorem (Diophantine approximation)
• Tijdeman's theorem (Diophantine equations)
• Tunnell's theorem (number theory)
• Turán–Kubilius theorem (number theory)
• Vantieghems theorem (number theory)
• Vinogradov's theorem (number theory)
• Von Staudt–Clausen theorem (number theory)
• Wilson's theorem (number theory)
• Wolstenholme's theorem (number theory)
• Zeckendorf's theorem (number theory)
• Zsigmondy's theorem (number theory)

Field theory and polynomials

• Abel–Ruffini theorem (theory of equations, Galois theory)
• Artin–Schreier theorem (real closed fields)
• Chevalley–Warning theorem (field theory)
• Diller–Dress theorem (field theory)
• Fundamental theorem of Galois theory (Galois theory)
• Hasse–Arf theorem (local class field theory)
• Hilbert's theorem 90 (number theory)
• Isomorphism extension theorem (abstract algebra)
• Joubert's theorem (algebra)
• Lagrange's theorem (number theory)
• Mason–Stothers theorem (polynomials)
• Polynomial remainder theorem (polynomials)
• Primitive element theorem (field theory)
• Rational root theorem (algebra, polynomials)
• Solutions of a general cubic equation (algebra)
• Solutions of a general quartic equation (algebra)
• Strassmann's theorem (field theory)
• Sturm's theorem (theory of equations)
• Vieta's formulas (quadratics)

Commutative algebra

• Artin approximation theorem (commutative algebra)
• Bézout's identity (number theory)
• Chinese remainder theorem (number theory)
• Cohen structure theorem (commutative algebra)
• Factor theorem (polynomials)
• Fundamental theorem of arithmetic (number theory)
• Going-up and going-down theorems (commutative algebra)
• Hilbert's basis theorem (commutative algebra,invariant theory)
• Hilbert's syzygy theorem (commutative algebra)
• Integral root theorem (algebra, polynomials)
• Krull's principal ideal theorem (commutative algebra)
• Lasker–Noether theorem (commutative algebra)
• Linear congruence theorem (number theory, modular arithmetic)
• Quillen–Suslin theorem (abstract algebra)
• Rédei's theorem (group theory)
• Schwartz–Zippel theorem (polynomials)
• Structure theorem for finitely generated modules over a principal ideal domain (abstract algebra)
• Unmixedness theorem (algebraic geometry)

Algebraic geometry

• AF+BG theorem (algebraic geometry)
• Abel–Jacobi theorem (algebraic geometry)
• Abhyankar–Moh theorem (algebraic geometry)
• Addition theorem (algebraic geometry)
• Andreotti–Frankel theorem (algebraic geometry)
• Arithmetic Riemann–Roch theorem (algebraic geometry)
• BBD decomposition theorem (algebraic geometry)
• Base change theorems (algebraic geometry)
• Beauville–Laszlo theorem (vector bundles)
• Belyi's theorem (algebraic geometry)
• Bertini's theorem (algebraic geometry)
• Bézout's theorem (algebraic geometry)
• Borel fixed-point theorem (algebraic geometry)
• Castelnuovo theorem (algebraic geometry)
• Cayley–Salmon theorem (algebraic surfaces)
• Chasles' theorem (algebraic geometry)
• Chevalley's structure theorem (algebraic geometry)
• Faltings's theorem (Diophantine geometry)
• Fulton–Hansen connectedness theorem (algebraic geometry)
• Grauert–Riemenschneider vanishing theorem (algebraic geometry)
• Grothendieck–Hirzebruch–Riemann–Roch theorem (algebraic geometry)
• Grothendieck's connectedness theorem (algebraic geometry)
• Haboush's theorem (algebraic groups, representation theory, invariant theory)
• Harnack's curve theorem (real algebraic geometry)
• Hasse's theorem on elliptic curves (number theory)
• Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)
• Hironaka theorem (algebraic geometry)
• Hodge index theorem (algebraic surfaces)
• Katz–Lang finiteness theorem (number theory)
• Lefschetz hyperplane theorem (algebraic topology)
• Leray's theorem (algebraic geometry)
• Manin–Drinfeld theorem (number theory)
• Max Noether's theorem (algebraic geometry)
• Mazur's torsion theorem (algebraic geometry)
• Mumford vanishing theorem (algebraic geometry)
• Nagata's compactification theorem (algebraic geometry)
• Noether's theorem on rationality for surfaces (algebraic surfaces)
• Proper base change theorem (algebraic geometry)
• Puiseux's theorem (algebraic geometry)
• Ramanujam vanishing theorem (algebraic geometry)
• Reider's theorem (algebraic surfaces)
• Riemann–Roch theorem for surfaces (algebraic surfaces)
• Sylvester pentahedral theorem (invariant theory)
• Theorem of the cube (algebraic varieties)
• Torelli theorem (algebraic geometry)
• Tsen's theorem (algebraic geometry)
• Weber's theorem (algebraic curves)
• Zariski's connectedness theorem (algebraic geometry)
• Zariski's main theorem (algebraic geometry)

Linear and multilinear algebra; matrix theory

• Amitsur–Levitzki theorem (linear algebra)
• Binomial inverse theorem (linear algebra)
• Birkhoff–Von Neumann theorem (linear algebra)
• Bregman–Minc inequality (discrete mathematics)
• Cauchy-Binet formula (linear algebra)
• Cayley–Hamilton theorem (Linear algebra)
• Dimension theorem for vector spaces (vector spaces, linear algebra)
• Euler's rotation theorem (geometry)
• Exchange theorem (linear algebra)
• Gamas's Theorem (multilinear algebra)
• Gershgorin circle theorem (matrix theory)
• Inverse eigenvalues theorem (linear algebra)
• Perron–Frobenius theorem (matrix theory)
• Principal axis theorem (linear algebra)
• Rank–nullity theorem (linear algebra)
• Rouché–Capelli theorem (Linear algebra)
• Sinkhorn's theorem (matrix theory)
• Specht's theorem (matrix theory)
• Spectral theorem (linear algebra, functional analysis)
• Sylvester's determinant theorem (determinants)
• Sylvester's law of inertia (quadratic forms)
• Witt's theorem (quadratic forms)

