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called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as theorems only the...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow...

Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply...

x ) {\displaystyle \log _{e}(x)} . In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named...

_{a}^{b}g(x)\,dx.} There are various slightly different theorems called the second mean value theorem for definite integrals. A commonly found version is...

general-sounding but only refer to a single theorem. Antidynamo theorems are a general category of theorems that restrict the type of magnetic fields that...

The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded...

by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to...

Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of...

theorems - theorems regarding the existence of lines separating objects in the plane without harming too many of them. Guillotine separation theorems...

S2CID 12076544. Media related to Fundamental theorems at Wikimedia Commons "Some Fundamental Theorems in Mathematics" (Knill, 2018) - self-described...

the complex plane. However, its usefulness is dwarfed by other general theorems in complex analysis. Namely, stronger versions of related results can be...

Integral Theorems of Vector Analysis". Vector Calculus (6th ed.). New York: W. H. Freeman and Company. ISBN 978-1-4292-1508-4. Green's Theorem on MathWorld...

theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem...

function over its domain. The Fubini and Tonelli theorems are usually combined and form the Fubini–Tonelli theorem, which gives the conditions under which it...

order. The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate. From A, draw a line...

theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which...

The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the...

formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the...

Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to an + bn = cn...

In mathematics, Ratner's theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner...

reciprocity theorem for group representations Stanley's reciprocity theorem for generating functions Reciprocity (engineering), theorems relating signals...

theorem may refer to any of several theorems developed by the mathematician Kurt Gödel: Gödel's incompleteness theorems Gödel's completeness theorem Gödel's...

and induced form automorphisms. The theorems are named after C. T. C. Wall, who proved them in 1964. Wall's theorem on h-cobordisms claims, that simply...

over a field Noether isomorphism theorems in abstract algebra Max Noether's theorem, several theorems Noether's theorem on rationality for surfaces Noether...

In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often...

appeared in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously derived no free lunch theorems for machine learning (statistical...

corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mathematician Emmy Noether in 1918. The...

supersymmetry a theory has, the more renormalization theorems apply. Therefore, a renormalization theorem that is valid for a theory with N {\displaystyle...

the orthogonal nature of these two sets of theorem. As with the summation theorems, the connectivity theorems can also be proved using more rigorous mathematical...

In mathematical analysis, the Szegő limit theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. They were first proved...

In mathematics, two Prüfer theorems, named after Heinz Prüfer, describe the structure of certain infinite abelian groups. They have been generalized by...

selection function from a given set-valued map. There are various selection theorems, and they are important in the theories of differential inclusions, optimal...

9, pp. 160–188, Theorems 7 and 8. In Theorem 7 Euler proves the formula in the special case s = 1 {\displaystyle s=1} , and in Theorem 8 he proves it more...

Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems: Gromov's compactness theorem (geometry)...

to already established results. These results, called theorems, include previously proved theorems, axioms, and—in case of abstraction from nature—some...

Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities...

homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier results of Henri Poincaré. The Hurewicz theorems are a key link between...

certain conditions identified by minimax theorems. The first theorem in this sense is von Neumann's minimax theorem about two-player zero-sum games published...

by d {\displaystyle d} is τ . {\displaystyle \tau .} Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable...

which is impossible. The theorems in this section simultaneously imply Euclid's theorem and other results. Dirichlet's theorem states that for any two...

twentieth century concerns the issue of purely theoretic existence theorems, that is, theorems which depend on non-constructive foundational material such as...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

These theorems are the result of the stoichiometric structure and mass conservation properties of biochemical networks. Equivalent theorems have not...

of the first known proofs of theorems in geometry. Eudoxus (408–355 BCE) and Theaetetus (417–369 BCE) formulated theorems but did not prove them. Aristotle...

of these theorems can be proven in a completely effective manner, each one can be effectively obtained from the other. The compactness theorem says that...

Arrow's theorem can thus be considered a special case of Harsanyi's utilitarian theorem and other utility representation theorems like the VNM theorem, which...

Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely related theorems, which...

In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide...

Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that...

Erdős–Ginzburg–Ziv theorem after its discoverers. It may also be deduced from the Cauchy–Davenport theorem. More general results than this theorem exist, such...

