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 1501–1650 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Comparison theorem | Theorem | Ordinary differential equations |
| Hasse's theorem on elliptic curves | Theorem | Number theory |
| Noether normalization lemma | Theorem | Commutative algebra |
| Splitting lemma | Lemma | Category theory; homological algebra |
| Sunada's theorem | Theorem | Global analysis, analysis on manifolds |
| Bishop's theorem on analytic sets | Theorem | Several complex variables and analytic spaces |
| Mazur's lemma | Lemma | Functional analysis |
| Hyperbolic law of cosines | Theorem | Geometry |
| Euler's integral representation of the hypergeometric function | Theorem | Special functions |
| Hard Lefschetz theorem | Theorem | Algebraic geometry |
| Donsker's theorem | Theorem | Probability theory and stochastic processes |
| Weil conjectures | Theorem | Algebraic geometry |
| Kolmogorov's normability criterion | Theorem | Functional analysis |
| Bishop–Gromov inequality | Theorem | Differential geometry |
| Moser's trick | Theorem | Differential geometry |
| Kingman's subadditive ergodic theorem | Theorem | Dynamical systems and ergodic theory |
| Nichols–Zoeller theorem | Theorem | Associative rings and algebras |
| Lax–Milgram theorem | Theorem | Partial differential equations |
| Reduction of an initial value problem to a Volterra equation | Proposition | Integral equations |
| Landweber iteration | Theorem | Numerical analysis |
| Radon's theorem | Theorem | Convex and discrete geometry |
| Mutual absolute continuity of harmonic measures | Proposition | Potential theory |
| Gauss–Hermite quadrature | Theorem | Numerical analysis |
| 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 |
| Thomson's principle | Theorem | Potential theory |
| 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 |
| Asymptotic normality of the maximum likelihood estimator | Theorem | Statistics |
| Borel determinacy theorem | Theorem | Mathematical logic and foundations |
| Box–Muller transform | Theorem | Numerical analysis |
| Legendre's relation | Theorem | Special functions |
| Ornstein isomorphism theorem | Theorem | Dynamical systems and ergodic theory |
| Besicovitch–Federer projection theorem | Theorem | Measure and integration |
| Robinson–Schensted–Knuth correspondence | Theorem | Combinatorics |
| Generalized Poincaré conjecture | Theorem | Manifolds and cell complexes |
| Uniform convergence of Bernstein approximations | Theorem | Approximations and expansions |
| Kaplansky's theorem on PI rings | Theorem | Associative rings and algebras |
| Density theorem | Theorem | Category theory; homological algebra |
| Ramanujan's series for 1/pi | Theorem | Number theory |
| Neumann series | Theorem | Operator theory |
| Cauchy interlacing theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Hartogs–Bochner extension theorem | Theorem | Several complex variables and analytic spaces |
| Alternating-direction implicit method | Theorem | Numerical analysis |
| Remez inequality | Theorem | Approximations and expansions |
| Singular cardinals hypothesis | Axiom | Mathematical logic and foundations |
| Tauber's theorem | Theorem | Sequences, series, summability |
| Toeplitz–Hausdorff theorem | Theorem | Operator theory |
| Freyd–Mitchell embedding theorem | Theorem | Category theory; homological algebra |
| Carleson embedding theorem | Theorem | Functions of a complex variable |
| Liouville's theorem (differential algebra) | Theorem | Field theory and polynomials |
| Cartan's theorem on fine continuity of superharmonic functions | Theorem | Potential theory |
| Tikhonov's theorem on slow-fast systems | Theorem | Ordinary differential equations |
| Nash embedding theorems | Theorem | Differential geometry |
| Loop theorem | Theorem | Manifolds and cell complexes |
| Cantor–Lebesgue theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Hall's theorem on solvable groups | Theorem | Group theory and generalizations |
| Hopf degree theorem | Theorem | Algebraic topology |
| Maximum modulus principle in several variables | Theorem | Several complex variables and analytic spaces |
| Feuerbach's theorem | Theorem | Geometry |
| Serre's theorem on regular local rings | Theorem | Commutative algebra |
| Period three implies chaos | Theorem | Dynamical systems and ergodic theory |
| Aoki–Rassias theorem | Theorem | Difference and functional equations |
| Suslin's theorem | Theorem | Mathematical logic and foundations |
| Finitely generated projective modules over local rings are free | Theorem | Commutative algebra |
| Adaptive quadrature | Proposition | Numerical analysis |
| Pascal's theorem | Theorem | Geometry |
| Ionescu-Tulcea theorem | Theorem | Probability theory and stochastic processes |
| Krull–Schmidt theorem | Theorem | Associative rings and algebras |
| Schur's inequality | Theorem | Real functions |
| Uhlenbeck compactness theorem | Theorem | Global analysis, analysis on manifolds |
