List of theorems

• 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) • 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) • Gentzen's consistency proof (proof theory) • 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) • Unique homomorphic extension theorem (mathematical logic) • 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's 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's theorem on perfect matchings (graph theory) • Turán's theorem (graph theory) • Van der Waerden's theorem (combinatorics) • Vizing's theorem (graph theory) • 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) • Kummer's 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' 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) • Yoneda lemma (category theory) ==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) • Nagao's theorem (group 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 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==