Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 2778
- Definitions 2634
- Statements 1926
- Conjectures 38
- Problems 54
- Examples 213
- Counterexamples 52
- Objects 99
- Proofs 10
- Computations 1
- Topics 1
Ideas 1801–1926 of 1926.
| Name | Kind | Subject |
|---|---|---|
| Slice theorem | Theorem | Manifolds and cell complexes |
| Chow–Rashevskii theorem | Theorem | Systems theory; control |
| Kolmogorov–Arnold representation theorem | Theorem | Real functions |
| Herbrand's theorem | Theorem | Mathematical logic and foundations |
| Lévy's upward theorem | Theorem | Probability theory and stochastic processes |
| Quartic reciprocity | Theorem | Number theory |
| De Finetti's theorem | Theorem | Probability theory and stochastic processes |
| Harris inequality | Theorem | Probability theory and stochastic processes |
| Serre's criterion for normality | Theorem | Commutative algebra |
| Balog–Szemerédi–Gowers theorem | Theorem | Number theory |
| Existence of transcendence bases | Theorem | Field theory and polynomials |
| Tennenbaum's theorem | Theorem | Mathematical logic and foundations |
| Sturm comparison theorem | Theorem | Ordinary differential equations |
| Impossibility of the classical construction problems | Theorem | Field theory and polynomials |
| Prime ideals of a localization | Proposition | Commutative algebra |
| Tube lemma | Lemma | General topology |
| Nielsen–Schreier theorem | Theorem | Group theory and generalizations |
| Cameron–Martin theorem | Theorem | Measure and integration |
| Jordan decomposition of a signed measure | Theorem | Measure and integration |
| Delzant's theorem on toric manifolds | Theorem | Differential geometry |
| Chen's theorem | Theorem | Number theory |
| Stable manifold theorem | Theorem | Ordinary differential equations |
| Reflection formula for the gamma function | Theorem | Special functions |
| Hadamard three-lines theorem | Theorem | Functions of a complex variable |
| Calabi conjecture | Theorem | Several complex variables and analytic spaces |
| Baker's theorem | Theorem | Number theory |
| Corona theorem | Theorem | Functions of a complex variable |
| Robertson–Seymour theorem | Theorem | Combinatorics |
| Penrose–Hawking singularity theorems | Theorem | Relativity and gravitational theory |
| Gödel's completeness theorem | Theorem | Mathematical logic and foundations |
| Easton's theorem | Theorem | Mathematical logic and foundations |
| McKay conjecture | Theorem | Group theory and generalizations |
| Kolmogorov extension theorem | Theorem | Probability theory and stochastic processes |
| Lebesgue's density theorem | Theorem | Measure and integration |
| Riemann–Lebesgue lemma | Theorem | Harmonic analysis on Euclidean spaces |
| Riesz–Fischer theorem | Theorem | Functional analysis |
| Fubini's theorem for series | Theorem | Sequences, series, summability |
| Wang sequence | Theorem | Algebraic topology |
| Koebe quarter theorem | Theorem | Functions of a complex variable |
| Mittag-Leffler's theorem | Theorem | Functions of a complex variable |
| Abel–Dini theorem | Theorem | Sequences, series, summability |
| Inner-outer factorization | Theorem | Functions of a complex variable |
| Spectral theorem for bounded normal operators | Theorem | Operator theory |
| Artin's theorem on fixed fields | Theorem | Field theory and polynomials |
| Bondy's theorem | Theorem | Combinatorics |
| Stinespring dilation theorem | Theorem | Functional analysis |
| Hilbert's tenth problem | Theorem | Number theory |
| Chebotarev's density theorem | Theorem | Number theory |
| F. and M. Riesz theorem | Theorem | Functions of a complex variable |
| Gödel's incompleteness theorems | Theorem | Mathematical logic and foundations |
| Weyl's theorem on compact perturbations | Theorem | Operator theory |
| Lindelöf's theorem | Theorem | Functions of a complex variable |
| Fubini's theorem on differentiation | Theorem | Real functions |
| Siegel–Walfisz theorem | Theorem | Number theory |
| Skorokhod's embedding theorem | Theorem | Probability theory and stochastic processes |
| Frobenius's theorem on Frobenius kernels | Theorem | Group theory and generalizations |
| Hilbert's theorem on the hyperbolic plane | Theorem | Differential geometry |
| AKS primality test | Theorem | Number theory |
| Triangle removal lemma | Lemma | Combinatorics |
| Bounded gaps between primes | Theorem | Number theory |