Associative rings and algebras

• Artin–Wedderburn theorem (abstract algebra)
• Artin–Zorn theorem (algebra)
• Brauer–Cartan–Hua theorem (ring theory)
• Frobenius theorem (abstract algebras)
• Goldie's theorem (ring theory)
• Jacobson density theorem (ring theory)
• Jacobson–Bourbaki theorem (algebra)
• Levitzky's theorem (ring theory)
• Regev's theorem (ring theory)
• Skolem–Noether theorem (simple algebras)
• Wedderburn's little theorem (ring theory)
• Wedderburn's theorem (abstract algebra)

Nonassociative rings and algebras

• Ado's theorem (Lie algebra)
• Goddard–Thorn theorem (vertex algebras)
• Hurwitz's theorem (normed division algebras)
• Jacobson–Morozov theorem (Lie algebra)
• Levi's theorem (Lie groups)
• Lie's theorem (Lie algebra)
• Poincaré–Birkhoff–Witt theorem (universal enveloping algebras)
• Shirshov–Cohn theorem (Jordan algebras)
• Shirshov–Witt theorem (Lie algebras)

Category theory and homological algebra

• Beck's monadicity theorem (category theory)
• Bruguières modularity theorem (category theory)
• Freyd's adjoint functor theorem (category theory)
• Golod–Shafarevich theorem (group theory)
• Lawvere's fixed-point theorem (mathematical logic)
• Mitchell's embedding theorem (category theory)
• The duality theorem (topology)

K-theory

• Atiyah–Segal completion theorem (homotopy theory)
• Snaith's theorem (algebraic topology)

Group theory and generalizations

• Alperin–Brauer–Gorenstein theorem (finite groups)
• Bass-Guirvarc'h formula (group theory)
• Bass-Serre theorem (group theory)
• Borel–Bott–Weil theorem (representation theory)
• Borel–Weil theorem (representation theory)
• Brauer–Nesbitt theorem (representation theory of finite groups)
• Brauer–Suzuki theorem (finite groups)
• Brauer–Suzuki–Wall theorem (group theory)
• Brauer's theorem (number theory)
• Brauer's theorem on induced characters (representation theory of finite groups)
• Burnside's theorem (group theory)
• Cartan–Dieudonné theorem (group theory)
• Cauchy's theorem (finite groups)
• Cayley's theorem (group theory)
• Chevalley–Shephard–Todd theorem (finite group)
• Classification of finite simple groups (group theory)
• Feit–Thompson theorem (finite groups)
• Fitting's theorem (group theory)
• Flat torus theorem (geometric group theory)
• Focal subgroup theorem (abstract algebra)
• Frobenius determinant theorem (group theory)
• Frobenius reciprocity theorem (group representations)
• Frucht's theorem (graph theory)
• Great orthogonality theorem (group theory)
• Gromov's theorem on groups of polynomial growth (geometric group theory)
• Grushko theorem (group theory)
• Higman's embedding theorem (group theory)
• Isoperimetric gap (geometric group theory, metric geometry)
• Jordan–Hölder theorem (group theory)
• Jordan–Schur theorem (group theory)
• Jordan's theorem (multiply transitive groups) (group theory)
• Krull–Schmidt theorem (group theory)
• Kurosh subgroup theorem (group theory)
• L-balance theorem (finite groups)
• Lagrange's theorem (group theory)
• Lie–Kolchin theorem (algebraic groups, representation theory)
• Maschke's theorem (group representations)
• Moufang's theorem (loop theory)
• Nielsen–Schreier theorem (free groups)
• Orbit-stabilizer theorem (group theory)
• Schreier refinement theorem (group theory)
• Schur's lemma (representation theory)
• Schur–Zassenhaus theorem (group theory)
• Sela's theorem (hyperbolic groups)
• Stallings theorem about ends of groups (group theory)
• Superrigidity theorem (algebraic groups)
• Švarc-Milnor lemma (geometric group theory)
• Sylow theorems (group theory)
• Thompson transitivity theorem (finite groups)
• Thompson uniqueness theorem (finite groups)
• Tits alternative (geometric group theory)
• Trichotomy theorem (finite groups)
• Walter theorem (finite groups)
• Z* theorem (finite groups)
• ZJ theorem (finite groups)

Topological groups, Lie groups

• Cartan's theorem (Lie group)
• Harish–Chandra theorem (representation theory)
• Harish–Chandra's regularity theorem (representation theory)
• Iwasawa decomposition (Lie theory)
• Kempf–Ness theorem (algebraic geometry)
• Lie's third theorem (Lie group)
• Montgomery-Zippin-Gleason theorem (Transformation groups)
• Plancherel theorem for spherical functions (representation theory)
• Trombi–Varadarajan theorem (Lie group)

Real functions

• Anderson's theorem (real analysis)
• Bernstein's theorem (functional analysis)
• Bohr–Mollerup theorem (gamma function)
• Bolzano's theorem (real analysis, calculus)
• Constant rank theorem ( multivariate calculus)
• Cousin's lemma (real analysis)
• Danskin's theorem (convex analysis)
• Darboux's theorem (real analysis)
• Denjoy–Carleman theorem (functional analysis)
• Denjoy-Young-Saks theorem (real analysis)
• Dini's theorem (analysis)
• Divergence theorem (vector calculus)
• Fermat's theorem (stationary points) (real analysis)
• Fraňková–Helly selection theorem (mathematical analysis)
• Froda's theorem (mathematical analysis)
• Fubini's theorem on differentiation (real analysis)
• Fundamental theorem of calculus (calculus)
• Gauss theorem (vector calculus)
• Gradient theorem (vector calculus)
• Green's theorem (vector calculus)
• Helly's selection theorem (mathematical analysis)
• Implicit function theorem (vector calculus)
• Increment theorem (mathematical analysis)
• Intermediate value theorem (calculus)
• Inverse function theorem (vector calculus)
• Kolmogorov–Arnold representation theorem (real analysis, approximation theory)
• Lebesgue differentiation theorem (real analysis)
• Luzin's theorem (real analysis)
• Malgrange preparation theorem (singularity theory)
• Mean value theorem (calculus)
• Monotone convergence theorem (mathematical analysis)
• Müntz–Szász theorem (functional analysis)
• Rademacher's theorem (mathematical analysis)
• Rising sun lemma (real analysis)
• Rolle's theorem (calculus)
• Squeeze theorem (mathematical analysis)
• Stokes's theorem (vector calculus, differential topology)
• Titchmarsh convolution theorem (complex analysis)
• Whitney extension theorem (mathematical analysis)
• Zahorski theorem (real analysis)

