List of theorems


List of theorems

This is a list of theorems, by Wikipedia page. See also
*list of fundamental theorems
*list of lemmas
*list of conjectures
*list of inequalities
*list of mathematical proofs
*list of misnamed theorems
*Existence theorem
*Classification of finite simple groups

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

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0–9

*15 and 290 theorems ("number theory")
*2π theorem ("Riemannian geometry")

A

*AF+BG theorem ("algebraic geometry")
*Abel's binomial theorem ("combinatorics")
*Abel's theorem ("mathematical analysis")
*Abelian and tauberian theorems ("mathematical analysis")
*Abel-Ruffini theorem ("theory of equations", "Galois theory")
*Abouabdillah's theorem ("geometry","number theory")
*Alperin-Brauer-Gorenstein theorem ("finite groups")
*Analytic Fredholm theorem ("functional analysis")
*Anderson's theorem ("real analysis")
*Ankeny-Artin-Chowla theorem ("number theory")
*Apéry's theorem ("number theory")
*Apollonius' theorem ("plane geometry")
*Aronszajn-Smith theorem ("functional analysis")
*Arrow's impossibility theorem ("game theory")
*Artin-Schreier theorem ("real closed fields")
*Artin-Wedderburn theorem ("abstract algebra")
*Arzelà-Ascoli theorem ("functional analysis")
*Atiyah–Bott fixed-point theorem ("differential topology")
*Atiyah-Segal completion theorem ("homotopy theory")
*Atiyah-Singer index theorem ("elliptic differential operators", "harmonic analysis")
*Atkinson's theorem ("operator theory")

B

*Babuška-Lax-Milgram theorem ("partial differential equations")
*Baily-Borel theorem ("algebraic geometry")
*Baire category theorem ("topology", "metric spaces")
*Balian-Low theorem ("Fourier analysis")
*Banach-Alaoglu theorem ("functional analysis")
*Banach fixed point theorem ("metric spaces, differential equations")
*Banach-Steinhaus theorem ("functional analysis")
*Barbier's theorem ("geometry")
*Bapat-Beg theorem ("statistics")
*Bass's theorem ("group theory")
*Bayes' theorem ("probability")
*Beatty's theorem ("diophantine approximation")
*Beauville–Laszlo theorem ("vector bundles")
*Beck's monadicity theorem ("category theory")
*Beck's theorem ("incidence geometry")
*Bell's theorem ("quantum theory - physics")
*Bendixson-Dulac theorem ("dynamical systems")
*Berger-Kazdan comparison theorem ("Riemannian geometry")
*Bernstein's theorem ("functional analysis")
*Berry-Esséen theorem ("probability theory")
*Bertrand's ballot theorem ("probability theory", "combinatorics")
*Bertrand's postulate ("prime numbers")
*Beurling–Lax theorem ("Hardy spaces")
*Bézout's theorem ("algebraic curves")
*Bing metrization theorem("general topology")
*Binomial theorem ("algebra, combinatorics")
*Birkhoff-Grothendieck theorem ("vector bundles")
*Birkhoff's theorem ("ergodic theory")
*Blaschke selection theorem ("geometric topology")
*Bloch's theorem ("complex analysis")
*Bôcher's theorem ("complex analysis")
*Bohr-Mollerup theorem ("gamma function")
*Bolyai-Gerwien theorem ("geometry")
*Bolzano's theorem ("real analysis, calculus")
*Bolzano-Weierstrass theorem ("real analysis, calculus")
*Bombieri's theorem ("number theory")
*Bombieri–Friedlander–Iwaniec theorem ("number theory")
*Bondy-Chvátal theorem ("graph theory")
*Bonnet theorem ("differential geometry")
*Boolean prime ideal theorem ("mathematical logic")
*Borel-Bott-Weil theorem ("representation theory")
*Borel-Weil theorem ("representation theory")
*Borel fixed-point theorem ("algebraic geometry")
*Borsuk-Ulam theorem ("topology")
*Bott-Duffin theorem ("network theory")
*Bott periodicity theorem ("homotopy theory")
*Bounded inverse theorem ("operator theory")
*Bourbaki–Witt theorem ("order theory")
*Branching theorem ("complex manifold")
*Brauer–Suzuki theorem ("finite groups")
*Brauer's three main theorems ("finite groups")
*Brouwer fixed point theorem ("topology")
*Browder-Minty theorem ("operator theory")
*Brown's representability theorem ("homotopy theory")
*Bruck-Chowla-Ryser theorem ("combinatorics")
*Brun's theorem ("number theory")
*Brun-Titchmarsh theorem ("number theory")
*Brunn-Minkowski theorem ("Riemannian geometry")
*Buckingham π theorem ("dimensional analysis")
*Busemann's theorem ("Euclidean geometry")
*Butterfly theorem ("Euclidean geometry")

