Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 5200
- Definitions 5023
- Statements 3076
- Conjectures 75
- Problems 147
- Examples 431
- Counterexamples 71
- Objects 132
- Proofs 10
- Computations 1
- Topics 1
Ideas 2851–3000 of 3076.
| Name | Kind | Subject |
|---|---|---|
| Antithetic variates | Theorem | Numerical analysis |
| Szegő limit theorems | Theorem | Operator theory |
| 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 |
| Wilks' theorem | Theorem | Statistics |
| McKay conjecture | Theorem | Group theory and generalizations |
| Jackson's inequality | Theorem | Approximations and expansions |
| Kolmogorov extension theorem | Theorem | Probability theory and stochastic processes |
| Uniqueness of solutions given initial values | Proposition | Difference and functional equations |
| Lebesgue's density theorem | Theorem | Measure and integration |
| Cartan's test for involutivity | Theorem | Global analysis, analysis on manifolds |
| Cox–de Boor recursion | Theorem | Approximations and expansions |
| Riemann–Lebesgue lemma | Theorem | Harmonic analysis on Euclidean spaces |
| Riesz–Fischer theorem | Theorem | Functional analysis |
| GAGA | Theorem | Several complex variables and analytic spaces |
| Fubini's theorem for series | Theorem | Sequences, series, summability |
| Wang sequence | Theorem | Algebraic topology |
| Koebe quarter theorem | Theorem | Functions of a complex variable |
| Poisson integral for the half-space | Theorem | Potential theory |
| Yoneda Ext and extensions | Theorem | Category theory; homological algebra |
| Asymptotic stability of linear recurrences | Theorem | Difference and functional equations |
| Mellin's inverse formula | Theorem | Integral transforms, operational calculus |
| Calabi–Weil rigidity | Corollary | Differential geometry |
| Tanh-sinh quadrature | Proposition | Numerical analysis |
| Schur's lemma | Lemma | Associative rings and algebras |
| Mittag-Leffler's theorem | Theorem | Functions of a complex variable |
| Colorful Carathéodory theorem | Theorem | Convex and discrete geometry |
| Milnor fibre is a bouquet of spheres | Theorem | Several complex variables and analytic spaces |
| Abel–Dini theorem | Theorem | Sequences, series, summability |
| Additive Schwarz method | Theorem | Numerical analysis |
| Inner-outer factorization | Theorem | Functions of a complex variable |
| Spectral theorem for bounded normal operators | Theorem | Operator theory |
| Robbins conjecture | Theorem | Order, lattices, ordered algebraic structures |
| Artin's theorem on fixed fields | Theorem | Field theory and polynomials |
| Bondy's theorem | Theorem | Combinatorics |
| Lie algebra of a compact group is reductive | Theorem | Topological groups, Lie groups |
| Jensen inequality as a functional inequality | Proposition | Difference and functional equations |
| Baker–Campbell–Hausdorff formula | Theorem | Topological groups, Lie groups |
| Mayer–Vietoris sequence | Theorem | Algebraic topology |
| Stinespring dilation theorem | Theorem | Functional analysis |
| Balancing domain decomposition | Theorem | Numerical analysis |
| Hilbert's tenth problem | Theorem | Number theory |
| Chebotarev's density theorem | Theorem | Number theory |
| Bangert–Franks theorem on closed geodesics on the sphere | Theorem | Global analysis, analysis on manifolds |
| 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 |
| Cotlar–Stein lemma | Lemma | Harmonic analysis on Euclidean spaces |
| Lindelöf's theorem | Theorem | Functions of a complex variable |
| Gromoll–Meyer theorem on closed geodesics | Theorem | Global analysis, analysis on manifolds |
| Fubini's theorem on differentiation | Theorem | Real functions |
| Gauss–Laguerre quadrature | Theorem | Numerical analysis |
| Siegel–Walfisz theorem | Theorem | Number theory |
| Filippov's existence theorem | Theorem | Calculus of variations and optimal control; optimization |
| Hadamard's two-constants theorem | Theorem | Functions of a complex variable |
| Cartan–Kähler theorem | Theorem | Global analysis, analysis on manifolds |
| Stability conjecture | Theorem | Dynamical systems and ergodic theory |
| Noether's theorem | Theorem | Mechanics of particles and systems |
| Skorokhod's embedding theorem | Theorem | Probability theory and stochastic processes |
| Beckman–Quarles theorem | Theorem | Geometry |
| Decay of Fourier coefficients and smoothness | Theorem | Harmonic analysis on Euclidean spaces |
| Gleason–Yamabe theorem | Theorem | Topological groups, Lie groups |
| Mellin inversion theorem | Theorem | Integral transforms, operational calculus |
| Frobenius's theorem on Frobenius kernels | Theorem | Group theory and generalizations |
| Pentagon identity | Fact | Category theory; homological algebra |
| Theta transformation formula | Theorem | Number theory |
| 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 |
| De la Vallée Poussin lower bound | Theorem | Approximations and expansions |
| Nesbitt's inequality | Proposition | Real functions |
