List of theorems
From Exampleproblems
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
Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.
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)
- 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 Pi theorem (dimensional analysis)
C
- Cantor–Bernstein–Schroeder theorem (Set theory, cardinal numbers)
- Cantor's theorem (Set theory, Cantor's diagonal argument)
- Carathéodory's theorem (conformal mapping)
- Carathéodory's theorem (convex hull)
- Carathéodory's theorem (measure theory)
- 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)
- 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)
- 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
- Faltings' theorem (diophantine geometry)
- Feit-Thompson theorem (finite groups)
- Fermat's last theorem (number theory)
- Fermat's little theorem (number theory)
- Fisher separation theorem (economics)
- Five color theorem (graph theory)
- Fixed point theorems in infinite-dimensional spaces
- Fluctuation dissipation theorem (physics)
- Fluctuation theorem
- Four color theorem (graph theory)
- Fourier inversion theorem (harmonic analysis)
- Frobenius reciprocity theorem (group representations)
- Frobenius theorem (foliations)
- Fubini's theorem (integration)
- Fuglede's theorem (functional analysis)
- 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-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)
- 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
- Intermediate value theorem (calculus)
- Implicit function theorem (vector calculus)
- Infinite monkey theorem (probability)
- Inverse function theorem (vector calculus)
- Isomorphism theorem (abstract algebra)
- Isoperimetric theorem (curves, calculus of variations)
J
- Jacobson density theorem (ring theory)
- Jordan curve theorem (topology)
- Jordan-Hölder theorem (group theory)
- Jordan-Schönflies theorem (geometric topology)
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)
- 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
- 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
- Mahler's compactness theorem (geometry of numbers)
- Mahler's theorem (p-adic analysis)
- Marcinkiewicz theorem (functional analysis)
- Marriage theorem (combinatorics)
- Master theorem (recurrence relations, asymptotic analysis)
- Maschke's theorem (group representations)
- Matiyasevich's theorem (mathematical logic)
- Max flow min cut theorem (graph theory)
- Maximum power theorem (electrical circuits)
- Maxwell's theorem (probability theory)
- Mean value theorem (calculus)
- Menger's theorem (graph theory)
- Mercer's theorem (functional analysis)
- Mertens' theorems (number theory)
- Metrization theorems (topological spaces)
- Min-max theorem (functional analysis)
- Minimax theorem
- Minkowski's theorem (geometry of numbers)
- Mitchell's embedding theorem (category theory)
- Mittag-Leffler's theorem (complex analysis)
- Modigliani-Miller theorem (finance theory)
- Mohr-Mascheroni theorem (geometry)
- Monotone convergence theorem (mathematical analysis)
- Mordell-Weil theorem (number theory)
- Morera's theorem (complex analysis)
- Morley's categoricity theorem (model theory)
- Morley's trisector theorem (geometry)
- Multinomial theorem (algebra, combinatorics)
- Myers theorem (differential geometry)
- Myhill-Nerode theorem (formal languages)
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-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
- Uniformization theorem (complex analysis, differential geometry)
- Universal coefficient theorem (algebraic topology)
V
- Van der Waerden's theorem (combinatorics)
- Virial theorem (classical mechanics)
- Vitali theorem (measure theory)
- Vitali-Hahn-Saks theorem (measure theory)
- Von Neumann bicommutant theorem (functional analysis)
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)
