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 1801–1950 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Cauchy's rigidity theorem | Theorem | Convex and discrete geometry |
| Positivity of Hankel matrices of moments | Proposition | Integral transforms, operational calculus |
| Courant–Fischer min-max theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Bias–variance decomposition | Proposition | Statistics |
| Makarov's theorem on harmonic measure | Theorem | Functions of a complex variable |
| Shapley–Folkman lemma | Lemma | Convex and discrete geometry |
| Inversion of the Hilbert transform | Theorem | Integral transforms, operational calculus |
| Weil's converse to Haar's theorem | Theorem | Measure and integration |
| Boundary integral equation for the Neumann problem | Theorem | Potential theory |
| Legendre duplication formula | Theorem | Special functions |
| Gleason's theorem on projective compact spaces | Theorem | General topology |
| Converse of the mean value property | Theorem | Potential theory |
| Direct summand conjecture | Theorem | Commutative algebra |
| Modularity theorem | Theorem | Number theory |
| Dougall's formula | Theorem | Special functions |
| Kaczmarz method | Theorem | Numerical analysis |
| Uniform convergence of absolutely summable Fourier series | Theorem | Harmonic analysis on Euclidean spaces |
| Wald's equation | Theorem | Probability theory and stochastic processes |
| Mackey imprimitivity theorem | Theorem | Topological groups, Lie groups |
| Local existence of harmonic conjugates | Theorem | Potential theory |
| Brenier's theorem | Theorem | Calculus of variations and optimal control; optimization |
| 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 |
| Gauss–Newton algorithm | Theorem | Numerical analysis |
| Birkhoff's subdirect representation theorem | Theorem | General algebraic systems |
| Kodaira–Nakano vanishing theorem | Theorem | Several complex variables and analytic spaces |
| Filtered colimits commute with finite limits | Theorem | Category theory; homological algebra |
| Conley's fundamental theorem of dynamical systems | Theorem | Dynamical systems and ergodic theory |
| Mahler's theorem | Theorem | Number theory |
| LYM inequality | Theorem | Combinatorics |
| Maximum principle | Theorem | Partial differential equations |
| Bass's theorem P | Theorem | Associative rings and algebras |
| Adams–Novikov spectral sequence | Theorem | Algebraic topology |
| Euler's formula for polytopes | Theorem | Convex and discrete geometry |
| Alexandrov–Fenchel inequality | Theorem | Convex and discrete geometry |
| Lax equivalence theorem | Theorem | Numerical analysis |
| De Giorgi's structure theorem | Theorem | Calculus of variations and optimal control; optimization |
| Yoneda lemma | Lemma | Category theory; homological algebra |
| Prokhorov's theorem | Theorem | Probability theory and stochastic processes |
| Post's inversion formula | Theorem | Integral transforms, operational calculus |
| Beck's theorem | Theorem | Convex and discrete geometry |
| 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 |
| Domain of convergence of a power series | Theorem | Several complex variables and analytic spaces |
| Gauss–Legendre Runge–Kutta methods | Theorem | Numerical analysis |
| Kolmogorov's inequality | Theorem | Probability theory and stochastic processes |
| Ahlfors–Bers theorem | Theorem | Functions of a complex variable |
| Blaschke selection theorem | Theorem | Convex and discrete geometry |
| Quantum ergodicity | Theorem | Global analysis, analysis on manifolds |
| Hadamard gap theorem | Theorem | Functions of a complex variable |
| Transversality conditions for variable endpoints | Theorem | Calculus of variations and optimal control; optimization |
| Fast marching method | Proposition | Numerical analysis |
| Thiele's interpolation formula | Proposition | Approximations and expansions |
| Monte Carlo integration | Theorem | Numerical analysis |
| Karamata's Tauberian theorem | Theorem | Sequences, series, summability |
| Differentiation operator as inverse of integration | Proposition | Integral transforms, operational calculus |
| 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 |
| FKG inequality | Theorem | Probability theory and stochastic processes |
| Adams spectral sequence | Theorem | Algebraic topology |
| Finite speed of propagation | Theorem | Partial differential equations |
| Bailey's lemma | Lemma | Special functions |
| Kleene fixed-point theorem | Theorem | Order, lattices, ordered algebraic structures |
| Earnshaw's theorem | Theorem | Potential theory |
| Newton's forward difference formula | Theorem | Difference and functional equations |
| Cartan's theorem on continuous homomorphisms | Theorem | Topological groups, Lie groups |
| Beurling's projection theorem | Theorem | Functions of a complex variable |
| Tameness theorem | Theorem | Manifolds and cell complexes |
| Segal conjecture | Theorem | Algebraic topology |
| Monad from an adjunction | Proposition | Category theory; homological algebra |
| Bochner's formula | Theorem | Differential geometry |
| Mal'cev's characterization of quasivarieties | Theorem | General algebraic systems |