C

*Cameron-Martin theorem ("measure theory")
*Cantor–Bernstein–Schroeder theorem ("Set theory", "cardinal numbers")
*Cantor's theorem ("Set theory", "Cantor's diagonal argument")
*Carathéodory-Jacobi-Lie theorem ("symplectic topology")
*Carathéodory's theorem ("conformal mapping")
*Carathéodory's theorem ("convex hull")
*Carathéodory's theorem ("measure theory")
*Carathéodory's extension theorem ("measure theory")
*Caristi fixed point theorem ("fixed points")
*Carmichael's theorem ("Fibonacci numbers")
*Carnot's theorem ("geometry")
*Carnot's theorem ("thermodynamics")
*Cartan–Hadamard theorem ("Riemannian geometry")
*Cartan–Kähler theorem ("partial differential equations")
*Cartan's theorem ("Lie group")
*Cartan's theorems A and B ("several complex variables")
*Castigliano's first and second theorems ("structural analysis")
*Cauchy integral theorem ("Complex analysis")
*Cauchy-Hadamard theorem ("Complex analysis")
*Cauchy-Kowalevski theorem ("partial differential equations")
*Cayley-Hamilton theorem ("Linear algebra")
*Cayley's theorem ("group theory")
*Central limit theorem ("probability")
*Ceva's theorem ("geometry")
*Chebotarev's density theorem ("number theory")
*Chen's theorem ("number theory")
*Chern-Gauss-Bonnet theorem ("differential geometry")
*Chevalley–Shephard–Todd theorem ("finite group")
*Chinese remainder theorem ("number theory")
*Choi's theorem on completely positive maps ("operator theory")
*Chowla-Mordell theorem ("number theory")
*Church-Rosser theorem ("lambda calculus")
*Clark-Ocone theorem ("stochastic processes")
*Classification of finite simple groups ("group theory")
*Closed graph theorem ("functional analysis")
*Cluster decomposition theorem ("quantum field theory")
*Coase theorem ("economics")
*Cochran's theorem ("statistics")
*Codd's theorem ("relational model")
*Cohn's irreducibility criterion ("polynomials")
*Coleman-Mandula theorem ("quantum field theory")
*Compactness theorem ("mathematical logic")
*Conservativity theorem ("mathematical logic")
*Convolution theorem ("Fourier transforms")
*Cook's theorem ("computational complexity theory")
*Corona theorem ("Complex analysis")
*Cox's theorem ("probability foundations")
*Critical line theorem ("number theory")
*Crystallographic restriction theorem ("group theory", "crystallography")
*Curtis–Hedlund–Lyndon theorem ("cellular automata")
*Cut-elimination theorem ("proof theory")
*Cybenko theorem ("neural networks")

