List of theorems
This is a list of theorems, by Wikipedia page. See also list of mathematical theorems, list of mathematical proofs, list of lemmas, list of conjectures.
In some fields, theorem can be considered as a courtesy title, given to major results, although with a content that would not satisfy a mathematician. No attempt is made here to comment on that aspect of usage: this is a list of results known as theorems. Most of the results do come from mathematics, but there are others from theoretical physics, economics and so on.
A
- Abel-Ruffini theorem (polynomial equations, Galois theory)
- Arrow's impossibility theorem (Game theory)
- Artin-Wedderburn theorem (abstract algebra)
- Arzelà-Ascoli theorem (functional analysis)
- Atiyah-Singer index theorem (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)
- Bell's theorem (quantum theory - physics)
- Bendixson-Dulac theorem (dynamical systems)
- Bezout's theorem (algebraic curves)
- Binomial theorem (algebra, combinatorics)
- Bolyai-Gerwien theorem (geometry)
- Bolzano-Weierstrass theorem (real analysis, calculus)
- Boolean prime ideal theorem (mathematical logic)
- Borsuk-Ulam theorem (topology)
- Brouwer fixed point theorem (topology)
- 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])
- Cartan's theorem (Lie group)
- Cartan's theorems A and B
- Cauchy integral theorem (Complex analysis)
- Cayley-Hamilton theorem (Linear algebra)
- Cayley's theorem
- Central limit theorem (probability)
- Ceva's theorem
- Chebotarev's density theorem
- Chinese remainder theorem
- Chowla-Mordell theorem
- Church-Rosser theorem
- Closed graph theorem
- Coase theorem
- Cochran's theorem
- Compactness theorem
- Convolution theorem
- Cox's theorem
D
- De Finetti's theorem
- Desargues' theorem
- Descartes' theorem
- Dimension theorem for vector spaces
- Dirichlet's theorem on arithmetic progressions
- Dirichlet's unit theorem
- Divergence theorem
- Dominated convergence theorem
E
- Earnshaw's theorem
- Equipartition theorem
- Erdös-Ko-Rado theorem
- Euler's theorem
- Euler's theorem on homogeneous functions
F
- Fermat's last theorem
- Fermat's little theorem
- Fixed point theorems in infinite-dimensional spaces
- Fluctuation dissipation theorem
- Four color theorem
- Frobenius theorem
- Fubini's theorem
- Fundamental theorem of algebra
- Fundamental theorem of arithmetic
- Fundamental theorem of calculus
- Fundamental theorem of poker
- Fundamental theorem on homomorphisms
G
- Gauss theorem
- Gauss's Theorema Egregium
- Gauss-Bonnet theorem
- Gauss-Markov theorem
- Gelfand-Naimark theorem
- Gelfond-Schneider theorem
- Gibbard-Satterthwaite theorem
- Gödel's completeness theorem
- Gödel's incompleteness theorem
- Goodstein's theorem
- Green's theorem
- Gromov's theorem
H
- H-theorem
- Hadwiger's theorem
- Hairy ball theorem
- Hahn-Banach theorem
- Hales-Jewett theorem
- Heine-Borel theorem
- Hellinger-Toeplitz theorem
- Hilbert's basis theorem
- Hilbert's Nullstellensatz (theorem of zeroes).
- Hurewicz theorem
I
- Intermediate value theorem
- Implicit function theorem
- Infinite monkey theorem
- Inverse function theorem
- Isomorphism theorem
- Isoperimetric theorem
J
K
- Knaster-Tarski theorem
- Kolmogorov-Arnold-Moser theorem
- König's theorem
- Kronecker's theorem
- Krull's principal ideal theorem
L
- Lagrange's theorem
- Lagrange inversion theorem
- Lefschetz fixed point theorem
- Lehmann-Scheffé theorem
- Lindemann-Weierstrass theorem
- Linear congruence theorem
- Linnik's theorem
- Liouville's theorem (complex analysis)
- Liouville's theorem (Hamiltonian)
- Löwenheim-Skolem theorem
M
- Mahler's compactness theorem
- Marriage theorem
- Master theorem
- Maschke's theorem
- Matiyasevich's theorem
- Max flow min cut theorem
- Maximum power theorem
- Maxwell's theorem
- Mean value theorem
- Metrization theorems
- Minkowski's theorem
- Mitchell's embedding theorem
- Monotone convergence theorem
- Mordell-Weil theorem
- Morera's theorem
- Myhill-Nerode theorem
N
- Nash embedding theorem
- No cloning theorem
- Noether's theorem
- Norton's theorem
- Nyquist-Shannon sampling theorem
O
P
- Paley-Wiener theorem
- Peter-Weyl theorem
- Pick's theorem
- Poincaré duality theorem
- Prime number theorem
- Pythagorean theorem
R
- Radon-Nikodym theorem
- Ramsey's theorem
- Rank-nullity theorem
- Rao-Blackwell theorem
- Rational root theorem
- Residue theorem
- Rice's theorem
- Riemann mapping theorem
- Riemann-Roch theorem
- Riesz representation theorem
- Robertson-Seymour theorem
- Rolle's theorem
S
- Sarkovskii's theorem
- Schauder fixed point theorem
- Seifert-van Kampen theorem
- Shannon's theorem
- Simplicial approximation theorem
- Spectral theorem
- Spin-statistics theorem
- Sprague-Grundy theorem
- Squeeze theorem
- Stokes' theorem
- Stone's representation theorem for Boolean algebras
- Stone-Weierstrass theorem
- Swan's theorem
- Sylow theorem
- Szeméredi's theorem
T
- Tarski's indefinability theorem
- Taylor's theorem
- Thales' theorem
- Tietze extension theorem
- Tikhonov fixed point theorem
- Time hierarchy theorem
- Tychonoff's theorem