| Fredholm's theorem | Theorem | Integral equations |
| Goodstein's theorem | Theorem | Mathematical logic and foundations |
| Montessus de Ballore's theorem | Theorem | Approximations and expansions |
| Hodge index theorem | Theorem | Algebraic geometry |
| Finiteness of associated primes | Theorem | Commutative algebra |
| Schwarz reflection principle for harmonic functions | Theorem | Potential theory |
| Cyclic term theorem | Theorem | General algebraic systems |
| Hadamard's lemma | Lemma | Real functions |
| Jordan–Schur theorem | Theorem | Group theory and generalizations |
| Kruskal's tree theorem | Theorem | Combinatorics |
| Blaschke–Lebesgue theorem | Theorem | Convex and discrete geometry |
| Bombieri–De Giorgi–Giusti theorem | Theorem | Calculus of variations and optimal control; optimization |
| Balian–Low theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Landau's necessary density conditions for sampling | Theorem | Information and communication theory, circuits |
| Poncelet's closure theorem | Theorem | Geometry |
| Kontsevich formality theorem | Theorem | Differential geometry |
| Bôcher's theorem | Theorem | Potential theory |
| Classification of regular polytopes | Theorem | Geometry |
| Generalized mean inequality | Theorem | Real functions |
| Erdős–Stone theorem | Theorem | Combinatorics |
| Fenchel–Moreau theorem | Theorem | Convex and discrete geometry |
| Tannery's theorem | Theorem | Sequences, series, summability |
| Rayleigh quotient iteration | Theorem | Numerical analysis |
| Carleson–Sjölin theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Symmetric successive over-relaxation | Theorem | Numerical analysis |
| Laguerre's method | Theorem | Numerical analysis |
| Singer's theorem | Theorem | Dynamical systems and ergodic theory |
| Borg–Marchenko uniqueness theorem | Theorem | Ordinary differential equations |
| Rao–Blackwell theorem | Theorem | Statistics |
| Fisher–Tippett–Gnedenko theorem | Theorem | Probability theory and stochastic processes |
| Serre's finiteness theorem | Theorem | Algebraic topology |
| Gauss multiplication formula | Theorem | Special functions |
| Kirchberger's theorem | Theorem | Convex and discrete geometry |
| Sauer–Shelah lemma | Lemma | Combinatorics |
| Schur–Horn theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Generic flatness | Theorem | Algebraic geometry |
| Girard's theorem | Theorem | Geometry |
| Minkowski–Hlawka theorem | Theorem | Number 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 |
| Böttcher's equation | Theorem | Dynamical systems and ergodic theory |
| Sharkovskii's theorem | Theorem | Dynamical systems and ergodic theory |
| Zariski's lemma | Lemma | Commutative algebra |
| Balinski's theorem | Theorem | Convex and discrete geometry |
| Sierpiński's theorem on measurable midpoint convex functions | Theorem | Real functions |
| Approximation by convolution with mollifiers | Theorem | Functional analysis |
| Artin–Schreier theorem on formally real fields | Theorem | Field theory and polynomials |
| Amitsur–Levitzki theorem | Theorem | Associative rings and algebras |
| Going-down theorem | Theorem | Commutative algebra |
| Mazur–Orlicz theorem | Theorem | Sequences, series, summability |
| Arnold's classification of simple singularities | Theorem | Several complex variables and analytic spaces |
| 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 |
| Birkhoff–Frink representation of algebraic closure systems | Theorem | General algebraic systems |
| Uniform boundedness principle | Theorem | Functional analysis |
| Chebyshev–Markov–Stieltjes inequalities | Theorem | Integral transforms, operational calculus |
| Gromov's compactness theorem | Theorem | Differential geometry |
| A Dedekind UFD is a PID | Proposition | Commutative algebra |
| Langlands classification | Theorem | Topological groups, Lie groups |
| Automorphism group of a bounded domain is a Lie group | Theorem | Several complex variables and analytic spaces |
| Doob decomposition theorem | Theorem | Probability theory and stochastic processes |
| Sphere packing in dimensions 8 and 24 | Theorem | Convex and discrete geometry |
| Wedderburn's theorem on simple Artinian rings | Theorem | Associative rings and algebras |
| Theorema Egregium | Theorem | Differential geometry |
| Rellich–Kondrachov theorem | Theorem | Functional analysis |
| Multiplication theorem | Theorem | Special functions |
| Bochner–Martinelli formula | Theorem | Several complex variables and analytic spaces |
| Bochner's tube theorem | Theorem | Several complex variables and analytic spaces |
| Harnack's inequality | Theorem | Potential theory |
| Likelihood principle | Axiom | Statistics |
| Nevanlinna parametrization of solutions | Theorem | Integral transforms, operational calculus |
| Tarski's undefinability theorem | Theorem | Mathematical logic and foundations |
| Three-term recurrence for orthogonal polynomials | Theorem | Harmonic analysis on Euclidean spaces |