D

*Dandelin's theorem ("geometry")
*Danskin's theorem ("convex analysis")
*Darboux's theorem ("real analysis")
*Darboux's theorem ("symplectic topology")
*Davenport–Schmidt theorem ("number theory", "Diophantine approximations")
*De Branges' theorem ("complex analysis")
*De Finetti's theorem ("probability")
*De Gua's theorem ("geometry")
*De Moivre's theorem ("complex analysis")
*De Rham's theorem ("differential topology")
*Deduction theorem ("logic")
*Desargues' theorem ("geometry")
*Descartes' theorem ("geometry")
*Dilworth's theorem ("combinatorics", "order theory")
*Dimension theorem for vector spaces ("vector spaces, linear algebra")
*Dini's theorem ("analysis")
*Dirichlet's theorem on arithmetic progressions ("number theory")
*Dirichlet's unit theorem ("algebraic number theory")
*Divergence theorem ("vector calculus")
*Dominated convergence theorem ("Lebesgue integration")
*Donaldson's theorem ("differential topology")
*Donsker's theorem ("probability theory")

E

*Earnshaw's theorem ("electrostatics")
*Easton's theorem ("set theory")
*Ehresmann's theorem ("differential topology")
*Eilenberg–Zilber theorem ("algebraic topology")
*Envelope theorem ("calculus of variations")
*Equal incircles theorem ("Euclidean geometry")
*Equidistribution theorem ("ergodic theory")
*Equipartition theorem ("ergodic theory")
*Erdős–Anning theorem ("discrete geometry")
*Erdos-Dushnik-Miller theorem ("set theory")
*Erdős-Kac theorem ("number theory")
*Erdős-Ko-Rado theorem ("combinatorics")
*Erdős-Stone theorem ("graph theory")
*Euclid's theorem ("number theory")
*Euclid-Euler Theorem ("number theory")
*Euler's rotation theorem ("geometry")
*Euler's theorem ("number theory")
*Euler's theorem on homogeneous functions ("multivariate calculus")
*Extreme value theorem

F

*Faltings' theorem ("diophantine geometry")
*Fáry's theorem ("graph theory")
*Fary-Milnor theorem ("knot theory")
*Fatou's theorem ("complex analysis")
*Fatou-Lebesgue theorem ("real analysis")
*Feit-Thompson theorem ("finite groups")
*Fermat's last theorem ("number theory")
*Fermat's little theorem ("number theory")
*Fermat polygonal number theorem ("number theory")
*Fieller's theorem ("statistics")
*Fisher separation theorem ("economics")
*Fitting's theorem ("group theory")
*Five color theorem ("graph theory")
*Fixed point theorems in infinite-dimensional spaces
*Fluctuation dissipation theorem ("physics")
*Fluctuation theorem ("statistical mechanics")
*Four color theorem ("graph theory")
*Fourier inversion theorem ("harmonic analysis")
*Fourier theorem ("harmonic analysis")
*Freudenthal suspension theorem ("homotopy theory")
*Freyd's adjoint functor theorem ("category theory")
*Frobenius reciprocity theorem ("group representations")
*Frobenius theorem ("foliations")
*Frobenius theorem ("abstract algebras")
*Fubini's theorem ("integration")
*Fuglede's theorem ("functional analysis")
*Fulton-Hansen connectedness theorem ("algebraic geometry")
*Fundamental theorem of algebra ("complex analysis")
*Fundamental theorem of arbitrage-free pricing ("financial mathematics")
*Fundamental theorem of arithmetic ("number theory")
*Fundamental theorem of calculus ("calculus")
*Fundamental theorem on homomorphisms ("abstract algebra")