| Nesbitt's inequality | Proposition | Real functions |
| Goodstein's theorem | Theorem | Mathematical logic and foundations |
| Finiteness of associated primes | Theorem | Commutative algebra |
| Jordan–Schur theorem | Theorem | Group theory and generalizations |
| Kruskal's tree theorem | Theorem | Combinatorics |
| Generalized mean inequality | Theorem | Real functions |
| Erdős–Stone theorem | Theorem | Combinatorics |
| Tannery's theorem | Theorem | Sequences, series, summability |
| Borg–Marchenko uniqueness theorem | Theorem | Ordinary differential equations |
| Fisher–Tippett–Gnedenko theorem | Theorem | Probability theory and stochastic processes |
| Serre's finiteness theorem | Theorem | Algebraic topology |
| Sauer–Shelah lemma | Lemma | Combinatorics |
| Schur–Horn theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Euler's continued fraction formula | Theorem | Sequences, series, summability |
| Sz.-Nagy's dilation theorem | Theorem | Operator theory |
| Grushko theorem | Theorem | Group theory and generalizations |
| Zariski's lemma | Lemma | Commutative algebra |
| Going-down theorem | Theorem | Commutative algebra |
| Mazur–Orlicz theorem | Theorem | Sequences, series, summability |
| Bieberbach theorems | Theorem | Group theory and generalizations |
| Sturm separation theorem | Theorem | Ordinary differential equations |
| Isomorphism theorem for measure algebras | Theorem | Measure and integration |
| Hilbert's Theorem 90 | Theorem | Field theory and polynomials |
| Uniform boundedness principle | Theorem | Functional analysis |
| Gromov's compactness theorem | Theorem | Differential geometry |
| A Dedekind UFD is a PID | Proposition | Commutative algebra |
| Doob decomposition theorem | Theorem | Probability theory and stochastic processes |
| Theorema Egregium | Theorem | Differential geometry |
| Harnack's inequality | Theorem | Potential theory |
| Tarski's undefinability theorem | Theorem | Mathematical logic and foundations |
| Weierstrass–Enneper parameterization | Theorem | Differential geometry |
| Smn theorem | Theorem | Mathematical logic and foundations |
| Classification of covering spaces | Theorem | Manifolds and cell complexes |
| Lying over theorem | Theorem | Commutative algebra |
| Lumer–Phillips theorem | Theorem | Operator theory |
| Littlewood's Tauberian theorem | Theorem | Sequences, series, summability |
| Myers–Steenrod theorem | Theorem | Differential geometry |
| Hairy ball theorem | Theorem | Manifolds and cell complexes |
| O'Nan–Scott theorem | Theorem | Group theory and generalizations |
| No-retraction theorem | Theorem | Algebraic topology |
| Four-vertex theorem | Theorem | Differential geometry |
| Girsanov theorem | Theorem | Probability theory and stochastic processes |
| Golden–Thompson inequality | Theorem | Linear and multilinear algebra; matrix theory |
| Sard's theorem | Theorem | Global analysis, analysis on manifolds |
| Undecidability of the halting problem | Theorem | Mathematical logic and foundations |
| Synge's theorem | Theorem | Differential geometry |
| Reeb stability theorem | Theorem | Manifolds and cell complexes |
| Hurewicz theorem | Theorem | Algebraic topology |
| First and second variation of arc length | Theorem | Differential geometry |
| Bernstein's theorem on monotone functions | Theorem | Real functions |
| Barratt–Priddy–Quillen theorem | Theorem | Algebraic topology |
| Adams' theorem on Hopf invariant one | Theorem | Algebraic topology |
| Frenet–Serret formulas | Theorem | Differential geometry |
| Banach–Zarecki theorem | Theorem | Real functions |
| Bieberbach conjecture | Theorem | Functions of a complex variable |
| Finite-dimensional Hausdorff vector topologies are Euclidean | Theorem | Functional analysis |
| Whitney–Graustein theorem | Theorem | Manifolds and cell complexes |
| Łoś–Vaught test | Theorem | Mathematical logic and foundations |
| Hindman's theorem | Theorem | Combinatorics |
| Montel's theorem | Theorem | Functions of a complex variable |
| Mason–Stothers theorem | Theorem | Number theory |
| Weak Nullstellensatz | Theorem | Commutative algebra |
| Newton–Puiseux theorem | Theorem | Commutative algebra |
| Hellinger–Toeplitz theorem | Theorem | Operator theory |
| Absolute continuity of the Lebesgue integral | Proposition | Measure and integration |
| Transitivity of integrality | Proposition | Commutative algebra |