Measure and integration

• Banach–Tarski theorem (measure theory)
• Brunn–Minkowski theorem (Riemannian geometry)
• Cameron–Martin theorem (measure theory)
• Carathéodory's theorem (measure theory)
• Carathéodory's extension theorem (measure theory)
• Cramér–Wold theorem (measure theory)
• Disintegration theorem (measure theory)
• Dominated convergence theorem (Lebesgue integration)
• Egorov's theorem (measure theory)
• Fatou–Lebesgue theorem (real analysis)
• Fubini's theorem (integration)
• Hahn decomposition theorem (measure theory)
• Hahn–Kolmogorov theorem (measure theory)
• Ham sandwich theorem (topology)
• Hobby–Rice theorem (mathematical analysis)
• Kōmura's theorem (measure theory)
• Lebesgue's decomposition theorem (measure theory)
• Lebesgue's density theorem (measure theory)
• Maharam's theorem (measure theory)
• Minlos's theorem (functional analysis)
• Monotone class theorem (measure theory)
• Prokhorov's theorem (measure theory)
• Radon–Nikodym theorem (measure theory)
• Schilder's theorem (stochastic processes)
• Schröder–Bernstein theorem for measurable spaces (measure theory)
• Stein–Strömberg theorem (measure theory)
• Steinhaus theorem (measure theory)
• Stone–Tukey theorem (topology)
• Structure theorem for Gaussian measures (measure theory)
• Vitali convergence theorem (measure theory)
• Vitali theorem (measure theory)
• Vitali–Hahn–Saks theorem (measure theory)

Functions of a complex variable

• Akhiezer's theorem (complex analysis)
• Arakelyan's theorem (complex analysis)
• Area theorem (conformal mapping) (complex analysis)
• Beurling–Lax theorem (Hardy spaces)
• Bloch's theorem (complex analysis)
• Bôcher's theorem (complex analysis)
• Borel–Carathéodory theorem (complex analysis)
• Branching theorem (complex manifold)
• Carathéodory's theorem (complex analysis)
• Carleson–Jacobs theorem (complex analysis)
• Carlson's theorem (complex analysis)
• Cauchy integral theorem (complex analysis)
• Cauchy–Hadamard theorem (complex analysis)
• Clifford's theorem on special divisors (algebraic curves)
• Corona theorem (complex analysis)
• de Branges's theorem (complex analysis)
• De Franchis theorem (Riemann surfaces)
• Edge-of-the-wedge theorem (complex analysis)
• Farrell–Markushevich theorem (complex analysis)
• Fatou's theorem (complex analysis)
• Fundamental theorem of algebra (complex analysis)
• Gauss–Lucas theorem (complex analysis)
• Grunsky's theorem (complex analysis)
• Hadamard three-circle theorem (complex analysis)
• Hadamard three-lines theorem (complex analysis)
• Hardy's theorem (complex analysis)
• Hartogs–Rosenthal theorem (complex analysis)
• Harnack's theorem (complex analysis)
• Hurwitz's automorphisms theorem (algebraic curves)
• Hurwitz's theorem (complex analysis)
• Identity theorem (complex analysis)
• Identity theorem for Riemann surfaces (Riemann surfaces)
• Koebe 1/4 theorem (complex analysis)
• Lagrange inversion theorem (mathematical analysis, combinatorics)
• Lagrange reversion theorem (mathematical analysis, combinatorics)
• Laurent expansion theorem (complex analysis)
• Lindelöf's theorem (complex analysis)
• Liouville's theorem (complex analysis, entire functions)
• Liouville's theorem (conformal mappings)
• Looman–Menchoff theorem (complex analysis)
• Marden's theorem (polynomials)
• Mergelyan's theorem (complex analysis)
• Measurable Riemann mapping theorem (conformal mapping)
• Mittag-Leffler's theorem (complex analysis)
• Monodromy theorem (complex analysis)
• Montel's theorem (complex analysis)
• Morera's theorem (complex analysis)
• Nachbin's theorem(complex analysis)
• Open mapping theorem (complex analysis)
• Ostrowski–Hadamard gap theorem (complex analysis)
• Phragmén–Lindelöf theorem (complex analysis)
• Picard theorem (complex analysis)
• Residue theorem (complex analysis)
• Riemann mapping theorem (complex analysis)
• Riemann's existence theorem (algebraic geometry)
• Riemann's theorem on removable singularities (complex analysis)
• Riemann–Roch theorem (Riemann surfaces, algebraic curves)
• Rouché's theorem (complex analysis)
• Routh–Hurwitz theorem (polynomials)
• Runge's theorem (complex analysis)
• Siu's semicontinuity theorem (complex analysis)
• Sokhatsky–Weierstrass theorem (complex analysis)
• Uniformization theorem (complex analysis, differential geometry)
• Van Vleck's theorem (mathematical analysis)
• Weierstrass–Casorati theorem (complex analysis)
• Weierstrass factorization theorem (complex analysis)

Several complex variables and analytic spaces

• Appell–Humbert theorem (complex manifold)
• Baily–Borel theorem (algebraic geometry)
• Behnke–Stein theorem (several complex variables)
• Birkhoff–Grothendieck theorem (complex geometry)
• Bochner's tube theorem (complex analysis)
• Cartan's theorems A and B (several complex variables)
• Castelnuovo–de Franchis theorem (algebraic geometry)
• Chow's theorem (algebraic geometry)
• Cramer's theorem (algebraic curves) (analytic geometry)
• Hartogs's theorem (complex analysis)
• Hartogs's extension theorem (several complex variables)
• Hirzebruch–Riemann–Roch theorem (complex manifolds)
• Kawamata–Viehweg vanishing theorem (algebraic geometry)
• Kodaira embedding theorem (algebraic geometry)
• Kodaira vanishing theorem (complex manifold)
• Lefschetz theorem on (1,1)-classes (algebraic geometry)
• Local invariant cycle theorem (algebraic geometry)
• Malgrange–Zerner theorem (complex analysis)
• Newlander–Niremberg theorem (differential geometry)
• Remmert–Stein theorem (complex analysis)
• Riemann singularity theorem (algebraic geometry)
• Skoda–El Mir theorem (complex geometry)
• Weierstrass preparation theorem (several complex variables, commutative algebra)

Special functions

• De Moivre's theorem (complex analysis)
• Hölder's theorem (mathematical analysis)
• Multiplication theorem (special functions)