G

*Gauss theorem ("vector calculus")
*Gauss's Theorema Egregium ("differential geometry")
*Gauss-Bonnet theorem ("differential geometry")
*Gauss-Lucas theorem ("complex analysis")
*Gauss-Markov theorem ("statistics")
*Gauss-Wantzel theorem ("geometry")
*Gelfand–Naimark theorem ("functional analysis")
*Gelfond-Schneider theorem ("transcendence theory")
*Gibbard-Satterthwaite theorem ("voting methods")
*Girsanov's theorem ("stochastic processes")
*Glaisher's theorem ("number theory")
*Gleason's theorem ("Hilbert space")
*Glivenko's theorem ("mathematical logic")
*Goddard-Thorn theorem ("vertex algebras")
*Gödel's completeness theorem ("mathematical logic")
*Gödel's incompleteness theorem ("mathematical logic")
*Going-up and going-down theorems ("commutative algebra")
*Goldie's theorem ("ring theory")
*Goodstein's theorem ("mathematical logic")
*Great orthogonality theorem ("group theory")
*Green-Tao theorem ("number theory")
*Green's theorem ("vector calculus")
*Gromov's compactness theorem ("Riemannian geometry")
*Gromov's theorem ("group theory")
*Gromov-Ruh theorem ("differential geometry")
*Gross-Zagier theorem ("number theory")
*Grothendieck's connectedness theorem ("algebraic geometry")
*Grushko theorem ("group theory")

H

*H-theorem ("thermodynamics")
*Haag's theorem ("quantum field theory")
*Haboush's theorem ("algebraic groups", "representation theory", "invariant theory")
*Hadamard three-circle theorem ("complex analysis")
*Hadwiger's theorem ("geometry", "measure theory")
*Hahn embedding theorem ("ordered groups")
*Hairy ball theorem ("algebraic topology")
*Hahn-Banach theorem ("functional analysis")
*Hahn–Kolmogorov theorem ("measure theory")
*Hales-Jewett theorem ("combinatorics")
*Ham sandwich theorem ("topology")
*Hardy–Littlewood maximal theorem ("real analysis")
*Hardy–Ramanujan theorem ("number theory")
*Harish-Chandra's regularity theorem ("representation theory")
*Harnack's theorem ("complex analysis")
*Hartogs' theorem ("complex analysis")
*Hasse's theorem on elliptic curves ("number theory")
*Hasse–Minkowski theorem ("number theory")
*Heine-Borel theorem ("real analysis")
*Heine–Cantor theorem ("metric geometry")
*Hellinger-Toeplitz theorem ("functional analysis")
*Helly's theorem ("convex sets")
*Herbrand's theorem ("logic")
*Herbrand–Ribet theorem ("cyclotomic fields")
*Higman's embedding theorem ("group theory")
*Hilbert's basis theorem ("commutative algebra","invariant theory")
*Hilbert's Nullstellensatz (theorem of zeroes) ("commutative algebra", "algebraic geometry")
*Hilbert-Schmidt theorem ("functional analysis")
*Hilbert-Speiser theorem ("cyclotomic fields")
*Hilbert's theorem (differential geometry)
*Hille–Yosida theorem ("functional analysis")
*Hindman's theorem ("Ramsey theory")
*Hinge theorem ("geometry")
*Hironaka theorem ("algebraic geometry")
*Hirzebruch–Riemann–Roch theorem ("complex manifolds")
*Holland's schema theorem ("genetic algorithm")
*Hopf-Rinow theorem ("differential geometry")
*Hurewicz theorem ("algebraic topology")
*Hurwitz's automorphisms theorem ("algebraic curves")

I

*Identity theorem for Riemann surfaces ("Riemann surfaces")
*Implicit function theorem ("vector calculus")
*Increment theorem ("mathematical analysis")
*Infinite monkey theorem ("probability")
*Integral root theorem ("algebra, polynomials")
*Integral representation theorem for classical Wiener space ("measure theory")
*Intermediate value theorem ("calculus")
*Intersection theorem ("projective geometry")
*Inverse function theorem ("vector calculus")
*Isomorphism extension theorem ("abstract algebra")
*Isomorphism theorem ("abstract algebra")
*Isoperimetric theorem ("curves", "calculus of variations")

J

*Jackson's theorem ("queueing theory")
*Jacobson density theorem ("ring theory")
*Japanese theorem ("geometry")
*Japanese theorem for concyclic polygons ("Euclidean geometry")
*Jordan curve theorem ("topology")
*Jordan-Hölder theorem ("group theory")
*Jordan-Schönflies theorem ("geometric topology")
*Jung's theorem ("geometry")

