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 1351–1500 of 1926.
| Name | Kind | Subject |
|---|---|---|
| Dehn–Lickorish theorem | Theorem | Manifolds and cell complexes |
| Fagin's theorem | Theorem | Mathematical logic and foundations |
| Dahlquist barriers | Theorem | Numerical analysis |
| Von Neumann bicommutant theorem | Theorem | Functional analysis |
| Soul theorem | Theorem | Differential geometry |
| Implicit function theorem in Banach spaces | Theorem | Global analysis, analysis on manifolds |
| Euler product for multiplicative functions | Theorem | Number theory |
| Watson's lemma | Lemma | Approximations and expansions |
| Hardy's Tauberian theorem for Cesàro means | Theorem | Sequences, series, summability |
| Gross–Zagier theorem | Theorem | Number theory |
| Erdős–Kac theorem | Theorem | Number theory |
| Dominated convergence theorem | Theorem | Measure and integration |
| Grönwall area theorem | Theorem | Functions of a complex variable |
| Mordell's theorem | Theorem | Number theory |
| Rado's theorem | Theorem | Combinatorics |
| Vinogradov's theorem | Theorem | Number theory |
| Borel–Ritt theorem | Theorem | Functions of a complex variable |
| Vitali convergence theorem | Theorem | Measure and integration |
| Landau–Kolmogorov inequality | Theorem | Real functions |
| Localization of a Noetherian ring is Noetherian | Proposition | Commutative algebra |
| Akizuki–Hopkins–Levitzki theorem | Theorem | Commutative algebra |
| Hochster's theorem on spectral spaces | Theorem | Algebraic geometry |
| Radó's theorem on triangulation of surfaces | Theorem | Manifolds and cell complexes |
| Steinitz's theorem on algebraically closed fields | Theorem | Field theory and polynomials |
| Witt's theorem | Theorem | Number theory |
| Raabe's test | Theorem | Sequences, series, summability |
| Reduction to diagonal form by transvections | Theorem | Linear and multilinear algebra; matrix theory |
| Continuous mapping theorem | Theorem | Probability theory and stochastic processes |
| Jacobi's four-square theorem | Theorem | Number theory |
| Hadamard's inequality | Theorem | Linear and multilinear algebra; matrix theory |
| Courant–Fischer min-max theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Gleason's theorem on projective compact spaces | Theorem | General topology |
| Direct summand conjecture | Theorem | Commutative algebra |
| Modularity theorem | Theorem | Number theory |
| Non-vanishing of the zeta function on the line Re s = 1 | Theorem | Number theory |
| Pólya's theorem on integer-valued entire functions | Theorem | Functions of a complex variable |
| LYM inequality | Theorem | Combinatorics |
| Adams–Novikov spectral sequence | Theorem | Algebraic topology |
| Prokhorov's theorem | Theorem | Probability theory and stochastic processes |
| Eigendecomposition | Theorem | Linear and multilinear algebra; matrix theory |
| Puppe sequence | Theorem | Algebraic topology |
| Hilbert's Nullstellensatz | Theorem | Commutative algebra |
| Ulm's theorem | Theorem | Group theory and generalizations |
| Kolmogorov's inequality | Theorem | Probability theory and stochastic processes |
| Ahlfors–Bers theorem | Theorem | Functions of a complex variable |
| Hadamard gap theorem | Theorem | Functions of a complex variable |
| Karamata's Tauberian theorem | Theorem | Sequences, series, summability |
| Optional stopping theorem | Theorem | Probability theory and stochastic processes |
| Marchenko–Pastur law | Theorem | Probability theory and stochastic processes |
| Schauder fixed-point theorem | Theorem | Operator theory |
| Adams spectral sequence | Theorem | Algebraic topology |
| Tameness theorem | Theorem | Manifolds and cell complexes |
| Segal conjecture | Theorem | Algebraic topology |
| Bochner's formula | Theorem | Differential geometry |
| Yau–Tian–Donaldson conjecture | Theorem | Several complex variables and analytic spaces |
| Nehari's theorem on univalence | Theorem | Functions of a complex variable |
| Euler's sine product | Theorem | Functions of a complex variable |
| Margulis superrigidity theorem | Theorem | Topological groups, Lie groups |
| Compactness via ultrafilters | Theorem | General topology |
| Stone's theorem on one-parameter unitary groups | Theorem | Operator theory |
| Riesz–Markov–Kakutani representation theorem | Theorem | Measure and integration |
| Fenichel's theorem | Theorem | Ordinary differential equations |
| Long exact sequence of homotopy groups | Theorem | Algebraic topology |
| Monstrous moonshine | Theorem | Number theory |
| s-cobordism theorem | Theorem | Manifolds and cell complexes |
| Craig interpolation theorem | Theorem | Mathematical logic and foundations |
| Completeness of the real numbers | Theorem | Real functions |
| Menger's theorem | Theorem | Combinatorics |
| Glivenko–Cantelli theorem | Theorem | Statistics |
| Roth's theorem on arithmetic progressions | Theorem | Number theory |
| Characterizations of discrete valuation rings | Proposition | Commutative algebra |
| Gordon–Luecke theorem | Theorem | Manifolds and cell complexes |