Differential privacy composition theorems are mathematical tools used in differential privacy to analyze and bound the accumulated privacy loss when multiple...

In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse...

automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a...

The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence...

formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely...

Tarski's theorem may refer to the following theorems of Alfred Tarski: Tarski's theorem about choice Tarski's undefinability theorem Tarski's theorem on the...

theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two...

concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for...

increases without bound. These theorems require stronger hypotheses than the forms of the central limit theorem given above. Theorems of this type are often called...

Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to say about...

generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by...

the Bondy–Chvátal theorem, which generalizes earlier results by G. A. Dirac (1952) and Øystein Ore. Both Dirac's and Ore's theorems can also be derived...

Several theorems in mathematical analysis bear the name of Giuseppe Vitali: Vitali covering theorem in the foundations of measure theory Various theorems concerning...

both simplifies and generalizes several theorems from vector calculus. In particular, the fundamental theorem of calculus is the special case where the...

sequentially compact, so that the Bolzano–Weierstrass and Heine–Borel theorems are essentially the same. There are different important equilibrium concepts...

1017/CBO9780511525919. ISBN 9780521598385. Allendoerfer, Carl B. (1974). "Theorems about Differentiable Functions". Calculus of Several Variables and Differentiable...

Fixed-point theorems in infinite-dimensional spaces Injective metric space Kakutani fixed-point theorem Kleene fixed-point theorem Knaster–Tarski theorem Lefschetz...

In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued...

There are several theorems known as the Helmholtz theorem: Helmholtz decomposition, also known as the fundamental theorem of vector calculus Helmholtz...

Tutte's theorem may refer to several theorems of W. T. Tutte, including: Tutte's theorem on Hamiltonian cycles, the existence of Hamiltonian cycles in...

Tutte's theorem on perfect matchings. A generalization of Hall's theorem to bipartite hypergraphs is provided by various Hall-type theorems for hypergraphs...

shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular...

the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally, these theorems say that given more...

are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast...

theory). This article focuses on prime ideal theorems from order theory. Although the various prime ideal theorems may appear simple and intuitive, they cannot...

on all of X. At a deeper level, these theorems were used by Jean-Pierre Serre to prove the GAGA theorem. Theorem B is sharp in the sense that if H1(X,...

one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance...

fundamental concepts in this field and the intractability of really general theorems, might try their hand at showing under what circumstances this simple relationship...

Budan de Boislaurent. A similar theorem was published independently by Joseph Fourier in 1820. Each of these theorems is a corollary of the other. Fourier's...

there are several finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical logic This...

The Bruck–Ryser–Chowla theorem is a result on the combinatorics of symmetric block designs that implies nonexistence of certain kinds of design. It states...

mathematics, Nash's theorem may refer to one of the following: the Nash embedding theorems in differential geometry Nash's theorem on the existence of...

operations of the theorem abstract type. Users can write arbitrarily complex ML programs to compute theorems; the validity of theorems does not depend on...

In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant...

Examples are Von Neumann–Morgenstern utility theorem and Debreu's representation theorems. Classification theorem – Describes the objects of a given type,...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by...

mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur...

There are several mathematical theorems named after Ferdinand Georg Frobenius. They include: Frobenius theorem (differential topology) in differential...

Limit theorem may refer to: Central limit theorem, in probability theory Edgeworth's limit theorem, in economics Plastic limit theorems, in continuum...

Glivenko–Cantelli theorem Kolmogorov–Smirnov test Donsker, M.D. (1951). "An invariance principle for certain probability limit theorems". Memoirs of the...

theorem that is proved from true premises by means of a sequence of syllogisms (inference rules), the premises being either already proved theorems or...

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle...

Sarkaria, K. S. (November 2000), "Tverberg partitions and Borsuk–Ulam theorems", Pacific Journal of Mathematics, 196 (1): 231–241, doi:10.2140/pjm.2000...

April 2023. Doron Zeilberger, Opinion 82: A Good Lemma is Worth a Thousand Theorems This article incorporates material from Lemma on PlanetMath, which is licensed...

space n. The somewhat weaker analogous theorems for time are the time hierarchy theorems. The time hierarchy theorems are important statements about time-bounded...