K

*Kachurovskii's theorem ("convex analysis")
*Kantorovich theorem ("functional analysis")
*Kaplansky density theorem ("von Neumann algebra")
*Khinchin's theorem ("probability")
*Kirchhoff's theorem ("graph theory")
*Kirszbraun theorem ("Lipschitz continuity")
*Kleene's recursion theorem ("recursion theory")
*Knaster-Tarski theorem ("order theory")
*Kneser theorem ("differential equations")
*Kodaira embedding theorem ("algebraic geometry")
*Koebe 1/4 theorem ("complex analysis")
*Kolmogorov-Arnold-Moser theorem ("dynamical systems")
*Kolmogorov extension theorem ("stochastic processes")
*König's theorem ("mathematical logic")
*König's theorem (graph theory) ("bipartite graphs")
*König's theorem (set theory) ("cardinal numbers")
*Kronecker's theorem ("diophantine approximation")
*Kronecker-Weber theorem ("number theory")
*Krull's principal ideal theorem ("commutative algebra")
*Krull-Schmidt theorem ("group theory")
*Kruskal's tree theorem ("order theory")
*Krylov-Bogolyubov theorem ("dynamical systems")
*Künneth theorem ("algebraic topology")
*Kurosh subgroup theorem ("group theory")

L

*Ladner's theorem ("computational complexity theory")
*Lagrange's theorem ("group theory")
*Lagrange's theorem ("number theory")
*Lagrange's four-square theorem ("number theory")
*Lagrange inversion theorem ("mathematical analysis", "combinatorics")
*Lagrange reversion theorem ("mathematical analysis", "combinatorics")
*Lambek-Moser theorem ("combinatorics")
*Lami's theorem ("statics")
*Landau prime ideal theorem ("number theory")
*Lasker–Noether theorem ("commutative algebra")
*Laurent expansion theorem ("complex analysis")
*Lax–Milgram theorem ("partial differential equations")
*Lax-Richtmyer theorem ("numerical analysis")
*Lebesgue covering dimension ("dimension theory")
*Lebesgue's decomposition theorem ("dimension theory")
*Lebesgue's density theorem ("dimension theory")
*Lee_Hwa_Chung_theorem ("symplectic topology")
*Lebesgue differentiation theorem ("real analysis")
*Le Cam's theorem ("probability theory")
*Lee–Yang theorem ("statistical mechanics")
*Lefschetz fixed point theorem ("algebraic topology")
*Lefschetz hyperplane theorem ("algebraic topology")
*Lehmann-Scheffé theorem ("statistics")
*Lester's theorem ("Euclidean plane geometry")
*Levi's theorem ("Lie groups")
*Lie's third theorem ("Lie algebra")
*Lindemann-Weierstrass theorem ("transcendence theory")
*Lie-Kolchin theorem ("algebraic groups", "representation theory")
*Liénard's theorem ("dynamical systems")
*Linear congruence theorem ("number theory", "modular arithmetic")
*Linear speedup theorem ("computational complexity theory")
*Linnik's theorem ("number theory")
*Lions-Lax-Milgram theorem ("partial differential equations")
*Liouville's theorem (complex analysis) ("entire functions")
*Liouville's theorem (conformal mappings) ("conformal mappings")
*Liouville's theorem (Hamiltonian) ("Hamiltonian mechanics")
*Löb's theorem ("mathematical logic")
*Lochs' theorem ("number theory")
*Looman–Menchoff theorem ("complex analysis")
*Löwenheim-Skolem theorem ("mathematical logic")
*Lucas' theorem ("number theory")
*Lumer-Phillips theorem ("semigroup theory")
*Luzin's theorem ("real analysis")
*Lyapunov's central limit theorem ("probability theory")

