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 1951–2100 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Duistermaat–Heckman formula | Theorem | Differential geometry |
| Lefschetz hyperplane theorem | Theorem | Algebraic geometry |
| Lyusternik–Fet theorem | Theorem | Global analysis, analysis on manifolds |
| Comparison principle | Theorem | Partial differential equations |
| Steinhaus theorem | Theorem | Measure and integration |
| Cauchy formula for repeated integration | Theorem | Real functions |
| Lidskii's trace formula for integral operators | Corollary | Integral equations |
| Varieties as categories of algebras over a monad | Theorem | Category theory; homological algebra |
| Steiner formula | Theorem | Convex and discrete geometry |
| Fenchel's theorem | Theorem | Differential geometry |
| Straszewicz's theorem | Theorem | Convex and discrete geometry |
| Bernstein's inequality for polynomials | Theorem | Approximations and expansions |
| Rokhlin lemma | Lemma | Dynamical systems and ergodic theory |
| Tridiagonal matrix algorithm | Theorem | Numerical analysis |
| Helly's theorem | Theorem | Convex and discrete geometry |
| Hartman–Wintner theorem | Theorem | Ordinary differential equations |
| Kleene's recursion theorem | Theorem | Mathematical logic and foundations |
| Einstein problem | Theorem | Convex and discrete geometry |
| Cauchy–Kovalevskaya theorem for ODEs | Theorem | Ordinary differential equations |
| McKean–Singer formula | Theorem | Global analysis, analysis on manifolds |
| Fitting's lemma | Lemma | Associative rings and algebras |
| Dini test | Theorem | Harmonic analysis on Euclidean spaces |
| Hörmander–Mikhlin multiplier theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Asymptotics of Bessel functions | Theorem | Special functions |
| Beltrami identity | Proposition | Calculus of variations and optimal control; optimization |
| Cauchy–Davenport theorem | Theorem | Number theory |
| Borel–Carathéodory theorem | Theorem | Functions of a complex variable |
| Finiteness of the class number | Theorem | Number theory |
| Classification of Fatou components | Theorem | Dynamical systems and ergodic theory |
| Compactness of the spectrum | Theorem | Functional analysis |
| Hamilton's principle | Theorem | Mechanics of particles and systems |
| Bayes risk is at most minimax risk | Proposition | Statistics |
| Cubic formula | Theorem | Field theory and polynomials |
| Whitney decomposition | Lemma | Harmonic analysis on Euclidean spaces |
| Carleson's theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Gabriel's theorem | Theorem | Associative rings and algebras |
| Vitali covering lemma | Lemma | Measure and integration |
| Nikodym convergence theorem | Theorem | Measure and integration |
| Noether theorems for singular integral equations | Theorem | Integral equations |
| Weierstrass division theorem | Theorem | Several complex variables and analytic spaces |
| Margulis arithmeticity theorem | Theorem | Topological groups, Lie groups |
| Sylow theorems | Theorem | Group theory and generalizations |
| Beck's monadicity theorem | Theorem | Category theory; homological algebra |
| M. Riesz extension theorem | Theorem | Functional analysis |
| Babenko–Beckner inequality | Theorem | Harmonic analysis on Euclidean spaces |
| Convolution property of the Z-transform | Theorem | Integral transforms, operational calculus |
| Cauchy integral formula on a polydisc | Theorem | Several complex variables and analytic spaces |
| Banach–Tarski paradox | Theorem | Mathematical logic and foundations |
| Dehn's lemma | Theorem | Manifolds and cell complexes |
| Chern–Moser normal form | Theorem | Several complex variables and analytic spaces |
| Erdős–Ko–Rado theorem | Theorem | Combinatorics |
| Approximation of a kernel by degenerate kernels | Proposition | Integral equations |
| Bott's Morse-theoretic proof of periodicity | Theorem | Algebraic topology |
| Prime avoidance lemma | Lemma | Commutative algebra |
| Hahn–Kolmogorov theorem | Theorem | Measure and integration |
| Positivstellensatz | Theorem | Algebraic geometry |
| Myers's theorem | Theorem | Differential geometry |
| Hopf lemma | Lemma | Partial differential equations |
| Nishida nilpotence theorem | Theorem | Algebraic topology |
| Courant–Friedrichs–Lewy condition | Theorem | Numerical analysis |
| Restricted Burnside problem | Theorem | Group theory and generalizations |
| Kunz's theorem | Theorem | Commutative algebra |
| Splitting principle | Theorem | Algebraic topology |
| Hartogs's extension theorem | Theorem | Several complex variables and analytic spaces |
| Quantifier elimination for real closed fields | Theorem | Mathematical logic and foundations |
| Krull–Akizuki theorem | Theorem | Commutative algebra |
| Gage–Hamilton–Grayson theorem | Theorem | Differential geometry |
| Hahn embedding theorem | Theorem | Order, lattices, ordered algebraic structures |
| Karamata's inequality | Theorem | Real functions |
| Rauch comparison theorem | Theorem | Differential geometry |
| Bipolar theorem | Theorem | Functional analysis |
| Freyd's adjoint functor theorem | Theorem | Category theory; homological algebra |
| Frostman lemma | Lemma | Measure and integration |
| Phragmén–Lindelöf principle | Theorem | Functions of a complex variable |
| Lindström's theorem | Theorem | Mathematical logic and foundations |