Several theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the...

supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Similarly, a non-conservative...

in the theory of stochastic processes – Doob's martingale convergence theorems are a collection of results on the limits of supermartingales, named after...

T\Vdash \rho } (by theorems 7 and 8) T ⊩ P r o v ( # ( ρ ) ) {\displaystyle T\Vdash Prov(\#(\rho ))} (by condition 1 and theorem 9) Thus T proves both...

the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections...

Stokes' theorem simultaneously generalizes the three theorems of vector calculus: the divergence theorem, Green's theorem, and the Kelvin-Stokes theorem. The...

In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued...

"Review of Art Gallery Theorems and Algorithms", Mathematical Reviews, MR 0921437 Vlach, M., "Review of Art Gallery Theorems and Algorithms", zbMATH...

Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville: In complex analysis, see Liouville's theorem (complex analysis)...

In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations...

Cohen–Seidenberg theorems, which were proved by Irvin S. Cohen and Abraham Seidenberg. These are known as the going-up and going-down theorems. Let A ⊆ B be...

In computability theory, there are a number of basis theorems. These theorems show that particular kinds of sets always must have some members that are...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

Suslin's theorem may refer to: The Quillen–Suslin theorem (formerly the Serre conjecture), due to Andrei Suslin. Any of several theorems about analytic...

In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after...

representation theory Hammersley–Clifford theorem in probability Clifford's circle theorems in Euclidean geometry This disambiguation page lists mathematics articles...

Dirichlet's theorem may refer to any of several mathematical theorems due to Peter Gustav Lejeune Dirichlet. Dirichlet's theorem on arithmetic progressions...

theorem may refer to several theorems named for the American mathematician George David Birkhoff: Birkhoff's theorem (relativity) Birkhoff's theorem (electromagnetism)...

must be near their own points. In this terminology, one has the following theorems: Every finite derivative has associated sets in M 3 {\displaystyle M_{3}}...

In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions...

In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left-half complex plane. Polynomials...

In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω ( n ) {\displaystyle...

In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The...

stronger mathematical assumptions than others. Significantly, Bell-type theorems do not refer to any particular theory of local hidden variables, but instead...

that there is no free lunch. Wolpert had previously derived no free lunch theorems for machine learning (statistical inference). Before Wolpert's article...

{u_{i}(X_{j})}} Weller's theorem - on the existence of PEEF allocations in cake-cutting. More related theorems by Hal Varian can be found in. Theorems about PEEF allocations...

named after Daniel Quillen. The precise statements of the theorems are as follows. Quillen's Theorem A—If f : C → D {\displaystyle f:C\to D} is a functor such...

characters (also called the Brauer-Tate theorem). Brauer's main theorems Brauer–Suzuki theorem Brouwer fixed-point theorem This disambiguation page lists mathematics...

shift of ⁠π/2⁠. These are also known as the angle addition and subtraction theorems (or formulae). sin ⁡ ( α + β ) = sin ⁡ α cos ⁡ β + cos ⁡ α sin ⁡ β sin...

ambiguous definitions of the foundations of calculus so that important theorems could not be proven with sufficient rigour. Although Bolzano had developed...

In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow: Chow's theorem: Any analytic subvariety in projective space is...

Brauer's main theorems are three theorems in representation theory of finite groups linking the blocks of a finite group (in characteristic p) with those...

his theorem is sometimes spelled (incorrectly) in German characters, with an umlaut. Kőnig's theorem is equivalent to many other min-max theorems in graph...

Schaefer's theorem may refer to two unrelated theorems: Schaefer's dichotomy theorem, a theorem about the theory of NP-completeness by Thomas J. Schaefer...

moving from finite to infinite graphs, theorems in this area are usually phrased in set-theoretic terminology. Theorem. Let X {\displaystyle X} be some infinite...

classical logic. the set of theorems generated is different from the set of theorems generated by classical logic. The set of theorems of a deviant logic can...

The Schröder–Bernstein theorem from set theory has analogs in the context of operator algebras. This article discusses such operator-algebraic results...