| Plünnecke–Ruzsa inequality | Theorem | Number theory |
| Markov brothers' inequality | Theorem | Approximations and expansions |
| Hermite normal form | Theorem | Linear and multilinear algebra; matrix theory |
| Eckmann–Hilton argument | Lemma | Algebraic topology |
| Cohen's independence of CH | Theorem | Mathematical logic and foundations |
| Cubic reciprocity | Theorem | Number theory |
| Choi's theorem on completely positive maps | Theorem | Functional analysis |
| Morse lemma | Lemma | Manifolds and cell complexes |
| Gauss–Bonnet theorem | Theorem | Differential geometry |
| Szemerédi regularity lemma | Lemma | Combinatorics |
| Duistermaat–Heckman formula | Theorem | Differential geometry |
| Cauchy formula for repeated integration | Theorem | Real functions |
| Fenchel's theorem | Theorem | Differential geometry |
| Bernstein's inequality for polynomials | Theorem | Approximations and expansions |
| Kleene's recursion theorem | Theorem | Mathematical logic and foundations |
| Cauchy–Kovalevskaya theorem for ODEs | Theorem | Ordinary differential equations |
| Cauchy–Davenport theorem | Theorem | Number theory |
| Borel–Carathéodory theorem | Theorem | Functions of a complex variable |
| Finiteness of the class number | Theorem | Number theory |
| Compactness of the spectrum | Theorem | Functional analysis |
| Cubic formula | Theorem | Field theory and polynomials |
| Vitali covering lemma | Lemma | Measure and integration |
| Nikodym convergence theorem | Theorem | Measure and integration |
| Sylow theorems | Theorem | Group theory and generalizations |
| Banach–Tarski paradox | Theorem | Mathematical logic and foundations |
| Dehn's lemma | Theorem | Manifolds and cell complexes |
| Erdős–Ko–Rado theorem | Theorem | Combinatorics |
| Prime avoidance lemma | Lemma | Commutative algebra |
| Hahn–Kolmogorov theorem | Theorem | Measure and integration |
| Myers's theorem | Theorem | Differential geometry |
| Nishida nilpotence theorem | Theorem | Algebraic topology |
| Restricted Burnside problem | Theorem | Group theory and generalizations |
| Kunz's theorem | Theorem | Commutative algebra |
| Splitting principle | Theorem | Algebraic topology |
| Quantifier elimination for real closed fields | Theorem | Mathematical logic and foundations |
| Krull–Akizuki theorem | Theorem | Commutative algebra |
| Gage–Hamilton–Grayson theorem | Theorem | Differential geometry |
| Karamata's inequality | Theorem | Real functions |
| Rauch comparison theorem | Theorem | Differential geometry |
| Bipolar theorem | Theorem | Functional analysis |
| Frostman lemma | Lemma | Measure and integration |
| Phragmén–Lindelöf principle | Theorem | Functions of a complex variable |
| Lindström's theorem | Theorem | Mathematical logic and foundations |
| Prime decomposition of 3-manifolds | Theorem | Manifolds and cell complexes |
| Cellular approximation theorem | Theorem | Manifolds and cell complexes |
| Wirtinger's inequality for functions | Theorem | Real functions |
| James's theorem | Theorem | Functional analysis |
| Monotone convergence theorem | Theorem | Measure and integration |
| Nagell–Lutz theorem | Theorem | Number theory |
| Hilbert's inequality | Theorem | Real functions |
| Kruskal–Katona theorem | Theorem | Combinatorics |
| Krasner's lemma | Lemma | Field theory and polynomials |
| Tubular neighborhood theorem | Theorem | Manifolds and cell complexes |
| Ostrowski's theorem | Theorem | Field theory and polynomials |
| Slutsky's theorem | Theorem | Probability theory and stochastic processes |
| Fabry gap theorem | Theorem | Functions of a complex variable |
| Tanaka's formula | Theorem | Probability theory and stochastic processes |
| Kramers–Kronig relations | Theorem | Functions of a complex variable |
| Chern–Gauss–Bonnet theorem | Theorem | Differential geometry |
| Talagrand's concentration inequality | Theorem | Probability theory and stochastic processes |
| Nagata's criterion for factoriality | Theorem | Commutative algebra |
| Going-up theorem | Theorem | Commutative algebra |
| Representability of cohomology by Eilenberg–MacLane spaces | Theorem | Algebraic topology |
| Circle packing theorem | Theorem | Convex and discrete geometry |
| Weyl's criterion | Theorem | Number theory |
| Adem relations | Theorem | Algebraic topology |
| Dilworth's theorem | Theorem | Order, lattices, ordered algebraic structures |
| Second main theorem of Nevanlinna theory | Theorem | Functions of a complex variable |
| Stallings theorem about ends of groups | Theorem | Group theory and generalizations |
| Closed graph theorem | Theorem | Functional analysis |
| Virtually Haken conjecture | Theorem | Manifolds and cell complexes |
| Lusin's theorem | Theorem | Measure and integration |
| Sobolev embedding theorem | Theorem | Functional analysis |
| Faltings's theorem | Theorem | Number theory |
| Focal subgroup theorem | Theorem | Group theory and generalizations |
| Jacobian criterion | Theorem | Commutative algebra |
| Layer cake representation | Theorem | Measure and integration |
| Green–Tao theorem | Theorem | Number theory |