List of theorems

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This is a list of theorems, by Wikipedia page. See also

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

Contents

Top · 0–9 · A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

[edit] 0–9

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

[edit] 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-Singer index theorem (elliptic differential operators, harmonic analysis)
Atkinson's theorem (operator theory)

[edit] B

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)
Brunn-Minkowski theorem (Riemannian geometry)
Buckingham π theorem (dimensional analysis)
Busemann's theorem (Euclidean geometry)

[edit] C

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'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)
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)
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)
Cut-elimination theorem (proof theory)
Cybenko theorem (neural networks)

[edit] D

Dandelin's theorem (geometry)
Danskin's theorem (convex analysis)
Darboux's theorem (real analysis)
Darboux's theorem (symplectic topology)
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)

[edit] 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

[edit] F

[edit] 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)
Grothendieck's connectedness theorem (algebraic geometry)

[edit] 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)
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)
Hindman's theorem (Ramsey theory)
Hinge theorem (geometry)
Hironaka theorem (algebraic geometry)
Holland's schema theorem (genetic algorithm)
Hopf-Rinow theorem (differential geometry)
Hurewicz theorem (algebraic topology)
Hurwitz's automorphisms theorem (algebraic curves)

[edit] I

[edit] J

Jackson's theorem (queueing theory)
Jacobson density theorem (ring theory)
Japanese theorem (geometry)
Jordan curve theorem (topology)
Jordan-Hölder theorem (group theory)
Jordan-Schönflies theorem (geometric topology)
Jung's theorem (geometry)

[edit] K

Kantorovich theorem (functional analysis)
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)

[edit] L

[edit] M

Mahler's compactness theorem (geometry of numbers)
Mahler's theorem (p-adic analysis)
Malgrange–Ehrenpreis theorem (differential equations)
Marcinkiewicz theorem (functional analysis)
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)
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)
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)

[edit] N

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)

[edit] 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)

[edit] 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)
Peter-Weyl theorem (representation theory)
Picard theorem (complex analysis)
Picard-Lindelöf theorem (ordinary differential equations)
Pick's theorem (geometry)
Pitman-Koopman-Darmois theorem (statistics)
Plancherel theorem (Fourier analysis)
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)

[edit] Q

[edit] 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–Hurwitz theorem (polynomials)
Runge's theorem (complex analysis)

[edit] S

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)
Schreier refinement theorem (group theory)
Schur's lemma (representation theory)
Schur's theorem (Ramsey theory)
Seifert-van Kampen theorem (algebraic topology)
Separating axis theorem (convex geometry)
Shannon's expansion theorem (Boolean algebra)
Shannon's theorem (information 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)
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)
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 theorem (number theory)
Sylvester-Gallai theorem (plane geometry)
Sz.-Nagy's dilation theorem (operator theory)
Szemerédi's theorem (combinatorics)
Szemerédi-Trotter theorem (combinatorics)

[edit] T

Takagi existence theorem (number theory)
Tarski's indefinability theorem (mathematical logic)
Taylor's theorem (calculus)
Thales' theorem (geometry)
Thébault's theorem (geometry)
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)

[edit] U

[edit] V

Van der Waerden's theorem (combinatorics)
Vantieghems theorem (number theory)
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)

[edit] W

[edit] Z

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

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