Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 5206
- Definitions 5027
- Statements 3081
- Conjectures 75
- Problems 147
- Examples 431
- Counterexamples 71
- Objects 132
- Proofs 11
- Computations 1
- Topics 1
Ideas 2251–2400 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Regular value theorem | Theorem | Manifolds and cell complexes |
| Parareal | Proposition | Numerical analysis |
| Independence of sample mean and sample variance for normal samples | Theorem | Statistics |
| Viscosity solution of the Hamilton–Jacobi–Bellman equation | Theorem | Calculus of variations and optimal control; optimization |
| McKenzie's undecidability of the finite basis problem | Theorem | General algebraic systems |
| Gibbs sampling | Proposition | Numerical analysis |
| Kakeya problem over finite fields | Theorem | Geometry |
| Milnor fibration theorem | Theorem | Several complex variables and analytic spaces |
| Denjoy–Carleman theorem | Theorem | Real functions |
| Bloch's theorem | Theorem | Functions of a complex variable |
| Dimension theorem for local rings | Theorem | Commutative algebra |
| Stanley–Wilf conjecture | Theorem | Combinatorics |
| Thom transversality theorem | Theorem | Manifolds and cell complexes |
| Bézout's theorem | Theorem | Algebraic geometry |
| Kontinuitätssatz | Theorem | Several complex variables and analytic spaces |
| Toponogov's theorem | Theorem | Differential geometry |
| Spectral radius formula | Theorem | Operator theory |
| Rayleigh monotonicity law | Theorem | Potential theory |
| Hadamard factorization theorem | Theorem | Functions of a complex variable |
| Borel's lemma | Lemma | Real functions |
| Initial value theorem | Theorem | Integral transforms, operational calculus |
| Stark–Heegner theorem | Theorem | Number theory |
| Viète's formula | Theorem | Sequences, series, summability |
| Widder's theorem | Theorem | Partial differential equations |
| Lie group–Lie algebra correspondence | Theorem | Topological groups, Lie groups |
| Jordan–Hölder theorem for modules | Theorem | Associative rings and algebras |
| Cobordism hypothesis | Theorem | Manifolds and cell complexes |
| Inverse function theorem in Banach spaces | Theorem | Global analysis, analysis on manifolds |
| Rogers–Ramanujan identities | Theorem | Number theory |
| Clausen's formula | Theorem | Special functions |
| Palais–Smale theory of critical points | Theorem | Global analysis, analysis on manifolds |
| Ax–Grothendieck theorem | Theorem | Mathematical logic and foundations |
| Complete class theorem | Theorem | Statistics |
| Time shift theorem | Theorem | Integral transforms, operational calculus |
| Tarski's HSP formula | Theorem | General algebraic systems |
| CORDIC | Theorem | Numerical analysis |
| Arnold's classification of simple critical points | Theorem | Global analysis, analysis on manifolds |
| Higher homotopy groups are abelian | Proposition | Algebraic topology |
| Backward Euler method | Proposition | Numerical analysis |
| Crank–Nicolson method | Theorem | Numerical analysis |
| Harish-Chandra's regularity theorem | Theorem | Topological groups, Lie groups |
| Fisher's inequality | Theorem | Combinatorics |
| Biconjugate gradient stabilized method | Proposition | Numerical analysis |
| Coordinatization of projective planes | Theorem | Geometry |
| Resolution of singularities | Theorem | Algebraic geometry |
| Duality of Lp spaces | Theorem | Functional analysis |
| Łojasiewicz inequality | Theorem | Several complex variables and analytic spaces |
| q-Vandermonde identity | Theorem | Special functions |
| Grötzsch's theorem | Theorem | Combinatorics |
| Goldie's theorem | Theorem | Associative rings and algebras |
| Raghunathan's conjecture | Theorem | Dynamical systems and ergodic theory |
| Prime ideal theorem for distributive lattices | Theorem | Order, lattices, ordered algebraic structures |
| Nested intervals theorem | Theorem | Real functions |
| Compactness of integral operators | Theorem | Integral equations |
| Strong perfect graph theorem | Theorem | Combinatorics |
| Borel fixed-point theorem | Theorem | Group theory and generalizations |
| Morse inequalities | Theorem | Manifolds and cell complexes |
| Predictor–corrector method | Proposition | Numerical analysis |
| Shift operator as an exponential of differentiation | Proposition | Integral transforms, operational calculus |
| Birkhoff–Kakutani theorem | Theorem | Topological groups, Lie groups |
| Casus irreducibilis | Theorem | Field theory and polynomials |
| Ekeland's variational principle | Theorem | Global analysis, analysis on manifolds |
| Theorem of the cube | Theorem | Algebraic geometry |
| Aubin–Lions lemma | Lemma | Functional analysis |
| Density of the graph of a discontinuous additive function | Proposition | Difference and functional equations |
| Blaschke–Santaló inequality | Theorem | Convex and discrete geometry |
| Fundamental theorem of the calculus of finite differences | Theorem | Difference and functional equations |
| Galois group of a finite field extension | Theorem | Field theory and polynomials |
| Picard's criterion for first-kind equations | Theorem | Integral equations |
| Cartan–Serre finiteness theorem | Theorem | Several complex variables and analytic spaces |
| Pólya enumeration theorem | Theorem | Combinatorics |
| Bernstein–Doetsch theorem | Theorem | Real functions |
| Genus–degree formula | Theorem | Algebraic geometry |
| Bounded inverse theorem | Theorem | Functional analysis |