Ordinary differential equations

• Carathéodory's existence theorem (ordinary differential equations)
• Floquet's theorem (differential equations)
• Fuchs's theorem (differential equations)
• Kharitonov's theorem (control theory)
• Kneser's theorem (differential equations)
• Liénard's theorem (dynamical systems)
• Markus−Yamabe theorem (dynamical systems)
• Peano existence theorem (ordinary differential equations)
• Picard–Lindelöf theorem (ordinary differential equations)
• Shift theorem (differential operators)
• Sturm–Picone comparison theorem (differential equations)

Partial differential equations

• Cartan–Kähler theorem (partial differential equations)
• Cartan–Kuranishi prolongation theorem (partial differential equations)
• Cauchy–Kowalevski theorem (partial differential equations)
• Malgrange–Ehrenpreis theorem (differential equations)

Dynamical systems and ergodic theory

• Autonomous convergence theorem (dynamical systems)
• Banach fixed-point theorem (metric spaces, differential equations)
• Bendixson–Dulac theorem (dynamical systems)
• Birkhoff's theorem (ergodic theory)
• Conley–Zehnder theorem (dynamical systems)
• Curtis–Hedlund–Lyndon theorem (cellular automata)
• Hartman–Grobman theorem (dynamical systems)
• Kolmogorov–Arnold–Moser theorem (dynamical systems)
• Krylov–Bogolyubov theorem (dynamical systems)
• Maximal ergodic theorem (ergodic theory)
• No wandering domain theorem (ergodic theory)
• Noether's theorem (Lie groups, calculus of variations, differential invariants, physics)
• Ornstein theorem (ergodic theory)
• Oseledec theorem (ergodic theory)
• Peixoto's theorem (dynamical systems)
• Poincaré–Bendixson theorem (dynamical systems)
• Poincaré recurrence theorem (dynamical systems)
• Ratner's theorems (ergodic theory)
• Sarkovskii's theorem (dynamical systems)
• Takens's theorem (dynamical systems)

Difference and functional equations

• Euler's theorem on homogeneous functions (multivariate calculus)

Sequence, series, summability

• Abel's theorem (mathematical analysis)
• Abelian and Tauberian theorems (mathematical analysis)
• Absolute convergence theorem (mathematical series)
• Cesàro's theorem (real analysis)
• Hardy–Littlewood tauberian theorem (mathematical analysis)
• Riemann series theorem (mathematical series)
• Silverman–Toeplitz theorem (mathematical analysis)
• Śleszyński–Pringsheim theorem (continued fraction)
• Stolz–Cesàro theorem (calculus)

Approximations and expansions

• Stone–Weierstrass theorem (functional analysis)
• Taylor's theorem (calculus)

Harmonic analysis on Euclidean spaces

• Balian–Low theorem (Fourier analysis)
• Bernstein's theorem (approximation theory)
• Carleson's theorem (harmonic analysis)
• Convolution theorem (Fourier transforms)
• Denjoy theorem (dynamical systems)
• Fourier inversion theorem (harmonic analysis)
• Fourier theorem (harmonic analysis)
• Hausdorff-Young inequality (Fourier analysis)
• Lauricella's theorem (functional analysis)
• Paley–Wiener theorem (Fourier transforms)
• Parseval's theorem (Fourier analysis)
• Plancherel theorem (Fourier analysis)
• Riesz–Fischer theorem (real analysis)
• Szegő limit theorems (mathematical analysis)
• Wiener's tauberian theorem (real analysis)
• Wiener–Ikehara theorem (number theory)

Abstract harmonic analysis

• F. and M. Riesz theorem (measure theory)
• Peter–Weyl theorem (representation theory)
• Pontryagin duality theorem (representation theory)

Integral transforms, operational calculus

• Final value theorem (mathematical analysis)
• Initial value theorem (integral transform)
• Mellin inversion theorem (complex analysis)
• Stahl's theorem (matrix analysis)
• Titchmarsh theorem (integral transform)

Integral equations

• Fredholm's theorem (linear algebra)

Functional analysis

• Analytic Fredholm theorem (functional analysis)
• Banach–Alaoglu theorem (functional analysis)
• Banach–Mazur theorem (functional analysis)
• Banach–Steinhaus theorem (functional analysis)
• Choquet–Bishop–de Leeuw theorem (functional analysis)
• Closed range theorem (functional analysis)
• Dunford–Schwartz theorem (functional analysis)
• Eberlein–Šmulian theorem (functional analysis)
• Goldstine theorem (functional analysis)
• Hahn–Banach theorem (functional analysis)
• Hilbert projection theorem (convex analysis)
• Kachurovskii's theorem (convex analysis)
• Kirszbraun theorem (Lipschitz continuity)
• M. Riesz extension theorem (functional analysis)
• Milman–Pettis theorem (Banach space)
• Moore–Aronszajn theorem (Hilbert space)
• Orlicz–Pettis theorem (functional analysis)
• Quotient of subspace theorem (functional analysis)
• Riesz representation theorem (functional analysis, Hilbert space)
• Schauder fixed-point theorem (functional analysis)
• Schwartz kernel theorem (generalized functions)
• Sobczyk's theorem (functional analysis)
• Sobolev embedding theorem (mathematical analysis)
• Solèr's theorem (mathematical logic)
• Tikhonov fixed-point theorem (functional analysis)
• Trudinger's theorem (functional analysis)

Operator theory

• Aronszajn–Smith theorem (functional analysis)
• Atiyah–Singer index theorem (elliptic differential operators, harmonic analysis)
• Atkinson's theorem (operator theory)
• Babuška–Lax–Milgram theorem (partial differential equations)
• Banach–Stone theorem (operator theory)
• Bauer–Fike theorem (spectral theory)
• Bounded inverse theorem (operator theory)
• Browder–Minty theorem (operator theory)
• Choi's theorem on completely positive maps (operator theory)
• Commutation theorem (von Neumann algebra)
• Fuglede's theorem (functional analysis)
• Gelfand–Mazur theorem (Banach algebra)
• Gelfand–Naimark theorem (functional analysis)
• Hardy–Littlewood maximal theorem (real analysis)
• Hellinger–Toeplitz theorem (functional analysis)
• Hilbert–Schmidt theorem (functional analysis)
• Hille–Yosida theorem (functional analysis)
• Kaplansky density theorem (von Neumann algebra)
• Kuiper's theorem (operator theory, topology)
• Lax–Milgram theorem (partial differential equations)
• Lions–Lax–Milgram theorem (partial differential equations)
• Lumer–Phillips theorem (semigroup theory)
• Marcinkiewicz theorem (functional analysis)
• Mazur–Ulam theorem (normed spaces)
• Mercer's theorem (functional analysis)
• Min-max theorem (functional analysis)
• Moreau's theorem (convex analysis)
• Nash–Moser theorem (mathematical analysis)
• Open mapping theorem (functional analysis)
• Peetre theorem (functional analysis)
• Riesz–Thorin theorem (functional analysis)
• Ryll-Nardzewski fixed-point theorem (functional analysis)
• Sazonov's theorem (functional analysis)
• Schröder–Bernstein theorems for operator algebras (operator algebras)
• Stinespring factorization theorem (operator theory)
• Stone's theorem on one-parameter unitary groups (functional analysis)
• Sz.-Nagy's dilation theorem (operator theory)
• Tomita's theorem (operator algebras)
• Von Neumann bicommutant theorem (functional analysis)
• Von Neumann's theorem (operator theory)