ISBN 978-0-486-81690-6. For the Sylow theorems see p. 43; for Lagrange's theorem, see p. 12; for Burnside's theorem see p. 143. Bryant, John; Sangwin, Christopher...

of his work in letters to friends, often with little or no proof of his theorems. In some of these letters to his friends, he explored many of the fundamental...

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for...

problem. Theorems in Ramsey theory are generally one of the following two types. Many such theorems, which are modeled after Ramsey's theorem itself, assert...

In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include:...

Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with...

theorem may refer to any of several mathematical theorems due to brothers Frigyes Riesz and Marcel Riesz: F. and M. Riesz theorem F. Riesz's theorem –...

addition theorems can be said to hold. A more modern aspect is the theory of formal groups. Timeline of abelian varieties Addition theorem for spherical...

In mathematics, Hall's theorem may refer to: Hall's marriage theorem One of several theorems about Hall subgroups This disambiguation page lists mathematics...

Folk theorem or folklore theorem may refer to: Mathematical folklore, theorems that are widely known to mathematicians but cannot be traced back to an...

Economic Theory. 8: 307–319. Ruben D Cohen: An Implication of the Modigliani-Miller Capital Structuring Theorems on the Relation between Equity and Debt...

as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the...

(Demailly 1996, p.30) (Manivel 1997) Demailly, Jean-Pierre (1988). "Vanishing theorems for tensor powers of an ample vector bundle" (PDF). Inventiones Mathematicae...

standard formula given for cantilever beams under end loads. Castigliano's theorems apply if the strain energy is finite. This is true if m − i > n / 2 {\displaystyle...

Bayesianism, Preprint: Nada, KTH (1999) — http://www.stats.org.uk/cox-theorems/ArnborgSjodin2001.pdf Stefan Arnborg and Gunnar Sjödin, A note on the foundations...

level mathematics. As of May 2025, mathlib had formalized over 210,000 theorems and 100,000 definitions in Lean. Other libraries include CSLib which is...

separation theorem, the theorem that disjoint compact convex sets are linearly separable Watson, Donald (1973), "A refinement of theorems of Kirchberger...

The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although...

"The Consistency Strengths of Some Finite Forms of the Higman and Kruskal Theorems". In Friedman, Harvey; Harrington, L. A. (eds.). Harvey Friedman's research...

In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after...

J. 24 (1957), 345–348. Cheng, Shiu Yuen (1975), "Eigenvalue comparison theorems and its geometric applications", Mathematische Zeitschrift, 143 (3): 289–297...

{\displaystyle B} . Deduction theorems exist for both propositional logic and first-order logic. The deduction theorem is an important tool in Hilbert-style...

above isomorphism. The base change theorems discussed below are statements of a similar kind. The base change theorems presented below all assert that (for...

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are...

displaying short descriptions of redirect targets Closed graph theorem (functional analysis) – Theorems connecting continuity to closure of graphs Closed linear...

characteristic functions. This theorem is the basis for one approach to prove the central limit theorem and is one of the major theorems concerning characteristic...

theorems associated with the name König or Kőnig: Kőnig's theorem (set theory), named after the Hungarian mathematician Gyula Kőnig. Kőnig's theorem (complex...

connectedness theorem "Bertini theorems", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Hartshorne, Ch. III.10. Poonen, Bjorn (2004). "Bertini theorems over...

the indicator function for the set C {\displaystyle C} . Theorems The following two theorems give sufficient conditions for the weak and strong versions...

Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous...

"semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically...

2013-02-01. Dorf, Richard C.; Svoboda, James A. (2010). "Chapter 5: Circuit Theorems". Introduction to Electric Circuits (8th ed.). Hoboken, New Jersey: John...

By 2023, Metamath had been used to prove 74 of the 100 theorems of the "Formalizing 100 Theorems" challenge. At least 19 proof verifiers use the Metamath...

1007/bf02546511. D.C. Champeney (1987). "Power spectra and Wiener's theorems". A Handbook of Fourier Theorems. Cambridge University Press. p. 102. ISBN 9780521265034...

In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k. Eichler...