| Mal'cev's theorem on congruence permutability | Theorem | General algebraic systems |
| Plancherel theorem for groups | Theorem | Topological groups, Lie groups |
| Curry–Schoenberg theorem | Theorem | Approximations and expansions |
| Cartier–Milnor–Moore theorem | Theorem | Associative rings and algebras |
| Existence of Leray weak solutions | Theorem | Partial differential equations |
| Yau–Tian–Donaldson conjecture | Theorem | Several complex variables and analytic spaces |
| Open subgroups are closed | Proposition | Topological groups, Lie groups |
| Delta method | Theorem | Statistics |
| The local ring of holomorphic germs is Noetherian and factorial | 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 |
| Monodromy theorem for singularities | Theorem | Several complex variables and analytic spaces |
| Supporting hyperplane theorem | Theorem | Convex and discrete geometry |
| Sokhotski–Plemelj formulae | Theorem | Functions of a complex variable |
| Hopf's theorem on cohomology of compact Lie groups | Theorem | Manifolds and cell complexes |
| Lazard's theorem on p-adic analytic groups | Theorem | Topological groups, Lie groups |
| 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 |
| Darcy's law | Fact | Fluid mechanics |
| Levi–Malcev decomposition | Theorem | Topological groups, Lie groups |
| Birkhoff–Frink theorem | Theorem | Order, lattices, ordered algebraic structures |
| Fenichel's theorem | Theorem | Ordinary differential equations |
| Long exact sequence of homotopy groups | Theorem | Algebraic topology |
| Arithmetic–geometric mean and elliptic integrals | Theorem | Special functions |
| Monstrous moonshine | Theorem | Number theory |
| s-cobordism theorem | Theorem | Manifolds and cell complexes |
| Closing lemma | Theorem | Dynamical systems and ergodic theory |
| Craig interpolation theorem | Theorem | Mathematical logic and foundations |
| Rosenbrock methods | Proposition | Numerical analysis |
| Special adjoint functor theorem | Theorem | Category theory; homological algebra |
| Completeness of the real numbers | Theorem | Real functions |
| Wigner's classification | Theorem | Topological groups, Lie groups |
| Furstenberg's multiple recurrence theorem | Theorem | Dynamical systems and ergodic theory |
| Muller's method | Theorem | Numerical analysis |
| Characterizations of semisimple modules | Theorem | Associative rings and algebras |
| Hájek–Le Cam convolution theorem | Theorem | Statistics |
| Menger's theorem | Theorem | Combinatorics |
| Glivenko–Cantelli theorem | Theorem | Statistics |
| Complexification of a real analytic manifold | Theorem | Several complex variables and analytic spaces |
| Roth's theorem on arithmetic progressions | Theorem | Number theory |
| Faber–Krahn inequality | Theorem | Partial differential equations |
| Characterizations of discrete valuation rings | Proposition | Commutative algebra |
| Convex functions of subharmonic functions | Proposition | Potential theory |
| Gauss–Kronrod quadrature | Theorem | Numerical analysis |
| Convolution ring has no zero divisors | Corollary | Integral transforms, operational calculus |
| Butterfly theorem | Theorem | Geometry |
| Differentiability of the Mellin transform | Theorem | Integral transforms, operational calculus |
| Gordon–Luecke theorem | Theorem | Manifolds and cell complexes |
| Plünnecke–Ruzsa inequality | Theorem | Number theory |
| Hartogs's theorem on separate holomorphicity | Theorem | Several complex variables and analytic spaces |
| Differences of polynomials vanish beyond the degree | Proposition | Difference and functional equations |
| Maximum principle for potentials | Theorem | Potential theory |
| Finite determinacy theorem | Theorem | Global analysis, analysis on manifolds |
| Lebedev quadrature | Theorem | Numerical analysis |
| Markov brothers' inequality | Theorem | Approximations and expansions |
| Hermite normal form | Theorem | Linear and multilinear algebra; matrix theory |
| Perron's formula | Theorem | Number theory |
| Eckmann–Hilton argument | Lemma | Algebraic topology |
| Jacobson density theorem | Theorem | Associative rings and algebras |
| Beurling–Deny formula | Theorem | Potential theory |
| Parabolic maximum principle | Theorem | Partial differential equations |
| Cohen's independence of CH | Theorem | Mathematical logic and foundations |
| Cubic reciprocity | Theorem | Number theory |
| Siegel's theorem on meromorphic function fields | Theorem | Several complex variables and analytic spaces |
| Mountain pass theorem | Theorem | Global analysis, analysis on manifolds |
| Heisenberg inequality for the Fourier transform | Theorem | Harmonic analysis on Euclidean spaces |
| Choi's theorem on completely positive maps | Theorem | Functional analysis |
| Cartan's uniqueness theorem | Theorem | Several complex variables and analytic spaces |
| Morse lemma | Lemma | Manifolds and cell complexes |
| Gauss–Bonnet theorem | Theorem | Differential geometry |
| Verlet integration | Proposition | Numerical analysis |
| Szemerédi regularity lemma | Lemma | Combinatorics |
| Schur orthogonality for compact groups | Theorem | Topological groups, Lie groups |