List of theorems

• 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

Logics and foundations

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

Combinatorics

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

Order, lattices, ordered algebraic structures

• Birkhoff's representation theorem
• Boolean prime ideal theorem
• Bourbaki–Witt theorem
• Cantor's isomorphism theorem
• Dilworth's theorem
• Four functions theorem
• Hahn embedding theorem
• Hausdorff maximality theorem
• Kleene fixed-point theorem
• Knaster–Tarski theorem
• Kruskal's tree theorem
• Shannon's expansion theorem
• Stone's representation theorem for Boolean algebras
• Szpilrajn extension theorem

General algebraic systems

• Fundamental theorem on homomorphisms
• Isomorphism theorem
• Lattice theorem

Number theory

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

Field theory and polynomials

• Abel–Ruffini theorem
• Artin–Schreier theorem
• Chevalley–Warning theorem
• Diller–Dress theorem
• Fundamental theorem of Galois theory
• Hasse–Arf theorem
• Hilbert's theorem 90
• Isomorphism extension theorem
• Joubert's theorem
• Lagrange's theorem
• Mason–Stothers theorem
• Polynomial remainder theorem
• Primitive element theorem
• Rational root theorem
• Solutions of a general cubic equation
• Solutions of a general quartic equation
• Strassmann's theorem
• Sturm's theorem
• Vieta's formulas

Commutative algebra

• Artin approximation theorem
• Bézout's identity
• Chinese remainder theorem
• Cohen structure theorem
• Factor theorem
• Fundamental theorem of arithmetic
• Going-up and going-down theorems
• Hilbert's basis theorem
• Hilbert's syzygy theorem
• Integral root theorem
• Krull's principal ideal theorem
• Lasker–Noether theorem
• Linear congruence theorem
• Quillen–Suslin theorem
• Rédei's theorem
• Schwartz–Zippel theorem
• Structure theorem for finitely generated modules over a principal ideal domain
• Unmixedness theorem

Algebraic geometry

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

Linear and multilinear algebra; matrix theory

• Amitsur–Levitzki theorem
• Binomial inverse theorem
• Birkhoff–Von Neumann theorem
• Bregman–Minc inequality
• Cauchy-Binet formula
• Cayley–Hamilton theorem
• Dimension theorem for vector spaces
• Euler's rotation theorem
• Exchange theorem
• Gamas's Theorem
• Gershgorin circle theorem
• Inverse eigenvalues theorem
• Perron–Frobenius theorem
• Principal axis theorem
• Rank–nullity theorem
• Rouché–Capelli theorem
• Sinkhorn's theorem
• Specht's theorem
• Spectral theorem
• Sylvester's determinant theorem
• Sylvester's law of inertia
• Witt's theorem

Associative rings and algebras

• Artin–Wedderburn theorem
• Artin–Zorn theorem
• Brauer–Cartan–Hua theorem
• Frobenius theorem
• Goldie's theorem
• Jacobson density theorem
• Jacobson–Bourbaki theorem
• Levitzky's theorem
• Regev's theorem
• Skolem–Noether theorem
• Wedderburn's little theorem
• Wedderburn's theorem

Nonassociative rings and algebras

• Ado's theorem
• Goddard–Thorn theorem
• Hurwitz's theorem
• Jacobson–Morozov theorem
• Levi's theorem
• Lie's theorem
• Poincaré–Birkhoff–Witt theorem
• Shirshov–Cohn theorem
• Shirshov–Witt theorem

Category theory and homological algebra

• Beck's monadicity theorem
• Bruguières modularity theorem
• Freyd's adjoint functor theorem
• Golod–Shafarevich theorem
• Lawvere's fixed-point theorem
• Mitchell's embedding theorem
• The duality theorem
• Yoneda lemma

K-theory

• Atiyah–Segal completion theorem
• Snaith's theorem

Group theory and generalizations

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

Topological groups, Lie groups

• Cartan's theorem
• Harish–Chandra theorem
• Harish–Chandra's regularity theorem
• Iwasawa decomposition
• Kempf–Ness theorem
• Lie's third theorem
• Montgomery-Zippin-Gleason theorem
• Plancherel theorem for spherical functions
• Trombi–Varadarajan theorem