In mathematics, the 15 theorem or Conway–Schneeberger Fifteen Theorem, proved by John H. Conway and W. A. Schneeberger in 1993, states that if a positive...

tool used in the analysis of many physical systems. Many of the critical theorems of vector calculus generalize elegantly to statements about the integration...

This is a list of misnamed theorems in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object)...

incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and consistent. Gödel's theorem applies...

intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel...

1090/S0002-9939-1987-0891165-X. Kirillov, A.A.; Gvishiani, A.D. (1982). Theorems and Problems in Functional Analysis. Springer-Verlag New York. ISBN 978-1-4613-8155-6...

Mazur's theorem may refer to: Ascoli–Mazur theorem, or Mazur's theorem, a corollary of the Hahn–Banach separation theorem in functional analysis Mazur's...

Primos Spectantium Demonstratio" (in English: "Demonstration of Certain Theorems Concerning Prime Numbers") in the Proceedings of the St. Petersburg Academy...

continuous in the usual sense. Hence these two theorems imply the boundedness theorem and the extreme value theorem. Spivak, Michael (September 1994). Calculus...

algebro-geometric objects of some fixed kind List of manifolds List of theorems "An enormous theorem: the classification of finite simple groups | plus.maths.org"...

Sylvester's theorem or the Sylvester theorem may refer to any of several theorems named after James Joseph Sylvester: The Sylvester–Gallai theorem, on the...

uniqueness theorems include: Cauchy's rigidity theorem and Alexandrov's uniqueness theorem for three-dimensional polyhedra. Black hole uniqueness theorem Cauchy–Kowalevski...

In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating to intersections of circles...

term Japanese theorem refers to either of the following two geometrical theorems: Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals...

integrals. After seeing Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy said the theorems "defeated me completely; I had...

Joyal's theorem may refer to: Joyal's extension theorem Joyal's lifting theorem Joyal's completeness theorem Quasi-category § Definition – with a result...

{\displaystyle n} must be coprime. The theorem is further generalized by some of Carmichael's theorems. The theorem may be used to easily reduce large powers...

determined. The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution...

refound the theorem. So the theorem is also called the Fontené's (Second) theorem. Fontené theorems [ja; vi] Weisstein, Eric W., "Griffiths' Theorem", MathWorld...

and extensions are called Jackson-type theorems. A converse to Jackson's inequality is given by Bernstein's theorem. See also constructive function theory...

theorems identified in mathematics, such as: Fundamental theorem of algebra, a theorem regarding the factorization of polynomials Fundamental theorem...

basic theorems of which are: Egorov's theorem, Lusin's theorem, Fatou's lemma, the monotone and dominated convergence theorems, and Fubini's theorem. Other...

problems now treated by integral calculus. In The Method of Mechanical Theorems he describes, for example, calculating the center of gravity of a solid...

functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects...

The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals...

prove theorems of mathematics. The field was founded by Harvey Friedman. Its defining method can be described as "going backwards from the theorems to the...

Chapter XVIII: Compactness, Embeddings and Definability. 645--716, see Theorems 4.5.9, 4.6.12 and Proposition 4.6.9. For compact logics for an extended...

Denjoy's theorem may refer to several theorems proved by Arnaud Denjoy, including Denjoy–Carleman theorem Denjoy–Koksma inequality Denjoy–Luzin theorem Denjoy–Luzin–Saks...

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes or a prime and a semiprime...

stochastic calculus on manifolds other than Rn. The dominated convergence theorem does not hold for the Stratonovich integral; consequently it is very difficult...

implemented as a library which defines an abstract data type of proven theorems such that new objects of this type can only be created using the functions...

In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on...

can be used to show that the Π02-theorems of various first-order theories of classical mathematics are also theorems of intuitionistic mathematics. It...

Lagrange's theorem usually refers to any of the following theorems, attributed to Joseph Louis Lagrange: Lagrange's theorem (group theory) Lagrange's theorem (number...

knowledge. They are accepted without demonstration. All other assertions (theorems, in the case of mathematics) must be proven with the aid of these basic...

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard...

Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime...

the Riesz extension theorems. However, there is a minor flaw (in the first edition) in the proof of one of the extension theorems, the discovery of which...

a comparison theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is closely related to Myers' theorem, and is the key...

from the Lie algebra. ¶ These seven theorems – the three theorems of Lie and their converses, and Taylor's theorem – provide an essential equivalence between...

Stone's theorem may refer to a number of theorems of Marshall Stone: Stone's representation theorem for Boolean algebras Stone–Weierstrass theorem Stone–von...

remainder theorem has been used to construct a Gödel numbering for sequences, which is involved in the proof of Gödel's incompleteness theorems. The prime-factor...

Concepts and Theorems of Mathematical Statistics. New York: Springer-Verlag. ISBN 0-387-96186-0. Serfling, Robert J. (1980). Approximation Theorems of Mathematical...

Gabriel Andrew Dirac (1925–1984), a graph theorist after whom these three theorems were named Paul Dirac (1902–1984), a mathematical physicist Dirac equation...

sets of theorems exist, the summation and connectivity theorems. Branched pathways have an additional set of branch centric summation theorems. When combined...

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices...

Chevalley's theorem is an immediate consequence of the Chevalley–Warning theorem since p {\displaystyle p} is at least 2. Both theorems are best possible...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose...

Several theorems proved by the French mathematician Claude Chevalley bear his name. Chevalley–Shephard–Todd theorem in invariant theory of finite groups...

time. One of the earliest existence and uniqueness theorems for convex polyhedra is Cauchy's theorem, which states that a convex polyhedron is uniquely...

The Thomas theorem is a theory of sociology which was formulated in 1928 by William Isaac Thomas and Dorothy Swaine Thomas: If men define situations as...

A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite...

Krylov–Bogolyubov theorem (also known as the existence of invariant measures theorem) may refer to either of the two related fundamental theorems within the...

social choice functions, and is a condition for Arrow's impossibility theorem. With unrestricted domain, the social welfare function accounts for all...

In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. For any n + 1 pairwise...

for societies. The theorem was first derived by Duncan Black in 1948, and independently by Kenneth Arrow. Similar median voter theorems exist for rules like...

is also Latin for "theorem", and a number of theorems are sometimes referred to by a Latin name in English, most notably two theorems of Carl Friedrich...

the GAGA comparison theorems. However, in 1987 Pierre Deligne and Luc Illusie gave a purely algebraic proof of the vanishing theorem in (Deligne & Illusie...

Kurt Gödel developed the concept for the proof of his incompleteness theorems. A Gödel numbering can be interpreted as an encoding in which a number...

Midpoint theorem may refer to the following mathematical theorems: Midpoint theorem (triangle) Midpoint theorem (conics) Midpoint theorem, describing the...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given...

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly...

Marguerite's Theorem (French: Le Théorème de Marguerite) is 2023 French-Swiss drama film co-written and directed by Anna Novion [fr]. It is about a female...

impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a...

that cannot be computed or explicitly described, and the existence of theorems of arithmetic that cannot be proved with Peano arithmetic. The result was...

recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first...

Alexander (1996). "Polynomial extensions of van der Waerden's and Szemerédi's theorems". Journal of the American Mathematical Society. 9 (3): 725–753. doi:10...

the theorems of a system. A logical system is decidable if there is an effective method for determining whether arbitrary formulas are theorems of the...

edges of the tetrahedron intersect in a common point. Bundle theorem Clifford's circle theorems Miquel configuration A high school teacher in the French countryside...

This theorem has a generalization to any compact even-dimensional Riemannian manifold, see generalized Gauss-Bonnet theorem. Nash embedding theorems. They...

p-complement. The Frobenius normal p-complement theorem is a strengthening of the Burnside normal p-complement theorem, which states that if the normalizer of...

fundamental theorems on polynomials, the Nullstellensatz (zero-locus theorem) and the syzygy theorem (theorem on relations). These three theorems were the...

field of limit analysis is based on a set of theorems, referred to as limit theorems, which are a set of theorems based on the law of conservation of energy...

mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher. In complex analysis, the theorem states that the...

complexes. Thus Künneth theorems can not be obtained by the above methods of homological algebra. Nevertheless, Künneth theorems in just the same form have...

geometry. Four theorems of fundamental importance in Diophantine geometry are: Mordell–Weil theorem Roth's theorem Siegel's theorem Faltings' theorem Another...