| Cauchy–Kovalevskaya theorem | Theorem | Partial differential equations |
| Ackermann function is not primitive recursive | Theorem | Mathematical logic and foundations |
| Baker–Pixley theorem | Theorem | General algebraic systems |
| Schwarz alternating method | Theorem | Numerical analysis |
| Thom–Sebastiani theorem | Theorem | Several complex variables and analytic spaces |
| Brunn–Minkowski theorem | Theorem | Convex and discrete geometry |
| Mehler kernel | Theorem | Special functions |
| Edgeworth expansion | Theorem | Statistics |
| Cahen–Mellin integral | Proposition | Integral transforms, operational calculus |
| Weyl's lemma | Lemma | Potential theory |
| Crofton formula | Theorem | Differential geometry |
| Nested dissection | Theorem | Numerical analysis |
| Sullivan conjecture | Theorem | Algebraic topology |
| Bourbaki–Witt theorem | Theorem | Order, lattices, ordered algebraic structures |
| Derivative of a convolution | Proposition | Integral transforms, operational calculus |
| Summation by parts | Theorem | Difference and functional equations |
| Δ-system lemma | Lemma | Mathematical logic and foundations |
| Keller's conjecture | Theorem | Convex and discrete geometry |
| Rader's FFT algorithm | Theorem | Numerical analysis |
| Kummer's test | Theorem | Sequences, series, summability |
| Bihari–LaSalle inequality | Lemma | Real functions |
| Minkowski's first inequality | Theorem | Convex and discrete geometry |
| Fishburn's theorem on interval orders | Theorem | Order, lattices, ordered algebraic structures |
| Nilpotence theorem | Theorem | Algebraic topology |
| Cooley–Tukey FFT algorithm | Theorem | Numerical analysis |
| Kalman rank condition | Theorem | Systems theory; control |
| Hadamard's inequality in Fredholm theory | Lemma | Integral equations |
| Euler–Maclaurin formula | Theorem | Numerical analysis |
| Cartan's classification of symmetric spaces | Theorem | Differential geometry |
| Quadratic convergence of Newton's method | Theorem | Numerical analysis |
| Kolmogorov–Nagumo characterization of quasi-arithmetic means | Theorem | Real functions |
| Napoleon's theorem | Theorem | Geometry |
| Łoś–Tarski preservation theorem | Theorem | Mathematical logic and foundations |
| Uniqueness of best approximation in strictly convex spaces | Theorem | Approximations and expansions |
| 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 |
| Bernstein's theorem on analytic functions | Theorem | Approximations and expansions |
| Pfaff–Saalschütz theorem | Theorem | Special functions |
| Maximum principle for subharmonic functions | Theorem | Potential theory |
| Herglotz representation theorem | Theorem | Potential theory |
| Artinian reduced rings are semisimple | Proposition | Associative rings and algebras |
| Secant method | Theorem | Numerical analysis |
| Nash–Moser theorem | Theorem | Global analysis, analysis on manifolds |
| Poisson–Jensen formula | Theorem | Potential theory |
| Combinatorial Nullstellensatz | Theorem | Combinatorics |
| Calderón–Vaillancourt theorem | Theorem | Partial differential equations |
| Landen's transformation | Theorem | Special functions |
| Hodge theorem | Theorem | Global analysis, analysis on manifolds |
| Spectral theorem for compact self-adjoint operators | Theorem | Operator theory |
| Courant–Fischer characterization of characteristic values | Theorem | Integral equations |
| Hopf invariant one problem | Theorem | Algebraic topology |
| Generalized minimal residual method | Theorem | Numerical analysis |
| Blichfeldt's theorem | Theorem | Number theory |
| Multiplication formula for the Fourier transform | Proposition | Harmonic analysis on Euclidean spaces |
| Gauss–Lucas theorem | Theorem | Real functions |
| Frullani integral | Theorem | Real functions |
| Cartan decomposition of a Lie group | Theorem | Topological groups, Lie groups |
| Minimum total potential energy principle | Theorem | Mechanics of deformable solids |
| 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 |
| Heine's transformation | Theorem | Special functions |
| du Bois-Reymond lemma | Lemma | Calculus of variations and optimal control; optimization |
| Log-convexity of the gamma function | Theorem | Special functions |
| Theorem of the three geodesics | Theorem | Differential geometry |
| Cantor's isomorphism theorem | Theorem | Order, lattices, ordered algebraic structures |
| Atkinson's theorem | Theorem | Operator theory |
| Smith conjecture | Theorem | Manifolds and cell complexes |
| Kantorovich duality | Theorem | Calculus of variations and optimal control; optimization |
| Multigrid method | Theorem | Numerical analysis |
| Sinai's factor theorem | Theorem | Dynamical systems and ergodic theory |
| Marcinkiewicz–Zygmund inequality | Theorem | Probability theory and stochastic processes |
| Calderón–Zygmund theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Kepler conjecture | Theorem | Convex and discrete geometry |