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 1051–1200 of 1926.
| Name | Kind | Subject |
|---|---|---|
| A function with nonnegative second derivative is convex | Corollary | Real functions |
| Burnside's lemma | Theorem | Group theory and generalizations |
| Determinant of the identity matrix | Proposition | Linear and multilinear algebra; matrix theory |
| Local homeomorphism from the inverse function theorem | Corollary | Real functions |
| Countable union of countable sets is countable | Theorem | Mathematical logic and foundations |
| Constant multiple rule | Corollary | Real functions |
| Dimension of the space of linear maps | Proposition | Linear and multilinear algebra; matrix theory |
| Cauchy criterion for sequences | Theorem | Sequences, series, summability |
| A complex number times its conjugate | Proposition | Functions of a complex variable |
| Gradient points in the direction of steepest ascent | Proposition | Real functions |
| Orbits partition the set | Proposition | Group theory and generalizations |
| g to the order of the group is the identity | Corollary | Group theory and generalizations |
| Universal property of the quotient space | Theorem | Linear and multilinear algebra; matrix theory |
| Transfinite induction | Theorem | Mathematical logic and foundations |
| Canonical isomorphism with the double dual | Theorem | Linear and multilinear algebra; matrix theory |
| Absorption law | Proposition | Order, lattices, ordered algebraic structures |
| Path-connected spaces are connected | Proposition | General topology |
| First isomorphism theorem for rings | Theorem | Associative rings and algebras |
| Determinant of a 2 by 2 matrix | Proposition | Linear and multilinear algebra; matrix theory |
| K(a) is isomorphic to K[x] modulo the minimal polynomial | Theorem | Field theory and polynomials |
| p-series test | Theorem | Sequences, series, summability |
| Matrix of the dual map is the transpose | Proposition | Linear and multilinear algebra; matrix theory |
| Tower law for indices | Proposition | Group theory and generalizations |
| The logarithm is strictly concave | Proposition | Real functions |
| Intersection of subgroups is a subgroup | Proposition | Group theory and generalizations |
| Uniqueness of limits | Proposition | Sequences, series, summability |
| Second supplement to quadratic reciprocity | Theorem | Number theory |
| Determinant of a transpose | Proposition | Linear and multilinear algebra; matrix theory |
| Doob's upcrossing inequality | Theorem | Probability theory and stochastic processes |
| Homotopy lifting for covering maps | Proposition | Manifolds and cell complexes |
| Willmore conjecture | Theorem | Differential geometry |
| Weierstrass factorization theorem | Theorem | Functions of a complex variable |
| Rokhlin's theorem | Theorem | Manifolds and cell complexes |
| Huisken's theorem on convex hypersurfaces | Theorem | Differential geometry |
| Hales–Jewett theorem | Theorem | Combinatorics |
| Ryll-Nardzewski theorem | Theorem | Mathematical logic and foundations |
| Nakayama's lemma | Lemma | Commutative algebra |
| Abel–Ruffini theorem | Theorem | Field theory and polynomials |
| Liénard's theorem | Theorem | Ordinary differential equations |
| Spectral theorem for unbounded self-adjoint operators | Theorem | Operator theory |
| Artin approximation theorem | Theorem | Commutative algebra |
| Wagner's theorem | Theorem | Combinatorics |
| Banach–Alaoglu theorem | Theorem | Functional analysis |
| Dirichlet's unit theorem | Theorem | Number theory |
| Regular local rings are UFDs | Theorem | Commutative algebra |
| Giroux correspondence | Theorem | Manifolds and cell complexes |
| Compactness theorem | Theorem | Mathematical logic and foundations |
| Stone–Weierstrass theorem | Theorem | Functional analysis |
| Pettis measurability theorem | Theorem | Measure and integration |
| Krull intersection theorem | Theorem | Commutative algebra |
| Arakelyan's theorem | Theorem | Functions of a complex variable |
| Robinson–Schensted correspondence | Theorem | Combinatorics |
| Cap set problem | Theorem | Combinatorics |
| Minkowski bound | Theorem | Number theory |
| Clarkson's inequalities | Theorem | Functional analysis |
| Lebesgue's theorem on differentiability of monotone functions | Theorem | Real functions |
| Loewner's torus inequality | Theorem | Differential geometry |
| Newton–Kantorovich theorem | Theorem | Numerical analysis |
| Lickorish–Wallace theorem | Theorem | Manifolds and cell complexes |
| Radon–Nikodym theorem | Theorem | Measure and integration |
| Berger's classification of holonomy groups | Theorem | Differential geometry |
| Paley–Zygmund inequality | Theorem | Probability theory and stochastic processes |
| Zassenhaus lemma | Lemma | Group theory and generalizations |
| Nonexistence of infinite-dimensional Lebesgue measure | Theorem | Measure and integration |
| Cohn's irreducibility criterion | Theorem | Number theory |
| Osgood uniqueness criterion | Theorem | Ordinary differential equations |
| Artin's induction theorem | Theorem | Group theory and generalizations |
| Martingale representation theorem | Theorem | Probability theory and stochastic processes |
| Von Neumann's theorem on self-adjoint extensions | Theorem | Operator theory |
| Whitney embedding theorem | Theorem | Manifolds and cell complexes |
