Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 3771
- Definitions 3614
- Statements 2208
- Conjectures 58
- Problems 76
- Examples 280
- Counterexamples 55
- Objects 107
- Proofs 10
- Computations 1
- Topics 1
Ideas 1951–2100 of 2208.
| Name | Kind | Subject |
|---|---|---|
| Rankine–Hugoniot conditions | Theorem | Partial differential equations |
| Unique factorization of ideals in a Dedekind domain | Theorem | Commutative algebra |
| Hardy's inequality | Theorem | Real functions |
| Chebyshev's sum inequality | Theorem | Real functions |
| Fatou's lemma | Lemma | Measure and integration |
| Lambek's lemma | Lemma | Category theory; homological algebra |
| Priestley duality | Theorem | Order, lattices, ordered algebraic structures |
| Clifford theory | Theorem | Group theory and generalizations |
| Lebesgue differentiation theorem | Theorem | Measure and integration |
| Denjoy–Carleman–Ahlfors theorem | Theorem | Functions of a complex variable |
| Weyl–von Neumann theorem | Theorem | Operator theory |
| Shafarevich's theorem on solvable Galois groups | Theorem | Field theory and polynomials |
| Excision theorem | Theorem | Algebraic topology |
| Cayley–Hamilton theorem for modules | Proposition | Commutative algebra |
| Krull's principal ideal theorem | Theorem | Commutative algebra |
| Lefschetz principle | Theorem | Mathematical logic and foundations |
| Whitney immersion theorem | Theorem | Manifolds and cell complexes |
| Wang's finiteness theorem | Theorem | Topological groups, Lie groups |
| Auslander–Buchsbaum formula | Theorem | Commutative algebra |
| Boolean prime ideal theorem | Theorem | Mathematical logic and foundations |
| Moise's theorem | Theorem | Manifolds and cell complexes |
| Burkholder–Davis–Gundy inequality | Theorem | Probability theory and stochastic processes |
| Doob–Meyer decomposition theorem | Theorem | Probability theory and stochastic processes |
| Bogomolov–Miyaoka–Yau inequality | Theorem | Algebraic geometry |
| Lusternik–Schnirelmann theorem | Theorem | Algebraic topology |
| Kantorovich–Rubinstein duality | Theorem | Calculus of variations and optimal control; optimization |
| Dimension of a polynomial ring | Theorem | Commutative algebra |
| Sylvester–Gallai theorem | Theorem | Convex and discrete geometry |
| Reidemeister's theorem | Theorem | Manifolds and cell complexes |
| Nerve theorem | Theorem | Algebraic topology |
| Gelfand's spectral radius formula | Theorem | Functional analysis |
| Gårding's inequality | Theorem | Partial differential equations |
| Ambrose–Singer theorem | Theorem | Differential geometry |
| Right adjoints preserve limits | Theorem | Category theory; homological algebra |
| Descartes' rule of signs | Theorem | Real functions |
| Bruhat decomposition | Theorem | Group theory and generalizations |
| Szpilrajn extension theorem | Theorem | Order, lattices, ordered algebraic structures |
| Abian–Brown theorem | Theorem | Order, lattices, ordered algebraic structures |
| Kawamata–Viehweg vanishing theorem | Theorem | Algebraic geometry |
| Krull's height theorem | Theorem | Commutative algebra |
| Foster's theorem on primal algebras | Theorem | General algebraic systems |
| Peixoto's theorem | Theorem | Dynamical systems and ergodic theory |
| Kaplansky density theorem | Theorem | Functional analysis |
| Hirzebruch signature theorem | Theorem | Manifolds and cell complexes |
| Chevalley's theorem on constructible sets | Theorem | Algebraic geometry |
| Paley–Wiener theorem | Theorem | Functions of a complex variable |
| Schur product theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Borel density theorem | Theorem | Topological groups, Lie groups |
| Friendship theorem | Theorem | Combinatorics |
| Fundamental theorem of space curves | Theorem | Differential geometry |
| Fejér's theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Simplicial approximation theorem | Theorem | Algebraic topology |
| Sato–Tate conjecture | Theorem | Number theory |
| Endomorphism ring of a simple module is a division ring | Corollary | Associative rings and algebras |
| Riesz representation theorem | Theorem | Functional analysis |
| Kolmogorov's three-series theorem | Theorem | Probability theory and stochastic processes |
| Bianchi identities | Theorem | Differential geometry |
| Poincaré recurrence theorem | Theorem | Dynamical systems and ergodic theory |
| JSJ decomposition | Theorem | Manifolds and cell complexes |
| Structure theorem for finitely generated modules over a principal ideal domain | Theorem | Commutative algebra |
| Measurable Riemann mapping theorem | Theorem | Functions of a complex variable |
| Cohen's theorem on Noetherian rings | Theorem | Commutative algebra |
| Hadamard three-circle theorem | Theorem | Functions of a complex variable |
| Fuglede's theorem | Theorem | Operator theory |
| Kolmogorov continuity theorem | Theorem | Probability theory and stochastic processes |
| Schur decomposition | Theorem | Linear and multilinear algebra; matrix theory |
| Schwarz–Pick theorem | Theorem | Functions of a complex variable |
| Wiener's Tauberian theorem | Theorem | Abstract harmonic analysis |
| Weil's local rigidity theorem | Theorem | Topological groups, Lie groups |
| Homotopy invariance of homology | Theorem | Algebraic topology |
| Eilenberg–Zilber theorem | Theorem | Algebraic topology |
| Regular local rings are domains | Theorem | Commutative algebra |
| Skolem–Noether theorem | Theorem | Associative rings and algebras |