Calculus of variations and optimal control; optimization

• Caristi fixed-point theorem (fixed points)
• Envelope theorem (calculus of variations)
• Isoperimetric theorem (curves, calculus of variations)
• Minimax theorem (game theory)
• Mountain pass theorem (calculus of variations)
• Noether's second theorem (calculus of variations, physics)
• Parthasarathy's theorem (game theory)
• Sion's minimax theorem (game theory)
• Tonelli's theorem (functional analysis)

Geometry

• Alternate Interior Angles Theorem (geometry)
• Alternate segment theorem (geometry)
• Angle bisector theorem (Euclidean geometry)
• Anne's theorem (geometry)
• Apollonius's theorem (plane geometry)
• Barbier's theorem (geometry)
• Beck's theorem (incidence geometry)
• Beckman–Quarles theorem (Euclidean geometry)
• Beer's theorem (metric geometry)
• Brahmagupta theorem (Euclidean geometry)
• Brianchon's theorem (conics)
• British flag theorem (Euclidean geometry)
• Butterfly theorem (Euclidean geometry)
• CPCTC (triangle geometry)
• Carnot's theorem (geometry)
• Casey's theorem (Euclidean geometry)
• Cayley–Bacharach theorem (projective geometry)
• Ceva's theorem (geometry)
• Clifford's circle theorems (Euclidean plane geometry)
• Commandino's theorem (geometry)
• Constant chord theorem (geometry)
• Conway circle theorem (Euclidean plane geometry)
• Crossbar theorem (Euclidean plane geometry)
• Dandelin's theorem (solid geometry)
• De Bruijn–Erdős theorem (incidence geometry)
• De Gua's theorem (geometry)
• Desargues's theorem (projective geometry)
• Descartes's theorem (plane geometry)
• Dinostratus' theorem (geometry, analysis)
• Equal incircles theorem (Euclidean geometry)
• Euler's quadrilateral theorem (geometry)
• Euler's theorem in geometry (triangle geometry)
• Exterior angle theorem (triangle geometry)
• Feuerbach's theorem (geometry)
• Finsler–Hadwiger theorem (geometry)
• Five circles theorem (circles)
• Gauss–Wantzel theorem (geometry)
• Geometric mean theorem (geometry)
• Hinge theorem (geometry)
• Hjelmslev's theorem (geometry)
• Impossibility of angle trisection (geometry)
• Independence of the parallel postulate (geometry)
• Inscribed angle theorem (geometry)
• Intercept theorem (Euclidean geometry)
• Intersecting chords theorem (Euclidean geometry)
• Intersecting secants theorem (Euclidean geometry)
• Intersection theorem (projective geometry)
• Japanese theorem for concyclic polygons (Euclidean geometry)
• Japanese theorem for concyclic quadrilaterals (Euclidean geometry)
• Kawasaki's theorem (mathematics of paper folding)
• Lester's theorem (Euclidean plane geometry)
• Lexell's theorem (spherical geometry)
• Menelaus's theorem (geometry)
• Miquel's theorem (geometry)
• Mohr–Mascheroni theorem (geometry)
• Monge's theorem (geometry)
• Morley's trisector theorem (geometry)
• Napoleon's theorem (triangle geometry)
• Newton's theorem about ovals (curves)
• Newton's theorem (quadrilateral) (geometry)
• Pappus's area theorem (geometry)
• Pappus's centroid theorem (geometry)
• Pappus's hexagon theorem (geometry)
• Pascal's theorem (conics)
• Pasch's theorem (order theory)
• Pitot theorem (plane geometry)
• Pivot theorem (circles)
• Pompeiu's theorem (Euclidean geometry)
• Poncelet's closure theorem (conics)
• Poncelet–Steiner theorem (geometry)
• Ptolemy's theorem (geometry)
• Pythagorean theorem (geometry)
• Reuschle's theorem (Euclidean geometry)
• Routh's theorem (triangle geometry)
• Saccheri–Legendre theorem (absolute geometry)
• Six circles theorem (circles)
• Steiner–Lehmus theorem (triangle geometry)
• Symphonic theorem (triangle geometry)
• Tangent-secant theorem (geometry)
• Thales's theorem (geometry)
• Thébault's theorem (geometry)
• Theorem of the gnomon (geometry)
• Thomsen's theorem (geometry)
• Van Aubel's theorem (quadrilaterals)
• Van Schooten's theorem (Euclidean geometry)
• Varignon's theorem (Euclidean geometry)
• Viviani's theorem (Euclidean geometry)

Convex and discrete geometry

• Alexandrov's uniqueness theorem (discrete geometry)
• Balinski's theorem (combinatorics)
• Bang's theorem (geometry)
• Besicovitch covering theorem (mathematical analysis)
• Blaschke selection theorem (geometric topology)
• Bolyai–Gerwien theorem (discrete geometry)
• Busemann's theorem (Euclidean geometry)
• Carathéodory's theorem (convex geometry)
• Cauchy's theorem (geometry)
• Classification of Platonic solids (geometry)
• de Bruijn's theorem (discrete geometry)
• Descartes's theorem on total angular defect (polyhedra)
• Erdős–Anning theorem (discrete geometry)
• Erdős–Nagy theorem (discrete geometry)
• Erdős–Szekeres theorem (discrete geometry)
• Fáry's theorem (graph theory)
• Fenchel's duality theorem (convex analysis)
• Fenchel–Moreau theorem (mathematical analysis)
• Hadwiger's theorem (geometry, measure theory)
• Helly's theorem (convex sets)
• Holditch's theorem (plane geometry)
• John ellipsoid (geometry)
• Jung's theorem (geometry)
• Kepler conjecture (discrete geometry)
• Kirchberger's theorem (discrete geometry)
• Krein–Milman theorem (mathematical analysis, discrete geometry)
• Minkowski's theorem (geometry of numbers)
• Minkowski's second theorem (geometry of numbers)
• Minkowski–Hlawka theorem (geometry of numbers)
• Monsky's theorem (discrete geometry)
• Pick's theorem (geometry)
• Pizza theorem (geometry)
• Radon's theorem (convex sets)
• Separating axis theorem (convex geometry)
• Steinitz theorem (graph theory)
• Stewart's theorem (plane geometry)
• Supporting hyperplane theorem (convex geometry)
• Sylvester–Gallai theorem (plane geometry)
• Szemerédi–Trotter theorem (combinatorics)
• Tverberg's theorem (discrete geometry)
• Vitali covering theorem (measure theory)
• Wallace–Bolyai–Gerwien theorem (discrete geometry)