M

*Mahler's compactness theorem ("geometry of numbers")
*Mahler's theorem ("p-adic analysis")
*Malgrange–Ehrenpreis theorem ("differential equations")
*Marcinkiewicz theorem ("functional analysis")
*Marden's theorem ("polynomials")
*Marriage theorem ("combinatorics")
*Martingale representation theorem ("probability theory")
*Master theorem ("recurrence relations", "asymptotic analysis")
*Maschke's theorem ("group representations")
*Matiyasevich's theorem ("mathematical logic")
*Max flow min cut theorem ("graph theory")
*Max Noether's theorem ("algebraic geometry")
*Maximum power theorem ("electrical circuits")
*Maxwell's theorem ("probability theory")
*May's theorem ("game theory")
*Mazur's torsion theorem ("algebraic geometry")
*Mean value theorem ("calculus")
*Menelaus' theorem ("geometry")
*Menger's theorem ("graph theory")
*Mercer's theorem ("functional analysis")
*Mertens' theorems ("number theory")
*Metrization theorems ("topological spaces")
*Meusnier's theorem ("differential geometry")
*Midy's theorem ("number theory")
*Mihăilescu's theorem ("number theory")
*Milliken-Taylor theorem ("Ramsey theory")
*Milliken's tree theorem ("Ramsey theory")
*Min-max theorem ("functional analysis")
*Minimax theorem ("game theory")
*Minkowski's theorem ("geometry of numbers")
*Minkowski-Hlawka theorem ("geometry of numbers")
*Minlos' theorem ("functional analysis")
*Mitchell's embedding theorem ("category theory")
*Mittag-Leffler's theorem ("complex analysis")
*Modigliani-Miller theorem ("finance theory")
*Modularity theorem ("number theory")
*Mohr-Mascheroni theorem ("geometry")
*Monge's theorem ("geometry")
*Monodromy theorem ("complex analysis")
*Monotone convergence theorem ("mathematical analysis")
*Montel's theorem ("complex analysis")
*Mordell-Weil theorem ("number theory")
*Moreau's theorem ("convex analysis")
*Morera's theorem ("complex analysis")
*Morley's categoricity theorem ("model theory")
*Morley's trisector theorem ("geometry")
*Mountain pass theorem ("calculus of variations")
*Multinomial theorem ("algebra", "combinatorics")
*Myers theorem ("differential geometry")
*Myhill-Nerode theorem ("formal languages")

N

*Nachbin's theorem("complex analysis")
*Nagata-Smirnov metrization theorem("general topology")
*Nagell-Lutz theorem ("elliptic curves")
*Nash embedding theorem ("differential geometry")
*Newlander-Niremberg theorem ("differential geometry")
*Nicomachus's theorem ("number theory")
*Nielsen-Schreier theorem ("free groups")
*No cloning theorem ("quantum computation")
*No wandering domain theorem ("ergodic theory")
*Noether's theorem ("Lie groups", "calculus of variations", "differential invariants", "physics")
*No-ghost theorem ("vertex algebras")
*Norton's theorem ("electrical networks")
*Nyquist-Shannon sampling theorem ("information theory")

O

*Open mapping theorem ("functional analysis")
*Ornstein theorem ("ergodic theory")
*Oseledec theorem ("ergodic theory")
*Ostrowski's theorem ("number theory")
*Ostrowski-Hadamard gap theorem ("complex analysis")

P

*Paley's theorem ("algebra")
*Paley-Wiener theorem ("Fourier transforms")
*Pappus's centroid theorem ("geometry")
*Pappus's hexagon theorem ("geometry")
*Paris–Harrington theorem ("mathematical logic")
*Parovicenko's theorem ("topology")
*Parseval's theorem ("Fourier analysis")
*Pascal's theorem ("conics")
*Pasch's theorem ("order theory")
*Pentagonal number theorem ("number theory")
*Perfect graph theorem ("graph theory")
*Perron–Frobenius theorem ("matrix theory")
*Peter-Weyl theorem ("representation theory")
*Picard theorem ("complex analysis")
*Picard-Lindelöf theorem ("ordinary differential equations")
*Pick's theorem ("geometry")
*Pitman-Koopman-Darmois theorem ("statistics")
*Planar separator theorem ("graph theory")
*Plancherel theorem ("Fourier analysis")
*Plancherel theorem for spherical functions ("representation theory")
*Poincaré-Bendixson theorem ("dynamical systems")
*Poincaré-Birkhoff-Witt theorem ("universal enveloping algebras")
*Poincaré duality theorem ("algebraic topology of manifolds")
*Pompeiu's theorem ("Euclidean geometry")
*Poncelet-Steiner theorem ("geometry")
*Post's theorem ("mathematical logic")
*Preimage theorem ("differential topology")
*Prime number theorem ("number theory")
*Primitive element theorem ("field theory")
*Principal axis theorem ("linear algebra")
*Prokhorov's theorem ("measure theory")
*Proth's theorem ("number theory")
*Ptolemaios' theorem ("geometry")
*Pythagorean theorem ("geometry")