| Abel's summation formula | Theorem | Sequences, series, summability |
| Schur's theorem | Theorem | Combinatorics |
| Morley's categoricity theorem | Theorem | Mathematical logic and foundations |
| Tsen's theorem | Theorem | Field theory and polynomials |
| Brauer's theorem on induced characters | Theorem | Group theory and generalizations |
| van der Waerden's theorem | Theorem | Combinatorics |
| Plancherel theorem for abelian groups | Theorem | Abstract harmonic analysis |
| Grothendieck's local duality | Theorem | Commutative algebra |
| Church's theorem on undecidability of first-order logic | Theorem | Mathematical logic and foundations |
| Krein–Rutman theorem | Theorem | Operator theory |
| Lyndon–Hochschild–Serre spectral sequence | Theorem | Group theory and generalizations |
| Hook length formula | Theorem | Combinatorics |
| Newlander–Nirenberg theorem | Theorem | Several complex variables and analytic spaces |
| Small object argument | Theorem | Category theory; homological algebra |
| von Neumann coordinatization theorem | Theorem | Order, lattices, ordered algebraic structures |
| Galois' theorem on solvability | Theorem | Field theory and polynomials |
| Horseshoe lemma | Lemma | Category theory; homological algebra |
| Bernstein–Kushnirenko theorem | Theorem | Algebraic geometry |
| Slice theorem | Theorem | Manifolds and cell complexes |
| Twenty-seven lines on a cubic surface | Theorem | Algebraic geometry |
| Chow–Rashevskii theorem | Theorem | Systems theory; control |
| Kolmogorov–Arnold representation theorem | Theorem | Real functions |
| Jónsson's lemma | Theorem | General algebraic systems |
| Amitsur's theorem on the radical of polynomial rings | Theorem | Associative rings and algebras |
| Herbrand's theorem | Theorem | Mathematical logic and foundations |
| Lévy's upward theorem | Theorem | Probability theory and stochastic processes |
| Toyoda–Bruck theorem | Theorem | Group theory and generalizations |
| Quartic reciprocity | Theorem | Number theory |
| De Finetti's theorem | Theorem | Probability theory and stochastic processes |
| Harris inequality | Theorem | Probability theory and stochastic processes |
| Feynman–Kac formula | Theorem | Probability theory and stochastic processes |
| Serre's criterion for normality | Theorem | Commutative algebra |
| Hopkins–Levitzki theorem | Theorem | Associative rings and algebras |
| Balog–Szemerédi–Gowers theorem | Theorem | Number theory |
| Existence of transcendence bases | Theorem | Field theory and polynomials |
| Five lemma | Lemma | Category theory; homological algebra |
| Tennenbaum's theorem | Theorem | Mathematical logic and foundations |
| Sturm comparison theorem | Theorem | Ordinary differential equations |
| Impossibility of the classical construction problems | Theorem | Field theory and polynomials |
| Prime ideals of a localization | Proposition | Commutative algebra |
| Tube lemma | Lemma | General topology |
| Nielsen–Schreier theorem | Theorem | Group theory and generalizations |
| Fully faithful essentially surjective functor is an equivalence | Theorem | Category theory; homological algebra |
| Cameron–Martin theorem | Theorem | Measure and integration |
| Jordan decomposition of a signed measure | Theorem | Measure and integration |
| Delzant's theorem on toric manifolds | Theorem | Differential geometry |
| Birkhoff's completeness theorem | Theorem | General algebraic systems |
| Chen's theorem | Theorem | Number theory |
| Stable manifold theorem | Theorem | Ordinary differential equations |
| Reflection formula for the gamma function | Theorem | Special functions |
| Post's functional completeness theorem | Theorem | Order, lattices, ordered algebraic structures |
| Hadamard three-lines theorem | Theorem | Functions of a complex variable |
| Castelnuovo's contraction theorem | Theorem | Algebraic geometry |
| Calabi conjecture | Theorem | Several complex variables and analytic spaces |
| Baker's theorem | Theorem | Number theory |
| Corona theorem | Theorem | Functions of a complex variable |
| Riemann–Roch theorem | Theorem | Algebraic geometry |
| Robertson–Seymour theorem | Theorem | Combinatorics |
| Penrose–Hawking singularity theorems | Theorem | Relativity and gravitational theory |
| Gödel's completeness theorem | Theorem | Mathematical logic and foundations |
| Easton's theorem | Theorem | Mathematical logic and foundations |
| McKay conjecture | Theorem | Group theory and generalizations |
| Kolmogorov extension theorem | Theorem | Probability theory and stochastic processes |
| Lebesgue's density theorem | Theorem | Measure and integration |
| Riemann–Lebesgue lemma | Theorem | Harmonic analysis on Euclidean spaces |
| Riesz–Fischer theorem | Theorem | Functional analysis |
| GAGA | Theorem | Several complex variables and analytic spaces |
| Fubini's theorem for series | Theorem | Sequences, series, summability |
| Wang sequence | Theorem | Algebraic topology |
| Koebe quarter theorem | Theorem | Functions of a complex variable |
| Yoneda Ext and extensions | Theorem | Category theory; homological algebra |
| Calabi–Weil rigidity | Corollary | Differential geometry |
| Schur's lemma | Lemma | Associative rings and algebras |
| Mittag-Leffler's theorem | Theorem | Functions of a complex variable |
| Abel–Dini theorem | Theorem | Sequences, series, summability |
| Inner-outer factorization | Theorem | Functions of a complex variable |
| Spectral theorem for bounded normal operators | Theorem | Operator theory |