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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.

: 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

A

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)
Ankeny-Artin-Chowla theorem (number theory)
Arrow's impossibility theorem (game theory)
Artin-Schreier theorem (real closed fields)
Artin-Wedderburn theorem (abstract algebra)
Arzelà-Ascoli theorem (functional analysis)
Atiyah-Singer index theorem (elliptic differential operators, harmonic analysis)

B

Baire category theorem (topology, metric spaces)
Banach-Alaoglu theorem (functional analysis)
Banach fixed point theorem (metric spaces, differential equations)
Banach-Steinhaus theorem (functional analysis)
Barbier's theorem (geometry)
Bass's theorem (group theory)
Bayes' theorem (probability)
Beatty's theorem (diophantine approximation)
Beck's monadicity theorem (category theory)
Beck's theorem (incidence geometry)
Bell's theorem (quantum theory - physics)
Bendixson-Dulac theorem (dynamical systems)
Berry-Esséen theorem (probability theory)
Bertrand's ballot theorem (probability theory, combinatorics)
Bertrand's postulate (prime numbers)
Bézout's theorem (algebraic curves)
Binomial theorem (algebra, combinatorics)
Birkhoff's theorem (ergodic theory)
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)
Boolean prime ideal theorem (mathematical logic)
Borel-Bott-Weil theorem (representation theory)
Bott periodicity theorem (homotopy theory)
Borsuk-Ulam theorem (topology)
Brouwer fixed point theorem (topology)
Brown's representability theorem (homotopy theory)
Bruck-Chowla-Ryser theorem (combinatorics)
Buckingham π theorem (dimensional analysis)

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)
Carmichael's theorem (Fibonacci numbers)
Cartan's theorem (Lie group)
Cartan's theorems A and B (several complex variables)
Cauchy integral theorem (Complex analysis)
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)
Chinese remainder theorem (number 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)
Compactness theorem (mathematical logic)
Conservativity theorem (mathematical logic)
Convolution theorem (Fourier transforms)
Cook's theorem (computational complexity theory)
Cox's theorem (probability foundations)
Crystallographic restriction theorem (group theory, crystallography)
Cut-elimination theorem (proof theory)

D

Dandelin's theorem (geometry)
Darboux's theorem (real analysis)
Darboux's theorem (symplectic topology)
De Branges' theorem (complex analysis)
De Finetti's theorem (probability)
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)
Dirichlet's theorem on arithmetic progressions (number theory)
Dirichlet's unit theorem (algebraic number theory)
Divergence theorem (vector calculus)
Dominated convergence theorem (Lebesgue integration)

E

Earnshaw's theorem (electrostatics)
Ehresmann's theorem (differential topology)
Equipartition theorem (ergodic theory)
Erdős-Ko-Rado theorem (combinatorics)
Euler's rotation theorem (geometry)
Euler's theorem (number theory)
Euler's theorem on homogeneous functions (multivariate calculus)
Extreme value theorem

F

G

Gauss theorem (vector calculus)
Gauss's Theorema Egregium (differential geometry)
Gauss-Bonnet theorem (differential geometry)
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)
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)
Goodstein's theorem (mathematical logic)
Green's theorem (vector calculus)
Gromov's compactness theorem (Riemannian geometry)
Gromov's theorem (group theory)
Gromov-Ruh theorem (differential geometry)

H

H-theorem (thermodynamics)
Haag's theorem (quantum field theory)
Haboush's theorem (algebraic groups, representation theory, invariant theory)
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)
Hasse–Minkowski theorem
Heine-Borel theorem (real analysis)
Hellinger-Toeplitz theorem (functional analysis)
Helly's theorem (convex sets)
Herbrand-Ribet theorem (cyclotomic fields)
Hilbert's basis theorem (commutative algebra,invariant theory)
Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)
Hilbert-Speiser theorem (cyclotomic fields)
Hinge theorem (geometry)
Hopf-Rinow theorem (differential geometry)
Hurewicz theorem (algebraic topology)
Hurwitz's automorphisms theorem (algebraic curves)

