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 1201–1350 of 1926.
| Name | Kind | Subject |
|---|---|---|
| Lasker–Noether theorem | Theorem | Commutative algebra |
| Mergelyan's theorem | Theorem | Functions of a complex variable |
| Itô isometry | Theorem | Probability theory and stochastic processes |
| Frobenius theorem | Theorem | Global analysis, analysis on manifolds |
| Norm residue isomorphism theorem | Theorem | K-theory |
| Sphere theorem for 3-manifolds | Theorem | Manifolds and cell complexes |
| Milnor conjecture on slice genus of torus knots | Theorem | Manifolds and cell complexes |
| May recognition principle | Theorem | Algebraic topology |
| High indices theorem | Theorem | Sequences, series, summability |
| Hille–Yosida theorem | Theorem | Operator theory |
| Tarski–Vaught test | Proposition | Mathematical logic and foundations |
| Ryll-Nardzewski fixed-point theorem | Theorem | Operator theory |
| Schwarz integral formula | Theorem | Functions of a complex variable |
| Perron–Frobenius theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Schur–Zassenhaus theorem | Theorem | Group theory and generalizations |
| Iwasawa main conjecture | Theorem | Number theory |
| Jordan curve theorem | Theorem | Manifolds and cell complexes |
| Gauss–Codazzi equations | Theorem | Differential geometry |
| Runge's theorem | Theorem | Functions of a complex variable |
| Rearrangement inequality | Theorem | Real functions |
| Lévy–Steinitz theorem | Theorem | Sequences, series, summability |
| Fuchs' theorem | Theorem | Ordinary differential equations |
| Carlson's theorem | Theorem | Functions of a complex variable |
| Preissmann's theorem | Theorem | Differential geometry |
| Cantor normal form | Theorem | Mathematical logic and foundations |
| Hahn–Banach separation theorem | Theorem | Functional analysis |
| Whitehead theorem | Theorem | Algebraic topology |
| Fundamental group of the circle | Theorem | Algebraic topology |
| Bertrand's test | Theorem | Sequences, series, summability |
| Feit–Thompson theorem | Theorem | Group theory and generalizations |
| Fundamental recurrence formulas | Theorem | Sequences, series, summability |
| Invariance of domain | Theorem | Algebraic topology |
| Besicovitch covering theorem | Theorem | Measure and integration |
| Explicit formula | Theorem | Number theory |
| Lebesgue decomposition theorem | Theorem | Measure and integration |
| Egorov's theorem | Theorem | Measure and integration |
| Fundamental theorem of Riemannian geometry | Theorem | Differential geometry |
| Jordan's theorem on primitive groups containing a prime cycle | Theorem | Group theory and generalizations |
| Artin reciprocity law | Theorem | Number theory |
| Kunen's inconsistency theorem | Theorem | Mathematical logic and foundations |
| Freudenthal suspension theorem | Theorem | Algebraic topology |
| Markov theorem | Theorem | Manifolds and cell complexes |
| Sphere theorem | Theorem | Differential geometry |
| Schaefer's fixed point theorem | Theorem | Operator theory |
| Mertens' theorems | Theorem | Number theory |
| Wu's formula | Theorem | Manifolds and cell complexes |
| von Neumann's inequality | Theorem | Operator theory |
| Omitting types theorem | Theorem | Mathematical logic and foundations |
| Quillen–Suslin theorem | Theorem | Commutative algebra |
| Stone's theorem on paracompactness of metric spaces | Theorem | General topology |
| Smale–Hirsch theorem | Theorem | Manifolds and cell complexes |
| Pontryagin's maximum principle | Theorem | Calculus of variations and optimal control; optimization |
| Sylvester's determinant identity | Theorem | Linear and multilinear algebra; matrix theory |
| Budan's theorem | Theorem | Real functions |
| Kakutani fixed-point theorem | Theorem | Operator theory |
| Comparison theorem | Theorem | Ordinary differential equations |
| Hasse's theorem on elliptic curves | Theorem | Number theory |
| Noether normalization lemma | Theorem | Commutative algebra |
| Mazur's lemma | Lemma | Functional analysis |
| Donsker's theorem | Theorem | Probability theory and stochastic processes |
| Kolmogorov's normability criterion | Theorem | Functional analysis |
| Bishop–Gromov inequality | Theorem | Differential geometry |
| Moser's trick | Theorem | Differential geometry |
| Fekete's lemma | Lemma | Sequences, series, summability |
| McDiarmid's inequality | Theorem | Probability theory and stochastic processes |
| Schlömilch's generalization of the condensation test | Theorem | Sequences, series, summability |
| Leray spectral sequence | Theorem | Algebraic topology |
| van der Waerden conjecture on permanents | Theorem | Linear and multilinear algebra; matrix theory |
| Lévy's characterization of Brownian motion | Theorem | Probability theory and stochastic processes |
| Borel determinacy theorem | Theorem | Mathematical logic and foundations |
| Besicovitch–Federer projection theorem | Theorem | Measure and integration |
| Robinson–Schensted–Knuth correspondence | Theorem | Combinatorics |
| Generalized Poincaré conjecture | Theorem | Manifolds and cell complexes |
| Neumann series | Theorem | Operator theory |