Differential geometry

• 2π theorem (Riemannian geometry)
• Abel's curve theorem (riemannian geometry)
• Beltrami's theorem (Riemannian geometry)
• Berger–Kazdan comparison theorem (Riemannian geometry)
• Bertrand–Diquet–Puiseux theorem (differential geometry)
• Bishop-Gromov inequality (riemannian geometry)
• Bonnet theorem (differential geometry)
• Carathéodory–Jacobi–Lie theorem (symplectic topology)
• Cartan–Hadamard theorem (Riemannian geometry)
• Cheng's eigenvalue comparison theorem (Riemannian geometry)
• Chern–Gauss–Bonnet theorem (differential geometry)
• Classification of symmetric spaces (Lie theory)
• Darboux's theorem (symplectic topology)
• Euler's theorem (differential geometry)
• Four-vertex theorem (differential geometry)
• Frobenius theorem (foliations)
• Gauss's lemma (riemannian geometry)
• Gauss's Theorema Egregium (differential geometry)
• Gauss–Bonnet theorem (differential geometry)
• Geroch's splitting theorem (differential geometry)
• Gromov's compactness theorem (Riemannian geometry)
• Gromov's compactness theorem (symplectic topology)
• Gromov–Ruh theorem (differential geometry)
• Hilbert's theorem (differential geometry)
• Hopf–Rinow theorem (differential geometry)
• Killing–Hopf theorem (Riemannian geometry)
• Lee Hwa Chung theorem (symplectic topology)
• Lie–Palais theorem (differential geometry)
• Meusnier's theorem (differential geometry)
• Mostow rigidity theorem (differential geometry)
• Myers theorem (differential geometry)
• Myers-Steenrod theorem (differential geometry)
• Nash embedding theorem (differential geometry)
• Non-squeezing theorem (symplectic geometry)
• Rashevsky–Chow theorem (control theory)
• Rauch comparison theorem (Riemannian geometry)
• Schwarz–Ahlfors–Pick theorem (differential geometry)
• Soul theorem (Riemannian geometry)
• Sphere theorem (Riemannian geometry)
• Synge's theorem (Riemannian geometry)
• Toponogov's theorem (Riemannian geometry)

General topology

• Arzelà–Ascoli theorem (functional analysis)
• Baire category theorem (topology, metric spaces)
• Bing metrization theorem (general topology)
• Bolzano–Weierstrass theorem (real analysis, calculus)
• Borsuk–Ulam theorem (topology)
• Brouwer fixed-point theorem (topology)
• Cantor's intersection theorem (real analysis)
• Closed graph theorem (functional analysis)
• Extreme value theorem (calculus)
• Fixed-point theorems in infinite-dimensional spaces
• Hairy ball theorem (algebraic topology)
• Hahn–Mazurkiewicz theorem (continuum theory)
• Heine–Borel theorem (real analysis)
• Heine–Cantor theorem (metric geometry)
• Jordan curve theorem (topology)
• Kuratowski's closure-complement problem (topology)
• Lebesgue covering dimension (dimension theory)
• Metrization theorems (topological spaces)
• Nagata–Smirnov metrization theorem(general topology)
• Netto's theorem (topology)
• Parovicenko's theorem (topology)
• Tietze extension theorem (general topology)
• Tychonoff's theorem (general topology)

Algebraic topology

• Acyclic models theorem (algebraic topology)
• Blakers–Massey theorem (homotopy theory)
• Bott periodicity theorem (homotopy theory)
• Brown's representability theorem (homotopy theory)
• Cellular approximation theorem (algebraic topology)
• Dold–Thom theorem (algebraic topology)
• Eilenberg–Ganea theorem (homological algebra, algebraic topology)
• Eilenberg–Zilber theorem (algebraic topology)
• Euler's polyhedron theorem (polyhedra)
• Excision theorem (homology theory)
• Freudenthal suspension theorem (homotopy theory)
• Hilton–Milnor theorem (algebraic topology)
• Homotopy excision theorem (algebraic topology)
• Hopf theorem (differential topology)
• Hurewicz theorem (algebraic topology)
• Künneth theorem (algebraic topology)
• Landweber exact functor theorem (algebraic topology)
• Lefschetz fixed-point theorem (fixed points, algebraic topology)
• Lefschetz–Hopf theorem (topology)
• Leray–Hirsch theorem (algebraic topology)
• Nielsen fixed-point theorem (fixed points)
• Nilpotence theorem (algebraic topology)
• Poincaré duality theorem (algebraic topology of manifolds)
• Seifert–van Kampen theorem (algebraic topology)
• Simplicial approximation theorem (algebraic topology)
• Stallings–Zeeman theorem (algebraic topology)
• Sullivan conjecture (homotopy theory)
• Universal coefficient theorem (algebraic topology)
• Vietoris–Begle mapping theorem (algebraic topology)
• Whitehead theorem (homotopy theory)
• Whitney–Graustein Theorem (algebraic topology)