| Baer's criterion | Theorem | Associative rings and algebras |
| Grauert's semicontinuity theorem | Theorem | Several complex variables and analytic spaces |
| Doob's martingale convergence theorems | Theorem | Probability theory and stochastic processes |
| Compactness of families of harmonic functions | Theorem | Potential theory |
| Oka coherence theorem | Theorem | Several complex variables and analytic spaces |
| Galois correspondence for coverings | Theorem | Manifolds and cell complexes |
| Zaslavsky's theorem | Theorem | Convex and discrete geometry |
| Smith normal form | Theorem | Linear and multilinear algebra; matrix theory |
| McShane–Whitney extension | Theorem | Real functions |
| Bockstein spectral sequence | Theorem | Algebraic topology |
| Bernstein inequalities | Theorem | Probability theory and stochastic processes |
| Mordell–Weil theorem | Theorem | Number theory |
| Hermite–Genocchi formula | Theorem | Numerical analysis |
| Chevalley's structure theorem | Theorem | Algebraic geometry |
| Interchange of summation order | Corollary | Sequences, series, summability |
| Inverse Mellin transform as inverse Fourier transform | Proposition | Integral transforms, operational calculus |
| Vitali–Hahn–Saks theorem | Theorem | Measure and integration |
| Hilbert's irreducibility theorem | Theorem | Field theory and polynomials |
| Killing–Hopf theorem | Theorem | Differential geometry |
| Laplace transform tends to zero at infinity | Proposition | Integral transforms, operational calculus |
| Curtis–Hedlund–Lyndon theorem | Theorem | Dynamical systems and ergodic theory |
| Serre duality | Theorem | Algebraic geometry |
| Cohen structure theorem | Theorem | Commutative algebra |
| Gauss–Markov theorem | Theorem | Statistics |
| Fefferman duality theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Hardy–Littlewood Tauberian theorem | Theorem | Sequences, series, summability |
| Dedekind's lemma on independence of characters | Lemma | Field theory and polynomials |
| Minkowski inequality | Theorem | Real functions |
| Schur's lemma in abelian categories | Lemma | Category theory; homological algebra |
| Thom isomorphism | Theorem | Algebraic topology |
| Complete reducibility of representations of compact groups | Theorem | Topological groups, Lie groups |
| Sunflower lemma | Lemma | Combinatorics |
| Gradient estimates for harmonic functions | Theorem | Potential theory |
| Homomorphism theorem | Theorem | General algebraic systems |
| Brouwer fixed-point theorem | Theorem | Algebraic topology |
| Shadowing lemma | Theorem | Dynamical systems and ergodic theory |
| Lawvere's fixed-point theorem | Theorem | Category theory; homological algebra |
| Disintegration theorem | Theorem | Measure and integration |
| Fefferman's theorem on extension of biholomorphisms | Theorem | Several complex variables and analytic spaces |
| Hunt's extension of Carleson's theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Brauer's main theorems | Theorem | Group theory and generalizations |
| Osgood's lemma | Lemma | Several complex variables and analytic spaces |
| Wiener's lemma | Theorem | Harmonic analysis on Euclidean spaces |
| Equidistribution theorem | Theorem | Number theory |
| Dyson conjecture | Theorem | Combinatorics |
| Śleszyński–Pringsheim theorem | Theorem | Sequences, series, summability |
| Dulac's theorem on finiteness of limit cycles | Theorem | Ordinary differential equations |
| Monotone operator method for Hammerstein equations | Theorem | Integral equations |
| Orlicz–Pettis theorem | Theorem | Functional analysis |
| Functional equation of the Riemann zeta function | Theorem | Number theory |
| Steinhaus theorem on regular methods | Theorem | Sequences, series, summability |
| Liouville's theorem on conformal mappings | Theorem | Differential geometry |
| Oseledets theorem | Theorem | Dynamical systems and ergodic theory |
| Tonelli's existence theorem | Theorem | Calculus of variations and optimal control; optimization |
| Alexander subbase theorem | Theorem | General topology |
| Douglas' lemma | Lemma | Operator theory |
| Eilenberg–Moore spectral sequence | Theorem | Algebraic topology |
| Completion is flat | Theorem | Commutative algebra |
| Veblen–Young theorem | Theorem | Geometry |
| Szemerédi–Trotter theorem | Theorem | Convex and discrete geometry |
| Bernstein's theorem on absolutely convergent Fourier series | Theorem | Harmonic analysis on Euclidean spaces |
| Dickson's lemma | Lemma | Order, lattices, ordered algebraic structures |
| Riemann's existence theorem | Theorem | Functions of a complex variable |
| Dvoretzky's theorem | Theorem | Functional analysis |
| Cantor's uniqueness theorem for trigonometric series | Theorem | Harmonic analysis on Euclidean spaces |
| Fenchel–Young inequality | Theorem | Convex and discrete geometry |
| Minkowski–Carathéodory theorem | Theorem | Convex and discrete geometry |
| Commutative Gelfand–Naimark theorem | Theorem | Functional analysis |
| Reiterman's theorem | Theorem | General algebraic systems |
| Švarc–Milnor lemma | Theorem | Group theory and generalizations |
| Steinitz theorem on convex hull interiors | Theorem | Convex and discrete geometry |
| Tauberian theorems for integral transforms | Theorem | Sequences, series, summability |
| Addition theorem for spherical harmonics | Theorem | Special functions |
| Inverse quadratic interpolation | Theorem | Numerical analysis |
| Browder–Minty theorem | Theorem | Operator theory |
| Lefschetz duality | Theorem | Algebraic topology |