| Itô's lemma | Theorem | Probability theory and stochastic processes |
| Weyl's law | Theorem | Partial differential equations |
| Eberlein–Šmulian theorem | Theorem | Functional analysis |
| Hahn decomposition theorem | Theorem | Measure and integration |
| Jordan–Brouwer separation theorem | Theorem | Algebraic topology |
| Classification of surfaces | Theorem | Manifolds and cell complexes |
| Monotone class theorem | Theorem | Measure and integration |
| Beurling's theorem | Theorem | Operator theory |
| Matlis duality | Theorem | Commutative algebra |
| Z* theorem | Theorem | Group theory and generalizations |
| Cartan formula | Theorem | Algebraic topology |
| Schwartz kernel theorem | Theorem | Functional analysis |
| Kirszbraun theorem | Theorem | Real functions |
| Lyapunov's convexity theorem | Theorem | Measure and integration |
| Artin–Rees lemma | Lemma | Commutative algebra |
| Jones index theorem | Theorem | Functional analysis |
| Cauchy–Pompeiu formula | Theorem | Functions of a complex variable |
| Donaldson's theorem | Theorem | Manifolds and cell complexes |
| Jacobi's formula | Theorem | Linear and multilinear algebra; matrix theory |
| Lovász local lemma | Lemma | Combinatorics |
| Lagrange's theorem | Theorem | Group theory and generalizations |
| Nilradical is the intersection of the prime ideals | Theorem | Commutative algebra |
| Gelfand–Mazur theorem | Theorem | Functional analysis |
| Vector fields on spheres | Theorem | Manifolds and cell complexes |
| Ending lamination theorem | Theorem | Manifolds and cell complexes |
| Löb's theorem | Theorem | Mathematical logic and foundations |
| Cramér–Wold theorem | Theorem | Probability theory and stochastic processes |
| Gelfand's formula | Theorem | Linear and multilinear algebra; matrix theory |
| Birkhoff–von Neumann theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Brouwer's characterization of the Cantor space | Theorem | General topology |
| Diagonal lemma | Lemma | Mathematical logic and foundations |
| Wigner semicircle law | Theorem | Probability theory and stochastic processes |
| Bendixson–Dulac theorem | Theorem | Ordinary differential equations |
| Poincaré conjecture | Theorem | Manifolds and cell complexes |
| Hurwitz's theorem (number theory) | Theorem | Number theory |
| Michael selection theorem | Theorem | General topology |
| Transfer principle | Theorem | Mathematical logic and foundations |
| Commutant lifting theorem | Theorem | Operator theory |
| Hermite–Hadamard inequality | Theorem | Real functions |
| Schoenflies theorem | Theorem | Manifolds and cell complexes |
| Tarski–Seidenberg theorem | Theorem | Algebraic geometry |
| Wiener–Khinchin theorem | Theorem | Probability theory and stochastic processes |
| Ahlswede–Daykin inequality | Theorem | Combinatorics |
| Cartan–Hadamard theorem | Theorem | Differential geometry |
| Scheffé's lemma | Lemma | Measure and integration |
| Löwenheim–Skolem theorem | Theorem | Mathematical logic and foundations |
| Jensen's formula | Theorem | Functions of a complex variable |
| Weierstrass preparation theorem | Theorem | Commutative algebra |
| Quartic formula | Theorem | Field theory and polynomials |
| Ramanujan–Petersson conjecture | Theorem | Number theory |
| Galois group of a prime degree polynomial with two nonreal roots | Theorem | Field theory and polynomials |
| g-theorem | Theorem | Convex and discrete geometry |
| Carathéodory's existence theorem | Theorem | Ordinary differential equations |
| Quillen's theorem on complex cobordism | Theorem | Algebraic topology |
| Doob's martingale inequality | Theorem | Probability theory and stochastic processes |
| Fredholm alternative | Theorem | Linear and multilinear algebra; matrix theory |
| Max-flow min-cut theorem | Theorem | Combinatorics |
| Mazur–Ulam theorem | Theorem | Functional analysis |
| Barbalat's lemma | Lemma | Ordinary differential equations |
| Siegel's theorem on integral points | Theorem | Number theory |
| Artin–Tate lemma | Lemma | Commutative algebra |
| Portmanteau theorem | Theorem | Probability theory and stochastic processes |
| Feldman–Hájek theorem | Theorem | Measure and integration |
| Nevanlinna–Pick interpolation | Theorem | Functions of a complex variable |
| Dehn–Sommerville equations | Theorem | Convex and discrete geometry |
| Poincaré–Hopf theorem | Theorem | Manifolds and cell complexes |
| Paris–Harrington theorem | Theorem | Mathematical logic and foundations |
| Monodromy theorem | Theorem | Functions of a complex variable |
| Fodor's lemma | Lemma | Mathematical logic and foundations |
| Class number formula | Theorem | Number theory |
| Hochster–Roberts theorem | Theorem | Commutative algebra |
| h-cobordism theorem | Theorem | Manifolds and cell complexes |
| Lieb–Thirring inequality | Theorem | Partial differential equations |
| Artin–Schreier theorem | Theorem | Field theory and polynomials |
| Perron's irreducibility criterion | Theorem | Field theory and polynomials |
| Karhunen–Loève theorem | Theorem | Probability theory and stochastic processes |
| Atiyah–Guillemin–Sternberg convexity theorem | Theorem | Differential geometry |
| Uniformization theorem | Theorem | Functions of a complex variable |
| Integral extensions of fields | Proposition | Commutative algebra |
| Minkowski's second theorem | Theorem | Number theory |