Real functions

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

Measure and integration

• Banach–Tarski theorem
• Brunn–Minkowski theorem
• Cameron–Martin theorem
• Carathéodory's extension theorem
• Cramér–Wold theorem
• Disintegration theorem
• Dominated convergence theorem
• Egorov's theorem
• Fatou–Lebesgue theorem
• Fubini's theorem
• Hahn decomposition theorem
• Hahn–Kolmogorov theorem
• Ham sandwich theorem
• Hobby–Rice theorem
• Kōmura's theorem
• Lebesgue's decomposition theorem
• Lebesgue's density theorem
• Maharam's theorem
• Minlos's theorem
• Monotone class theorem
• Prokhorov's theorem
• Radon–Nikodym theorem
• Schilder's theorem
• Schröder–Bernstein theorem for measurable spaces
• Stein–Strömberg theorem
• Steinhaus theorem
• Stone–Tukey theorem
• Structure theorem for Gaussian measures
• Vitali convergence theorem
• Vitali theorem
• Vitali–Hahn–Saks theorem

Functions of a complex variable

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

Several complex variables and analytic spaces

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

Special functions

• De Moivre's theorem
• Hölder's theorem
• Multiplication theorem

Ordinary differential equations

• Carathéodory's existence theorem
• Floquet's theorem
• Fuchs's theorem
• Kharitonov's theorem
• Kneser's theorem
• Liénard's theorem
• Markus−Yamabe theorem
• Peano existence theorem
• Picard-Lindelöf theorem
• Shift theorem
• Sturm–Picone comparison theorem

Partial differential equations

• Cartan–Kähler theorem
• Cartan–Kuranishi prolongation theorem
• Cauchy–Kowalevski theorem
• Malgrange–Ehrenpreis theorem

Dynamical systems and ergodic theory

• Autonomous convergence theorem
• Banach fixed-point theorem
• Bendixson–Dulac theorem
• Birkhoff's theorem
• Conley–Zehnder theorem
• Curtis–Hedlund–Lyndon theorem
• Hartman–Grobman theorem
• Kolmogorov–Arnold–Moser theorem
• Krylov–Bogolyubov theorem
• Maximal ergodic theorem
• No wandering domain theorem
• Noether's theorem
• Ornstein theorem
• Oseledec theorem
• Peixoto's theorem
• Poincaré–Bendixson theorem
• Poincaré recurrence theorem
• Ratner's theorems
• Sarkovskii's theorem
• Takens's theorem

Difference and functional equations

• Euler's theorem on homogeneous functions

Sequence, series, summability

• Abel's theorem
• Abelian and Tauberian theorems
• Absolute convergence theorem
• Cesàro's theorem
• Hardy–Littlewood tauberian theorem
• Riemann series theorem
• Silverman–Toeplitz theorem
• Śleszyński–Pringsheim theorem
• Stolz–Cesàro theorem

Approximations and expansions

• Stone–Weierstrass theorem
• Taylor's theorem

Harmonic analysis on Euclidean spaces

• Balian–Low theorem
• Bernstein's theorem
• Carleson's theorem
• Convolution theorem
• Denjoy theorem
• Fourier inversion theorem
• Fourier theorem
• Hausdorff-Young inequality
• Lauricella's theorem
• Paley-Wiener theorem
• Parseval's theorem
• Plancherel theorem
• Riesz–Fischer theorem
• Szegő limit theorems
• Wiener's tauberian theorem
• Wiener–Ikehara theorem

Abstract harmonic analysis

• F. and M. Riesz theorem
• Peter–Weyl theorem
• Pontryagin duality theorem

Integral transforms, operational calculus

• Final value theorem
• Initial value theorem
• Mellin inversion theorem
• Stahl's theorem
• Titchmarsh theorem

Integral equations

• Fredholm's theorem

Functional analysis

• Analytic Fredholm theorem
• Banach–Alaoglu theorem
• Banach–Mazur theorem
• Banach–Steinhaus theorem
• Choquet–Bishop–de Leeuw theorem
• Closed range theorem
• Dunford–Schwartz theorem
• Eberlein–Šmulian theorem
• Goldstine theorem
• Hahn–Banach theorem
• Hilbert projection theorem
• Kachurovskii's theorem
• Kirszbraun theorem
• M. Riesz extension theorem
• Milman–Pettis theorem
• Moore–Aronszajn theorem
• Orlicz–Pettis theorem
• Quotient of subspace theorem
• Riesz representation theorem
• Schauder fixed-point theorem
• Schwartz kernel theorem
• Sobczyk's theorem
• Sobolev embedding theorem
• Solèr's theorem
• Tikhonov fixed-point theorem
• Trudinger's theorem