Q

*Quillen–Suslin theorem ("abstract algebra")
*Quadratic reciprocity theorem

R

*Radon's theorem ("convex sets")
*Radon-Nikodym theorem ("measure theory")
*Ramanujan-Skolem's theorem ("diophantine equations")
*Ramsey's theorem ("graph theory,combinatorics")
*Rank-nullity theorem ("linear algebra")
*Rao-Blackwell theorem ("statistics")
*Rational root theorem ("algebra,polynomials")
*Rédei's theorem ("group theory")
*Reeh-Schlieder theorem ("local quantum field theory")
*Residue theorem ("complex analysis")
*Reynolds transport theorem ("fluid dynamics")
*Rice's theorem ("recursion theory, computer science")
*Rice-Shapiro theorem ("computer science")
*Riemann mapping theorem ("complex analysis")
*Riemann-Roch theorem ("Riemann surfaces", "algebraic curves")
*Riesz representation theorem ("functional analysis,Hilbert space")
*Riesz-Thorin theorem ("functional analysis")
*Robertson-Seymour theorem ("graph theory")
*Robinson's joint consistency theorem ("mathematical logic")
*Rokhlin's theorem ("geometric topology")
*Rolle's theorem ("calculus")
*Rosser's theorem ("number theory")
*Roth's theorem ("diophantine approximation")
*Rouché's theorem ("complex analysis")
*Routh's theorem ("triangle geometry")
*Routh–Hurwitz theorem ("polynomials")
*Runge's theorem ("complex analysis")

*Sahlqvist correspondence theorem ("modal logic")
*Sarkovskii's theorem ("dynamical systems")
*Savitch's theorem ("computational complexity theory")
*Sazonov's theorem ("functional analysis")
*Schauder fixed point theorem ("functional analysis")
*Schilder's theorem ("stochastic processes")
*Schreier refinement theorem ("group theory")
*Schur's lemma ("representation theory")
*Schur's theorem ("Ramsey theory")
*Scott core theorem ("3-manifolds")
*Seifert-van Kampen theorem ("algebraic topology")
*Separating axis theorem ("convex geometry")
*Shannon's expansion theorem ("Boolean algebra")
*Shannon's theorem ("information theory")
*Siegel–Walfisz theorem ("analytic number theory")
*Silverman–Toeplitz theorem ("mathematical analysis")
*Simplicial approximation theorem ("algebraic topology")
*Sklar's theorem ("statistics")
*Skoda-El Mir theorem ("complex geometry")
*Skolem-Noether theorem ("simple algebras")
*Slutsky's theorem ("probability theory")
*Sokhatsky-Weierstrass theorem ("complex analysis")
*Soundness theorem ("mathematical logic")
*Space hierarchy theorem ("computational complexity theory")
*Spectral theorem ("functional analysis")
*Speedup theorem ("computational complexity theory")
*Sperner's theorem ("combinatorics")
*Spin-statistics theorem ("physics")
*Sprague-Grundy theorem ("combinatorial game theory")
*Squeeze theorem ("mathematical analysis")
*Stallings-Zeeman theorem ("algebraic topology")
*Stanley's reciprocity theorem ("combinatorics")
*Stark-Heegner theorem ("number theory")
*Steiner-Lehmus theorem ("triangle geometry")
*Stewart's theorem ("plane geometry")
*Stirling's theorem ("mathematical analysis")
*Stokes' theorem ("vector calculus, differential topology")
*Stolper-Samuelson theorem ("economics")
*Stone's representation theorem for Boolean algebras ("mathematical logic")
*Stone's theorem on one-parameter unitary groups ("functional analysis")
*Stone-Tukey theorem ("topology")
*Stone-von Neumann theorem ("functional analysis", "representation theory" of the "Heisenberg group", "quantum mechanics")
*Stone-Weierstrass theorem ("functional analysis")
*Strassman's theorem ("field theory")
*Structured program theorem ("computer science")
*Sturm's theorem ("theory of equations")
*Sturm-Picone comparison theorem ("differential equations")
*Subspace theorem ("Diophantine approximation")
*Supporting hyperplane theorem ("convex geometry")
*Swan's theorem ("module theory")
*Sylow theorems ("group theory")
*Sylvester's determinant theorem ("determinants")
*Sylvester's theorem ("number theory")
*Sylvester-Gallai theorem ("plane geometry")
*Sz.-Nagy's dilation theorem ("operator theory")
*Szemerédi's theorem ("combinatorics")
*Szemerédi-Trotter theorem ("combinatorics")