| Farkas' lemma | Lemma | Operations research, mathematical programming |
| Semistable reduction theorem | Theorem | Algebraic geometry |
| Prime decomposition of 3-manifolds | Theorem | Manifolds and cell complexes |
| Gauss's principle of least constraint | Fact | Mechanics of particles and systems |
| Cellular approximation theorem | Theorem | Manifolds and cell complexes |
| Koenigs linearization theorem | Theorem | Dynamical systems and ergodic theory |
| Gauss–Seidel method | Theorem | Numerical analysis |
| Wirtinger's inequality for functions | Theorem | Real functions |
| Min-max theorem | Theorem | Calculus of variations and optimal control; optimization |
| James's theorem | Theorem | Functional analysis |
| Davis's converse of the Knaster–Tarski theorem | Theorem | Order, lattices, ordered algebraic structures |
| Dolbeault isomorphism | Theorem | Several complex variables and analytic spaces |
| Monotone convergence theorem | Theorem | Measure and integration |
| Nagell–Lutz theorem | Theorem | Number theory |
| Hirzebruch–Riemann–Roch theorem | Theorem | Algebraic geometry |
| Lefschetz fixed-point theorem | Theorem | Algebraic topology |
| Erdős–Anning theorem | Theorem | Convex and discrete geometry |
| Hilbert's inequality | Theorem | Real functions |
| Art gallery theorem | Theorem | Convex and discrete geometry |
| Thie's theorem on multiplicity | Theorem | Several complex variables and analytic spaces |
| Kruskal–Katona theorem | Theorem | Combinatorics |
| Krasner's lemma | Lemma | Field theory and polynomials |
| Mohr–Mascheroni theorem | Theorem | Geometry |
| Yule–Walker equations | Theorem | Statistics |
| Posner's theorem | Theorem | Associative rings and algebras |
| Pointwise Kan extension formula | Theorem | Category theory; homological algebra |
| Poisson summation formula | Theorem | Harmonic analysis on Euclidean spaces |
| Brown representability theorem | Theorem | Algebraic topology |
| Tubular neighborhood theorem | Theorem | Manifolds and cell complexes |
| Ostrowski's theorem | Theorem | Field theory and polynomials |
| Slutsky's theorem | Theorem | Probability theory and stochastic processes |
| d'Alembert's principle | Fact | Mechanics of particles and systems |
| Uniqueness of identity element | Proposition | |
| Ham sandwich theorem | Theorem | Convex and discrete geometry |
| Fabry gap theorem | Theorem | Functions of a complex variable |
| Steffensen's method | Theorem | Numerical analysis |
| Tanaka's formula | Theorem | Probability theory and stochastic processes |
| Rosenberg's classification of maximal clones | Theorem | General algebraic systems |
| Martin representation theorem | Theorem | Potential theory |
| Kramers–Kronig relations | Theorem | Functions of a complex variable |
| Chern–Gauss–Bonnet theorem | Theorem | Differential geometry |
| Talagrand's concentration inequality | Theorem | Probability theory and stochastic processes |
| Nagata's criterion for factoriality | Theorem | Commutative algebra |
| Atiyah–Patodi–Singer index theorem | Theorem | Global analysis, analysis on manifolds |
| Higman's lemma | Theorem | Order, lattices, ordered algebraic structures |
| Going-up theorem | Theorem | Commutative algebra |
| von Neumann's minimax theorem | Theorem | Game theory, economics, finance, and other social and behavioral sciences |
| Behnke–Stein theorem | Theorem | Several complex variables and analytic spaces |
| Fundamental theorem of projective geometry | Theorem | Geometry |
| Levi's extension theorem for meromorphic functions | Theorem | Several complex variables and analytic spaces |
| Reduction of a first-kind Volterra equation to the second kind | Proposition | Integral equations |
| Superlinear convergence of the secant method | Theorem | Numerical analysis |
| Representability of cohomology by Eilenberg–MacLane spaces | Theorem | Algebraic topology |
| Continuity principle | Theorem | Potential theory |
| Fefferman's expansion of the Bergman kernel | Theorem | Several complex variables and analytic spaces |
| Circle packing theorem | Theorem | Convex and discrete geometry |
| Weyl's criterion | Theorem | Number theory |
| Adem relations | Theorem | Algebraic topology |
| Dilworth's theorem | Theorem | Order, lattices, ordered algebraic structures |
| Universal coefficient theorem | Theorem | Algebraic topology |
| Bohr's approximation theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Hironaka's resolution for complex spaces | Theorem | Several complex variables and analytic spaces |
| Second main theorem of Nevanlinna theory | Theorem | Functions of a complex variable |
| Stallings theorem about ends of groups | Theorem | Group theory and generalizations |
| Closed graph theorem | Theorem | Functional analysis |
| Integration in the transform variable | Proposition | Integral transforms, operational calculus |
| Virtually Haken conjecture | Theorem | Manifolds and cell complexes |
| Broyden's method | Theorem | Numerical analysis |
| Lusin's theorem | Theorem | Measure and integration |
| Sobolev embedding theorem | Theorem | Functional analysis |
| Faltings's theorem | Theorem | Number theory |
| Exponential integrator | Proposition | Numerical analysis |
| Focal subgroup theorem | Theorem | Group theory and generalizations |
| Jacobian criterion | Theorem | Commutative algebra |
| Liouville–Neumann series | Theorem | Integral equations |