Operator theory

• Aronszajn–Smith theorem
• Atiyah–Singer index theorem
• Atkinson's theorem
• Babuška–Lax–Milgram theorem
• Banach–Stone theorem
• Bauer–Fike theorem
• Bounded inverse theorem
• Browder–Minty theorem
• Choi's theorem on completely positive maps
• Commutation theorem
• Fuglede's theorem
• Gelfand–Mazur theorem
• Gelfand–Naimark theorem
• Hardy–Littlewood maximal theorem
• Hellinger-Toeplitz theorem
• Hilbert–Schmidt theorem
• Hille–Yosida theorem
• Kaplansky density theorem
• Kuiper's theorem
• Lax–Milgram theorem
• Lions–Lax–Milgram theorem
• Lumer–Phillips theorem
• Marcinkiewicz theorem
• Mazur–Ulam theorem
• Mercer's theorem
• Min-max theorem
• Moreau's theorem
• Nash–Moser theorem
• Open mapping theorem
• Peetre theorem
• Riesz–Thorin theorem
• Ryll-Nardzewski fixed-point theorem
• Sazonov's theorem
• Schröder–Bernstein theorems for operator algebras
• Stinespring factorization theorem
• Stone's theorem on one-parameter unitary groups
• Sz.-Nagy's dilation theorem
• Tomita's theorem
• Von Neumann bicommutant theorem
• Von Neumann's theorem

Calculus of variations and optimal control; optimization

• Caristi fixed-point theorem
• Envelope theorem
• Isoperimetric theorem
• Minimax theorem
• Mountain pass theorem
• Noether's second theorem
• Parthasarathy's theorem
• Sion's minimax theorem
• Tonelli's theorem

Geometry

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

Convex and discrete geometry

• Alexandrov's uniqueness theorem
• Balinski's theorem
• Bang's theorem
• Besicovitch covering theorem
• Blaschke selection theorem
• Bolyai–Gerwien theorem
• Busemann's theorem
• Carathéodory's theorem
• Cauchy's theorem
• Classification of Platonic solids
• de Bruijn's theorem
• Descartes's theorem on total angular defect
• Erdős–Anning theorem
• Erdős–Nagy theorem
• Erdős–Szekeres theorem
• Fáry's theorem
• Fenchel's duality theorem
• Fenchel–Moreau theorem
• Hadwiger's theorem
• Helly's theorem
• Holditch's theorem
• John ellipsoid
• Jung's theorem
• Kepler conjecture
• Kirchberger's theorem
• Krein–Milman theorem
• Minkowski's theorem
• Minkowski's second theorem
• Minkowski–Hlawka theorem
• Monsky's theorem
• Pick's theorem
• Pizza theorem
• Radon's theorem
• Separating axis theorem
• Steinitz theorem
• Stewart's theorem
• Supporting hyperplane theorem
• Sylvester–Gallai theorem
• Szemerédi–Trotter theorem
• Tverberg's theorem
• Vitali covering theorem
• Wallace–Bolyai–Gerwien theorem

Differential geometry

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

General topology

• Arzelà–Ascoli theorem
• Baire category theorem
• Bing metrization theorem
• Bolzano–Weierstrass theorem
• Borsuk–Ulam theorem
• Brouwer fixed-point theorem
• Cantor's intersection theorem
• Closed graph theorem
• Extreme value theorem
• Fixed-point theorems in infinite-dimensional spaces
• Hairy ball theorem
• Hahn–Mazurkiewicz theorem
• Heine–Borel theorem
• Heine–Cantor theorem
• Jordan curve theorem
• Kuratowski's closure-complement problem
• Lebesgue covering dimension
• Metrization theorems
• Nagata–Smirnov metrization theorem
• Netto's theorem
• Parovicenko's theorem
• Tietze extension theorem
• Tychonoff's theorem

Algebraic topology

• Acyclic models theorem
• Blakers–Massey theorem
• Bott periodicity theorem
• Brown's representability theorem
• Cellular approximation theorem
• Dold–Thom theorem
• Eilenberg–Ganea theorem
• Eilenberg–Zilber theorem
• Euler's polyhedron theorem
• Excision theorem
• Freudenthal suspension theorem
• Hilton–Milnor theorem
• Homotopy excision theorem
• Hopf theorem
• Hurewicz theorem
• Künneth theorem
• Invariance of domain
• Landweber exact functor theorem
• Lefschetz fixed-point theorem
• Lefschetz–Hopf theorem
• Leray–Hirsch theorem
• Nielsen fixed-point theorem
• Nilpotence theorem
• Poincaré duality theorem
• Seifert–van Kampen theorem
• Simplicial approximation theorem
• Stallings–Zeeman theorem
• Sullivan conjecture
• Universal coefficient theorem
• Vietoris–Begle mapping theorem
• Whitehead theorem
• Whitney–Graustein Theorem

Manifolds and cell complexes

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

Global analysis, analysis on manifolds

• Radó's theorem

Probability theory and stochastic processes

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

Statistics

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

Numerical analysis

• Godunov's theorem
• Kantorovich theorem
• Lax-Richtmyer theorem
• Lax–Wendroff theorem
• Marsaglia's theorem