Manifolds and cell complexes

• Atiyah–Bott fixed-point theorem (differential topology)
• Bing's recognition theorem (geometric topology)
• Birman short exact sequence (geometric topology)
• Classification of compact surfaces (Topology)
• De Rham's theorem (differential topology)
• Dehn-Nielsen-Baer theorem (geometric topology)
• Donaldson's theorem (differential topology)
• Ehresmann's theorem (differential topology)
• Fáry–Milnor theorem (knot theory)
• Fenchel's theorem (differential geometry)
• H-cobordism theorem (differential topology)
• Hirzebruch signature theorem (topology, algebraic geometry)
• Jordan–Schönflies theorem (geometric topology)
• JSJ theorem (3-manifolds)
• Lickorish twist theorem (geometric topology)
• Lickorish–Wallace theorem (3-manifolds)
• Nielsen realization problem (geometric topology)
• Nielsen-Thurston classification (low-dimensional topology)
• Novikov's compact leaf theorem (foliations)
• Perelman's Geometrization theorem (3-manifolds)
• Poincaré–Hopf theorem (differential topology)
• Poincaré conjecture (topology)
• Preimage theorem (differential topology)
• Reeb sphere theorem (foliations)
• Reidemeister–Singer Theorem (geometric topology)
• Riemann–Roch theorem for smooth manifolds (differential topology)
• Rokhlin's theorem (geometric topology)
• S–cobordism theorem (differential topology)
• Sard's theorem (differential geometry)
• Scott core theorem (3-manifolds)
• Swan's theorem (module theory)
• Tameness theorem (3-manifolds)
• Thom transversality theorem (differential topology)
• Thurston's geometrization theorem (3-manifolds)
• Waldhausen's theorem (geometric topology)
• Whitney embedding theorem (differential manifolds)
• Whitney immersion theorem (differential topology)

Global analysis, analysis on manifolds

• Radó's theorem (harmonic analysis)

Probability theory and stochastic processes

• Bayes' theorem (probability)
• Bertrand's ballot theorem (probability theory, combinatorics)
• Burke's theorem (probability theory, queueing theory)
• Central limit theorem (probability)
• Clark–Ocone theorem (stochastic processes)
• Continuous mapping theorem (probability theory)
• Cramér's theorem (large deviations) (probability)
• Dawson–Gärtner theorem (asymptotic analysis)
• Donsker's theorem (probability theory)
• Doob decomposition theorem (stochastic processes)
• Doob's martingale convergence theorems (stochastic processes)
• Doob–Meyer decomposition theorem (stochastic processes)
• Dudley's theorem (probability)
• Dunford–Pettis theorem (probability theory)
• Fernique's theorem (measure theory)
• Foster's theorem (statistics)
• Freidlin–Wentzell theorem (stochastic processes)
• Girsanov's theorem (stochastic processes)
• Glivenko's theorem (probability)
• Gordon–Newell theorem (queueing theory)
• Hammersley–Clifford theorem (probability)
• Helly–Bray theorem (probability theory)
• Integral representation theorem for classical Wiener space (measure theory)
• Ionescu-Tulcea theorem (probability theory)
• Jackson's theorem (queueing theory)
• Karhunen–Loève theorem (stochastic processes)
• Kolmogorov extension theorem (stochastic processes)
• Kolmogorov's three-series theorem (mathematical series)
• Le Cam's theorem (probability theory)
• Lévy continuity theorem (probability)
• Lévy's modulus of continuity theorem (probability)
• Martingale representation theorem (probability theory)
• Maxwell's theorem (probability theory)
• Optional stopping theorem (probability theory)
• Poisson limit theorem (probability)
• Raikov's theorem (probability)
• Skorokhod's embedding theorem (statistics)
• Skorokhod's representation theorem (statistics)
• Slutsky's theorem (probability theory)
• Theorem of de Moivre–Laplace (probability theory)

Statistics

• Aumann's agreement theorem (statistics)
• Bapat–Beg theorem (statistics)
• Basu's theorem (statistics)
• Berry–Esséen theorem (probability theory)
• Cochran's theorem (statistics)
• Cox's theorem (probability)
• Cramér’s decomposition theorem (statistics)
• De Finetti's theorem (probability)
• FWL theorem (economics)
• Fieller's theorem (statistics)
• Fisher–Tippett–Gnedenko theorem (statistics)
• Gauss–Markov theorem (statistics)
• Glivenko–Cantelli theorem (probability)
• Infinite monkey theorem (probability)
• Lehmann–Scheffé theorem (statistics)
• Lukacs's proportion-sum independence theorem (probability)
• Lyapunov's central limit theorem (probability theory)
• Pickands–Balkema–de Haan theorem (extreme value theory)
• Pitman–Koopman–Darmois theorem (statistics)
• Rao–Blackwell theorem (statistics)
• Sklar's theorem (statistics)
• Wold's theorem (statistics)

Numerical analysis

• Godunov's theorem (numerical analysis)
• Kantorovich theorem (functional analysis)
• Lax–Richtmyer theorem (numerical analysis)
• Lax–Wendroff theorem (numerical analysis)
• Marsaglia's theorem (number theory)

Computer science

• Akra–Bazzi theorem (computer science)
• Art gallery theorem (geometry)
• CAP theorem (theoretical computer science)
• Chomsky–Schützenberger enumeration theorem (formal language theory)
• Chomsky–Schützenberger representation theorem (formal language theory)
• Codd's theorem (relational model)
• Compression theorem (computational complexity theory, structural complexity theory)
• Cook's theorem (computational complexity theory)
• Fagin's theorem (computational complexity theory)
• Full employment theorem (theoretical computer science)
• Gap theorem (computational complexity theory)
• Gottesman–Knill theorem (quantum computation)
• Holland's schema theorem (genetic algorithm)
• Immerman–Szelepcsényi theorem (computational complexity theory)
• Karp–Lipton theorem (computational complexity theory)
• Ladner's theorem (computational complexity theory)
• Lamé’s theorem (computational complexity theory)
• Linear speedup theorem (computational complexity theory)
• Master theorem (analysis of algorithms) (recurrence relations, asymptotic analysis)
• Max/min_CSP/Ones_classification_theorems (computational complexity theory)
• Myhill–Nerode theorem (formal languages)
• No free lunch in search and optimization (computational complexity theory)
• PCP theorem (computational complexity theory)
• Pseudorandom generator theorem (computational complexity theory)
• Quantum threshold theorem (computer science) (theoretical computer science)
• Reversed compound agent theorem (probability)
• Rice's theorem (recursion theory, computer science)
• Rice–Shapiro theorem (computer science)
• Savitch's theorem (computational complexity theory)
• Schaefer's dichotomy theorem (computational complexity theory)
• Sipser–Lautemann theorem (probabilistic complexity theory) (structural complexity theory)
• Smn theorem (recursion theory, computer science)
• Space hierarchy theorem (computational complexity theory)
• Speedup theorem (computational complexity theory)
• Structured program theorem (computer science)
• Time hierarchy theorem (computational complexity theory)
• Toda's theorem (computational complexity theory)
• Universal approximation theorem (artificial neural networks)
• Valiant–Vazirani theorem (computational complexity theory)