T

*Takagi existence theorem ("number theory")
*Tarski's indefinability theorem ("mathematical logic")
*Taylor's theorem ("calculus")
*Thales' theorem ("geometry")
*Thébault's theorem ("geometry")
*Theorem of de Moivre–Laplace ("probability theory")
*Thevenin's theorem ("electrical circuits")
*Thue's theorem
*Thue-Siegel-Roth theorem ("diophantine approximation")
*Tietze extension theorem ("general topology")
*Tijdeman's theorem ("diophantine equations")
*Tikhonov fixed point theorem ("functional analysis")
*Time hierarchy theorem ("computational complexity theory")
*Tits alternative ("geometric group theory")
*Tonelli's theorem ("functional analysis")
*Tsen's theorem ("algebraic geometry")
*Tunnell's theorem ("number theory")
*Tutte theorem ("graph theory")
*Turán's theorem ("graph theory")
*Tychonoff's theorem ("general topology")

U

*Ugly duckling theorem ("computer science")
*Uniformization theorem ("complex analysis", "differential geometry")
*Universal approximation theorem ("neural networks")
*Universal coefficient theorem ("algebraic topology")
*Unmixedness theorem ("algebraic geometry")

V

*Van der Waerden's theorem ("combinatorics")
*Vantieghems theorem ("number theory")
*Varignon's theorem ("Euclidean geometry")
*Vinogradov's theorem ("number theory")
*Virial theorem ("classical mechanics")
*Vitali convergence theorem ("measure theory")
*Vitali theorem ("measure theory")
*Vitali-Hahn-Saks theorem ("measure theory")
*Viviani's theorem ("Euclidean geometry")
*Von Neumann bicommutant theorem ("functional analysis")
*Von Neumann's theorem ("operator theory")

W

*Wedderburn's theorem ("abstract algebra")
*Weierstrass-Casorati theorem ("complex analysis")
*Weierstrass preparation theorem ("several complex variables","commutative algebra")
*Well-ordering theorem ("mathematical logic")
*Whitehead theorem ("homotopy theory")
*Whitney embedding theorem ("differential manifolds")
*Whitney extension theorem ("mathematical analysis")
*Wiener's tauberian theorem ("real analysis")
*Wiener-Ikehara theorem ("number theory")
*Wigner-Eckart theorem ("Clebsch-Gordan coefficients")
*Wilson's theorem ("number theory")

Z

*Z* theorem ("finite groups")
*ZJ theorem ("finite groups")
*Zariski's main theorem ("algebraic geometry")
*Zeckendorf's theorem ("number theory")


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