Computer science

• Akra–Bazzi theorem
• Art gallery theorem
• CAP theorem
• Chomsky–Schützenberger enumeration theorem
• Chomsky–Schützenberger representation theorem
• Codd's theorem
• Compression theorem
• Cook's theorem
• Fagin's theorem
• Full employment theorem
• Gap theorem
• Gottesman–Knill theorem
• Holland's schema theorem
• Immerman–Szelepcsényi theorem
• Karp–Lipton theorem
• Ladner's theorem
• Lamé’s theorem
• Linear speedup theorem
• Master theorem (analysis of algorithms)
• Max/min_CSP/Ones_classification_theorems
• Myhill–Nerode theorem
• No free lunch theorem (search and optimization)
• PCP theorem
• Pseudorandom generator theorem
• Quantum threshold theorem
• Reversed compound agent theorem
• Rice's theorem
• Rice–Shapiro theorem
• Savitch's theorem
• Schaefer's dichotomy theorem
• Sipser–Lautemann theorem
• Smn theorem
• Space hierarchy theorem
• Speedup theorem
• Structured program theorem
• Time hierarchy theorem
• Toda's theorem
• Universal approximation theorem
• Valiant–Vazirani theorem

Mechanics of particles and systems

• Chasles' theorem
• Chasles' theorem
• Helmholtz theorem (classical mechanics)
• König's theorem
• Lami's theorem
• Liouville's theorem
• Parallel axis theorem
• Perpendicular axis theorem
• Virial theorem

Mechanics of deformable solids

• Betti's theorem
• Castigliano's first and second theorems
• Clapeyron's theorem
• Saint-Venant's theorem
• Theorem of three moments

Fluid mechanics

• Buckingham π theorem
• Helmholtz's theorems
• Kelvin's circulation theorem
• Kutta–Joukowski theorem
• Reynolds transport theorem
• Taylor–Proudman theorem

Optics, electromagnetic theory

• Blondel's theorem
• Earnshaw's theorem
• Maximum power theorem
• Norton's theorem
• Optical theorem
• Poynting's theorem
• Thévenin's theorem

Classical thermodynamics, heat transfer

• Carnot's theorem
• Clausius theorem

Quantum theory

• Adiabatic theorem
• Bell's theorem
• Bogoliubov–Parasyuk theorem
• Byers–Yang theorem
• C-theorem
• Cluster decomposition theorem
• Coleman–Mandula theorem
• Elitzur's theorem
• Furry's theorem
• Gell-Mann and Low theorem
• Gleason's theorem
• Goldstone's theorem
• Haag's theorem
• Haag–Łopuszański–Sohnius theorem
• Hellmann–Feynman theorem
• Kinoshita–Lee–Nauenberg theorem
• Kochen–Specker theorem
• Kramers' theorem
• Nielsen–Ninomiya theorem
• No-broadcasting theorem
• No-cloning theorem
• No-communication theorem
• No-deleting theorem
• Optical equivalence theorem
• Osterwalder–Schrader theorem
• Pandya theorem
• Pomeranchuk's theorem
• Reeh–Schlieder theorem
• Solovay–Kitaev theorem
• Spin–statistics theorem
• Stone–von Neumann theorem
• Supersymmetry nonrenormalization theorems
• Vafa–Witten theorem
• Weinberg–Witten theorem
• Wick's theorem
• Wigner–Eckart theorem

Statistical mechanics, structure of matter

• Bohr–van Leeuwen theorem
• Crooks fluctuation theorem
• Crystallographic restriction theorem
• Equipartition theorem
• Fluctuation dissipation theorem
• Fluctuation theorem
• H-theorem
• Hohenberg–Kohn theorems
• Lee–Yang theorem
• Mermin–Wagner theorem

Relativity and gravitational theory

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

Astronomy and astrophysics

• Clairaut's theorem
• Shell theorem

Operations research, mathematical programming

• Analyst's traveling salesman theorem
• Arrival theorem
• Blum's speedup theorem
• Max flow min cut theorem
• No free lunch theorem
• Topkis's theorem

Game theory, economics, social and behavioral sciences

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

Biology and other natural sciences

• Marginal value theorem

Systems theory; control

• Artstein's theorem
• Krener's theorem
• Lyapunov-Malkin theorem
• Orbit theorem (Nagano–Sussmann)

Information and communication, circuits

• Kraft–McMillan theorem
• Nyquist–Shannon sampling theorem
• Shannon–Hartley theorem
• Shannon's source coding theorem
• Shannon's theorem
• Ugly duckling theorem