Mechanics of particles and systems

• Chasles' theorem, (kinematics)
• Chasles' theorem (gravity)
• Helmholtz theorem (classical mechanics) (physics)
• König's theorem (physics)
• Lami's theorem (statics)
• Liouville's theorem (Hamiltonian mechanics)
• Parallel axis theorem (physics)
• Perpendicular axis theorem (physics)
• Virial theorem (classical mechanics)

Mechanics of deformable solids

• Betti's theorem (physics)
• Castigliano's first and second theorems (structural analysis)
• Clapeyron's theorem (physics)
• Saint-Venant's theorem (physics)
• Theorem of three moments (physics)

Fluid mechanics

• Buckingham π theorem (dimensional analysis)
• Helmholtz's theorems (physics)
• Kelvin's circulation theorem (physics)
• Kutta–Joukowski theorem (physics)
• Reynolds transport theorem (fluid dynamics)
• Taylor–Proudman theorem (physics)

Optics, electromagnetic theory

• Blondel's theorem (electric power) (physics)
• Earnshaw's theorem (electrostatics)
• Maximum power theorem (electrical circuits)
• Norton's theorem (electrical networks)
• Optical theorem (physics)
• Poynting's theorem (physics)
• Thévenin's theorem (electrical circuits)

Classical thermodynamics, heat transfer

• Carnot's theorem (thermodynamics)
• Clausius theorem (physics)

Quantum theory

• Adiabatic theorem (physics)
• Bell's theorem (quantum mechanics)
• Bogoliubov–Parasyuk theorem (quantum field theory)
• Byers–Yang theorem (quantum mechanics)
• C-theorem (physics)
• Cluster decomposition theorem (quantum field theory)
• Coleman–Mandula theorem (quantum field theory)
• Elitzur's theorem (quantum field theory, statistical field theory)
• Furry's theorem (quantum field theory)
• Gell-Mann and Low theorem (quantum field theory)
• Gleason's theorem (Hilbert space)
• Goldstone's theorem (physics)
• Haag's theorem (quantum field theory)
• Haag–Łopuszański–Sohnius theorem (physics)
• Hellmann–Feynman theorem (physics)
• Kinoshita–Lee–Nauenberg theorem (quantum field theory)
• Kochen–Specker theorem (physics)
• Kramers' theorem (physics)
• Nielsen–Ninomiya theorem (quantum field theory)
• No-broadcasting theorem (quantum information theory)
• No-cloning theorem (quantum computation)
• No-communication theorem (quantum information theory)
• No-deleting theorem (quantum information theory)
• Optical equivalence theorem (quantum optics)
• Osterwalder–Schrader theorem (physics)
• Pandya theorem (nuclear physics)
• Pomeranchuk's theorem (physics)
• Reeh–Schlieder theorem (local quantum field theory)
• Spin–statistics theorem (physics)
• Stone–von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics)
• Supersymmetry nonrenormalization theorems (physics)
• Vafa–Witten theorem (physics)
• Weinberg–Witten theorem (quantum field theory)
• Wick's theorem (physics)
• Wigner–Eckart theorem (Clebsch–Gordan coefficients)

Statistical mechanics, structure of matter

• Bohr–van Leeuwen theorem (physics)
• Crooks fluctuation theorem (physics)
• Crystallographic restriction theorem (group theory, crystallography)
• Equipartition theorem (ergodic theory)
• Fluctuation dissipation theorem (physics)
• Fluctuation theorem (statistical mechanics)
• H-theorem (thermodynamics)
• Hohenberg–Kohn theorems (density functional theory)
• Lee–Yang theorem (statistical mechanics)
• Mermin–Wagner theorem (physics)

Relativity and gravitational theory

• Birkhoff's theorem (general relativity)
• Goldberg–Sachs theorem (physics)
• Lovelock's theorem (physics)
• No-hair theorem (physics)
• Odd number theorem (physics)
• Peeling theorem (physics)
• Penrose–Hawking singularity theorems (physics)
• Positive energy theorem (physics)
• Price's theorem (general relativity)

Astronomy and astrophysics

• Clairaut's theorem (physics)
• Shell theorem (physics)

Operations research, mathematical programming

• Analyst's traveling salesman theorem (discrete mathematics)
• Arrival theorem (queueing theory)
• Blum's speedup theorem (computational complexity theory)
• Max flow min cut theorem (graph theory)
• No free lunch theorem (philosophy of mathematics)
• Topkis's theorem (economics)

Game theory, economics, social and behavioral sciences

• Alchian–Allen theorem (economics)
• Arrow's impossibility theorem (game theory)
• Arrow-Lind theorem (welfare economics)
• Bishop–Cannings theorem (economics)
• Bondareva–Shapley theorem (economics)
• Coase theorem (economics)
• Duggan–Schwartz theorem (voting theory)
• Edgeworth's limit theorem (economics)
• Faustman–Ohlin theorem (economics)
• Fisher separation theorem (economics)
• Folk theorem (game theory)
• Fundamental theorem of arbitrage-free pricing (financial mathematics)
• Fundamental theorems of welfare economics (economics)
• Gibbard–Satterthwaite theorem (voting methods)
• Heckscher–Ohlin theorem (economics)
• Holmström's theorem (economics)
• Kuhn's theorem (game theory)
• Lerner symmetry theorem (economics)
• May's theorem (game theory)
• Modigliani–Miller theorem (finance theory)
• Morton's theorem (game theory)
• Moving equilibrium theorem (economics)
• Mutual fund separation theorem (financial mathematics)
• No-trade theorem (economics)
• Rationality theorem (politics)
• Rybczynski theorem (economics)
• Sonnenschein–Mantel–Debreu Theorem (economics)
• Sprague–Grundy theorem (combinatorial game theory)
• Stolper–Samuelson theorem (economics)

Biology and other natural sciences

• Marginal value theorem (biology, optimization)

Systems theory; control

• Artstein's theorem (control theory)
• Krener's theorem (control theory)
• Lyapunov–Malkin theorem (stability theory)
• Orbit theorem (Nagano–Sussmann) (control theory)

Information and communication, circuits

• Kraft–McMillan theorem (coding theory)
• Nyquist–Shannon sampling theorem (information theory)
• Shannon–Hartley theorem (information theory)
• Shannon's source coding theorem (information theory)
• Shannon's theorem (information theory)
• Ugly duckling theorem (computer science)