- List of theorems
This is a

**list of**, by Wikipedia page. See alsotheorem s

*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 fromtheoretical physics ,economics , and other applied fields.__NOTOC__

**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 field s")

*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 operator s", "harmonic analysis ")

*Atkinson's theorem ("operator theory ")**B***

Babuška-Lax-Milgram theorem ("partial differential equation s")

*Baily-Borel theorem ("algebraic geometry ")

*Baire category theorem ("topology ", "metric space s")

*Balian-Low theorem ("Fourier analysis ")

*Banach-Alaoglu theorem ("functional analysis ")

*Banach fixed point theorem ("metric space s,differential equation s")

*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 system s")

*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 number s")

*Beurling–Lax theorem ("Hardy space s")

*Bézout's theorem ("algebraic curve s")

*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 number s")

*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 number s")

*Carnot's theorem ("geometry ")

*Carnot's theorem ("thermodynamics ")

*Cartan–Hadamard theorem ("Riemannian geometry ")

*Cartan–Kähler theorem ("partial differential equation s")

*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 equation s")

*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 transform s")

*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 space s,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 group s")

*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 representation s")

*Frobenius theorem ("foliation s")

*Frobenius theorem ("abstract algebra s")

*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 method s")

*Girsanov's theorem ("stochastic process es")

*Glaisher's theorem ("number theory ")

*Gleason's theorem ("Hilbert space ")

*Glivenko's theorem ("mathematical logic ")

*Goddard-Thorn theorem ("vertex algebra s")

*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 group s", "representation theory ", "invariant theory ")

*Hadamard three-circle theorem ("complex analysis ")

*Hadwiger's theorem ("geometry ", "measure theory ")

*Hahn embedding theorem ("ordered group s")

*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 set s")

*Herbrand's theorem ("logic ")

*Herbrand–Ribet theorem ("cyclotomic field s")

*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 field s")

*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 curve s")**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 ("curve s", "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 graph s")

*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 group s", "representation theory ")

*Liénard's theorem ("dynamical system s")

*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 function s")

*Liouville's theorem (conformal mappings) ("conformal mapping s")

*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 relation s", "asymptotic analysis ")

*Maschke's theorem ("group representation s")

*Matiyasevich's theorem ("mathematical logic ")

*Max flow min cut theorem ("graph theory ")

*Max Noether's theorem ("algebraic geometry ")

*Maximum power theorem ("electrical circuit s")

*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 space s")

*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 language s")**N***

Nachbin's theorem ("complex analysis ")

*Nagata-Smirnov metrization theorem ("general topology ")

*Nagell-Lutz theorem ("elliptic curve s")

*Nash embedding theorem ("differential geometry ")

*Newlander-Niremberg theorem ("differential geometry ")

*Nicomachus's theorem ("number theory ")

*Nielsen-Schreier theorem ("free group s")

*No cloning theorem ("quantum computation ")

*No wandering domain theorem ("ergodic theory ")

*Noether's theorem ("Lie group s", "calculus of variations ", "differential invariant s", "physics ")

*No-ghost theorem ("vertex algebra s")

*Norton's theorem ("electrical network s")

*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 transform s")

*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 ("conic s")

*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 system s")

*Poincaré-Birkhoff-Witt theorem ("universal enveloping algebra s")

*Poincaré duality theorem ("algebraic topology ofmanifold s")

*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 set s")

*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 surface s", "algebraic curve s")

*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 system s")

*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 algebra s")

*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 circuit s")

*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 manifold s")

*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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