I

J

K

Kirchhoff's theorem (graph theory)
Kirszbraun theorem (Lipschitz continuity)
Kleene's recursion theorem (recursion theory)
Knaster-Tarski theorem (order theory)
Kolmogorov-Arnold-Moser theorem (dynamical systems)
Kolmogorov extension theorem
König's theorem (mathematical logic)
Kronecker's theorem (diophantine approximation)
Kronecker-Weber theorem (number theory)
Krull's principal ideal theorem (commutative algebra)
Künneth theorem (algebraic topology)

L

Ladner's theorem (computational complexity theory)
Lagrange's theorem (group theory)
Lagrange's four-square theorem (number theory)
Lagrange inversion theorem (mathematical analysis, combinatorics)
Lagrange reversion theorem (mathematical analysis, combinatorics)
Lami's theorem (statics)
Laurent expansion theorem (complex analysis)
Lefschetz fixed point theorem (algebraic topology)
Lehmann-Scheffé theorem (statistics)
Lindemann-Weierstrass theorem (transcendence theory)
Lie-Kolchin theorem (algebraic groups, representation theory)
Linear congruence theorem (number theory, modular arithmetic)
Linear speedup theorem (computational complexity theory)
Linnik's theorem (number theory)
Liouville's theorem (complex analysis) (entire functions)
Liouville's theorem (Hamiltonian) (Hamiltonian mechanics)
Löb's theorem (mathematical logic)
Löwenheim-Skolem theorem (mathematical logic)
Lyapunov's central limit theorem (probability theory)

M

N

Nagell-Lutz theorem (elliptic curves)
Nash embedding theorem (differential geometry)
Nielsen-Schreier theorem (free groups)
No cloning theorem (quantum computation)
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

P

Paley-Wiener theorem (Fourier transforms)
Pappus's centroid theorem (geometry)
Parseval's theorem (Fourier analysis)
Pascal's theorem (conics)
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)
Poncelet-Steiner theorem (geometry)
Post's theorem (mathematical logic)
Prime number theorem (number theory)
Primitive element theorem (field theory)
Ptolemaios' theorem (geometry)
Pythagorean theorem (geometry)

R

Radon's theorem (convex sets)
Radon-Nikodym theorem (measure theory)
Ramsey's theorem (graph theory,combinatorics)
Rank-nullity theorem (linear algebra)
Rao-Blackwell theorem (statistics)
Rational root theorem (algebra,polynomials)
Reeh-Schlieder theorem (local quantum field theory)
Residue theorem (complex analysis)
Rice's theorem (recursion theory, 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)
Rolle's theorem (calculus)
Roth's theorem (diophantine approximation)
Rouché's theorem (complex analysis)

S

Sahlqvist correspondence theorem (modal logic)
Sarkovskii's theorem (dynamical systems)
Savitch's theorem (computational complexity theory)
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)
Shannon's theorem (information theory)
Simplicial approximation theorem (algebraic topology)
Skolem-Noether theorem (simple algebras)
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)
Stanley's reciprocity theorem (combinatorics)
Stark-Heegner theorem (number theory)
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)
Sturm's theorem (theory of equations)
Swan's theorem (module theory)
Sylow theorem (group theory)
Sylvester's theorem (number theory)
Sylvester-Gallai theorem (plane geometry)
Szemerédi's theorem (combinatorics)
Szemerédi-Trotter theorem (combinatorics)

T

Takagi existence theorem (number theory)
Taniyama-Shimura theorem (number theory)
Tarski's indefinability theorem (mathematical logic)
Taylor's theorem (calculus)
Thales' theorem (geometry)
Thevenin's theorem (electrical circuits)
Thue's theorem
Thue-Siegel-Roth theorem (diophantine approximation)
Tietze extension theorem (general topology)
Tikhonov fixed point theorem (functional analysis)
Time hierarchy theorem (computational complexity theory)
Tutte theorem (graph theory)
Turán's theorem (graph theory)
Tychonoff's theorem (general topology)

U

V

W

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)
Wigner-Eckhart theorem (Clebsch-Gordan coefficients)
Wilson's theorem (number theory)
Wolstenholme's theorem (number theory)

Z

Zeckendorf's theorem
Zermelo's theorem[link] (game theory)

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