Liouville's theorem | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem | Wedderburn's little theorem | Vietoris–Begle mapping theorem | Veblen–Young theorem |
Adiabatic quantum computation, a quantum computing model that relies on the adiabatic theorem to do calculations
It may be viewed as a parametrized version of the classical theorem which states that equivalence classes of h-cobordisms on are in 1-to-1 correspondence with elements in the Whitehead group of .
In 1978 Constantine Callias, at the suggestion of his Ph.D. advisor Roman Jackiw, used the axial anomaly to derive this index theorem on spaces equipped with a Hermitian matrix called the Higgs field.
For the theorem named after Felix Bloch on wave functions of a particle in a periodic potential, see Bloch wave.
The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.
In formal language theory, the Chomsky–Schützenberger theorem is either of two different theorems derived by Noam Chomsky and Marcel-Paul Schützenberger.
The theorem was proved by Stefan Banach in his 1932 Théorie des opérations linéaires.
In mathematics, the corners theorem is an important result, proved by Miklós Ajtai and Endre Szemerédi, of a statement in arithmetic combinatorics.
This theorem shows the Second law of thermodynamics and the Zeroth law of thermodynamics can be derived mathematically rather than postulated as laws of Nature.
In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on converge in a suitable sense.
Their catalog includes foreign film classics such as La Dolce Vita, Peau d'Âne (Donkey Skin), The Umbrellas of Cherbourg, The Official Story, and Theorem as well as contemporary releases such as The Syrian Bride, Changing Times, Man Push Cart and the documentaries Our Brand Is Crisis and The Bridge.
Daniel Pedoe named it the most elementary theorem in Euclidean geometry since it only concerns straight lines and distances.
The works of 17th century mathematician Pierre de Fermat engendered many theorems.
The first proof of the fold-and-cut theorem, solving the problem, was published in 1999 by Erik Demaine, Martin Demaine, and Anna Lubiw.
The Gelfond–Schneider theorem answers affirmatively Hilbert's seventh problem.
Giordano is most noted nowadays for a theorem on Saccheri quadrilaterals that he proved in his 1668 book Euclide restituo (named after Borelli's Euclides Restitutus of 1658).
Almost immediately, John Milnor observed that a theorem due to Ernst Witt implied the existence of a pair of 16-dimensional tori that have the same eigenvalues but different shapes.
Kellogg's theorem is a pair of related results in the mathematical study of the regularity of harmonic functions on sufficiently smooth domains by Oliver Dimon Kellogg.
This result may also be known as the Kolmogorov theorem; see Kolmogorov's theorem for disambiguation.
Lagrange's reversion theorem is used to obtain numerical solutions to Kepler's equation.
The following lemma is usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem.
Clauser, 1978: J. F. Clauser and A. Shimony, Bell’s theorem: experimental tests and implications, Reports on Progress in Physics 41, 1881 (1978)
His name is attached to Böttcher theorem, in which he introduced Böttcher's equation and solved it under certain assumptions.
; Weiss, B.: An anti-classification theorem for ergodic measure
Viscardi's theorem is an expansion of the 19th-century work of Peter Gustav Lejeune Dirichlet.
This theorem was developed by Mohr and later stated namely by Charles E. Greene in 1873.
For example, the first version of Montel's theorem stated above is the analog of Liouville's theorem, while the second version corresponds to Picard's theorem.
Morley's categoricity theorem, a theorem related to model theory, discovered by Michael D. Morley
Olry Terquem (1782–1862), French mathematician who proved Feuerbach's theorem about the nine-point circle of a triangle
The Pandya theorem is a good illustration of the richness of information forthcoming from a judicious use of subtle symmetry principles connecting vastly different sectors of nuclear systems.
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.
The quantum ergodicity theorem of Shnirelman, Yves Colin de Verdière, and Zelditch states that a compact Riemannian manifold whose unit tangent bundle is ergodic under the geodesic flow is also ergodic in the sense that the probability density associated to the nth eigenfunction of the Laplacian tends weakly to the uniform distribution on the unit cotangent bundle as n → ∞.
Leonid Vaseršteĭn later gave a simpler and much shorter proof of the theorem which can be found in Serge Lang's Algebra.
Kleene's recursion theorem, also called the fixed point theorem, in computability theory
In algebraic number theory, a reflection theorem or Spiegelungssatz (German for reflection theorem – see Spiegel and Satz) is one of a collection of theorems linking the sizes of different ideal class groups (or ray class groups), or the sizes of different isotypic components of a class group.
The theorem for compact Riemann surfaces can be deduced from the algebraic version using Chow's theorem and the GAGA principle: in fact, every compact Riemann surface is defined by algebraic equations in some complex projective space.
In 1646 John Wallis received from Foster a theorem on spherical triangles which he afterwards published in his Mechanica.
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity.
The theorem was first published by Thoralf Skolem in 1927 in his paper Zur Theorie der assoziativen Zahlensysteme (German: On the theory of associative number systems) and later rediscovered by Emmy Noether.
It was introduced by Arnold Schönhage in his 1982 paper The fundamental theorem of algebra in terms of computational complexity (Technical report, Mathematisches Institut der Universität Tübingen).
Stagnation zones theorems are closely related to pre-Liouville's theorems about evaluation of solutions fluctuation, which direct consequences are the different versions of the classic Liouville theorem about conversion of the entire doubly periodic function into the identical constant.
The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.
1260 — Al-Farisi gave a new proof of Thabit ibn Qurra's theorem, introducing important new ideas concerning factorization and combinatorial methods.
Fritz Zwicky was the first to use the virial theorem to deduce the existence of unseen matter, which is now called dark matter.
The first result in this direction was given by David Preiss in 1979: there exists a Gaussian measure γ on an (infinite-dimensional) separable Hilbert space H so that the Vitali covering theorem fails for (H, Borel(H), γ).
Hohenberg-Kohn theorem was further developed, in collaboration with Lu Jeu Sham, to produce the Kohn-Sham equations.
The Weyl–Schouten theorem in mathematics says that a Riemannian manifold of dimension n with n ≥ 3 is conformally flat if and only if the Schouten tensor is a Codazzi tensor for n = 3, or the Weyl tensor vanishes for n > 3.
Scott E. Page introduced the diversity prediction theorem: "The squared error of the collective prediction equals the average squared error minus the predictive diversity".
Conley–Zehnder theorem, a mathematical theorem named after Charles C. Conley and Eduard Zehnder