| Cauchy interlacing theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Tauber's theorem | Theorem | Sequences, series, summability |
| Toeplitz–Hausdorff theorem | Theorem | Operator theory |
| Liouville's theorem (differential algebra) | Theorem | Field theory and polynomials |
| Tikhonov's theorem on slow-fast systems | Theorem | Ordinary differential equations |
| Nash embedding theorems | Theorem | Differential geometry |
| Loop theorem | Theorem | Manifolds and cell complexes |
| Hall's theorem on solvable groups | Theorem | Group theory and generalizations |
| Hopf degree theorem | Theorem | Algebraic topology |
| Serre's theorem on regular local rings | Theorem | Commutative algebra |
| Suslin's theorem | Theorem | Mathematical logic and foundations |
| Finitely generated projective modules over local rings are free | Theorem | Commutative algebra |
| Ionescu-Tulcea theorem | Theorem | Probability theory and stochastic processes |
| Schur's inequality | Theorem | Real functions |
| Ackermann function is not primitive recursive | Theorem | Mathematical logic and foundations |
| Brunn–Minkowski theorem | Theorem | Convex and discrete geometry |
| Sullivan conjecture | Theorem | Algebraic topology |
| Δ-system lemma | Lemma | Mathematical logic and foundations |
| Kummer's test | Theorem | Sequences, series, summability |
| Bihari–LaSalle inequality | Lemma | Real functions |
| Nilpotence theorem | Theorem | Algebraic topology |
| Kalman rank condition | Theorem | Systems theory; control |
| Euler–Maclaurin formula | Theorem | Numerical analysis |
| Cartan's classification of symmetric spaces | Theorem | Differential geometry |
| Liouville's theorem on phase-space volume | Theorem | Dynamical systems and ergodic theory |
| Schmidt subspace theorem | Theorem | Number theory |
| Poincaré duality | Theorem | Algebraic topology |
| Deduction theorem | Theorem | Mathematical logic and foundations |
| Herglotz representation theorem | Theorem | Potential theory |
| Combinatorial Nullstellensatz | Theorem | Combinatorics |
| Hodge theorem | Theorem | Global analysis, analysis on manifolds |
| Spectral theorem for compact self-adjoint operators | Theorem | Operator theory |
| Hopf invariant one problem | Theorem | Algebraic topology |
| Gauss–Lucas theorem | Theorem | Real functions |
| Frullani integral | Theorem | Real functions |
| Collar neighbourhood theorem | Theorem | Manifolds and cell complexes |
| Marden's theorem | Theorem | Functions of a complex variable |
| Gauss's test | Theorem | Sequences, series, summability |
| Determinant trick | Lemma | Commutative algebra |
| Atkinson's theorem | Theorem | Operator theory |
| Smith conjecture | Theorem | Manifolds and cell complexes |
| Hilbert–Burch theorem | Theorem | Commutative algebra |
| Riesz–Thorin theorem | Theorem | Functional analysis |
| Łoś's theorem | Theorem | Mathematical logic and foundations |
| Serre spectral sequence | Theorem | Algebraic topology |
| Milman–Pettis theorem | Theorem | Functional analysis |
| Bauer–Fike theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Rice's theorem | Theorem | Mathematical logic and foundations |
| Lüroth's theorem | Theorem | Field theory and polynomials |
| Tensor-hom adjunction | Theorem | Category theory; homological algebra |
| Kronecker–Weber theorem | Theorem | Number theory |
| Long exact sequence of a pair | Theorem | Algebraic topology |
| Schur orthogonality relations | Theorem | Group theory and generalizations |
| Cut-elimination theorem | Theorem | Mathematical logic and foundations |
| Carathéodory's theorem on boundary extension | Theorem | Functions of a complex variable |
| Convergence to equilibrium of ergodic Markov chains | Theorem | Probability theory and stochastic processes |
| Fáry–Milnor theorem | Theorem | Differential geometry |
| Szemerédi's theorem | Theorem | Number theory |
| Geometrization conjecture | Theorem | Manifolds and cell complexes |
| Magnus's Freiheitssatz | Theorem | Group theory and generalizations |
| Bombieri–Vinogradov theorem | Theorem | Number theory |
| Stallings–Swan theorem | Theorem | Group theory and generalizations |
| Carleman's inequality | Theorem | Real functions |
| Density of simple functions in Lp | Proposition | Functional analysis |
| Dieudonné's theorem on paracompact Hausdorff spaces | Theorem | General topology |
| Möbius inversion on posets | Theorem | Order, lattices, ordered algebraic structures |
| Ravenel conjectures | Theorem | Algebraic topology |
| Kesten's theorem on planar bond percolation | Theorem | Probability theory and stochastic processes |
| Vizing's theorem | Theorem | Combinatorics |
| Lagrange inversion theorem | Theorem | Combinatorics |
| Hyperbolic Dehn surgery theorem | Theorem | Manifolds and cell complexes |
| Dynkin's π-λ theorem | Theorem | Measure and integration |
| Varadhan's lemma | Lemma | Probability theory and stochastic processes |
| Azuma's inequality | Theorem | Probability theory and stochastic processes |
| Weitzenböck identity | Theorem | Differential geometry |
| Pólya's recurrence theorem | Theorem | Probability theory and stochastic processes |