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial...

system to evolve between two distinguishable (orthogonal) states. QSL theorems are closely related to time-energy uncertainty relations. In 1945, Leonid...

Open mapping theorem may refer to: Open mapping theorem (functional analysis) (also known as the Banach–Schauder theorem), states that a surjective continuous...

theorem. The original theorems did not use the language of distributions, and instead applied to square-integrable functions. The first such theorem using...

the other player's punishment in the future. There are many results in theorems which deal with how to achieve and maintain a socially optimal equilibrium...

of the opposite side Ostermann, Alexander; Wanner, Gerhard (2012). "The Theorems of Apollonius–Pappus–Stewart". Geometry by Its History. Springer. § 4.5...

In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic...

(1951). Both theorems are often merged in the Bing-Nagata-Smirnov metrization theorem. It is a common tool to prove other metrization theorems, e.g. the...

mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard any suitable collection of random...

Moreover, computable normal numbers exist. These non-probabilistic existence theorems follow from probabilistic results: (a) a number chosen at random (uniformly...

Trapezoidal rule Coddington & Levinson (1955), Theorem I.3.1 Murray, Francis; Miller, Kenneth. Existence Theorems for Ordinary Differential Equations. p. 50...

each in terms of cross-ratios, the two theorems may be seen as projective duals. Several proofs of the theorem have been created. Two proofs are given...

consequence of Tychonoff's theorem. Tychonoff's theorem has been used to prove many other mathematical theorems. These include theorems about compactness of...

not requiring infinite sets, and is the weakest known set theory whose theorems include the first-order Peano axioms. The ontology of GST is identical...

hence the use of the limit inferior. Converses to a theorem like Abel's are called Tauberian theorems: There is no exact converse, but results conditional...

highest weights Lie's third theorem, an equivalence between Lie algebras and simply-connected Lie groups Cartan's theorems A and B, c.1931 results by Henri...

Theorems about abelian groups (i.e. modules over the principal ideal domain Z {\displaystyle \mathbb {Z} } ) can often be generalized to theorems about...

ring with a Hecke algebra (now referred to as an R=T theorem) to prove modularity lifting theorems has been an influential development in algebraic number...

Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex...

For Mertens' results on the distribution of prime numbers, see Mertens' theorems. For Mertens' result on convergence of Cauchy products of series, see Cauchy...

collection in 13 books of definitions, postulates, geometric constructions, and theorems with their proofs that covers plane and solid Euclidean geometry, elementary...

(2001) [1994], "Liouville theorems", Encyclopedia of Mathematics, EMS Press Nelson, Edward (1961). "A proof of Liouville's theorem". Proceedings of the American...

Tasos; Patsopoulos, Dimitris (January 2006). "The Theorem of Thales: A Study of the Naming of Theorems in School Geometry Textbooks". The International...

mean field theory, limit theorems (as the number of objects becomes large) are considered and generalise the central limit theorem for empirical measures...

In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a (univariate) polynomial...

once thought that certain theorems, like the prime number theorem, could only be proved by invoking "higher" mathematical theorems or techniques. However...

the field of complex numbers. By invoking the Kodaira embedding theorem and Chow's theorem, one may equivalently define a complex abelian variety of dimension...

The fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and...

fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Continuous fixed-point theorems often require...

(1978). "Abstract families and the adjoint functor theorems, ch. IV The adjoint functor theorems". Indexed Categories and Their Applications. Lecture...

Mathematiker-Vereinigung, 19: 155–159 Thomas, Robin (1999), "Recent Excluded Minor Theorems for Graphs", in Lamb, John D.; Preece, D. A. (eds.), Surveys in combinatorics...

In probability theory, the dimension doubling theorems are two results about the Hausdorff dimension of an image of a Brownian motion. In their core both...

Claude Chevalley realized that after an appropriate reformulation, many theorems about semisimple Lie groups admit analogues for algebraic groups over an...

There are multiple theorems named after the French mathematician Camille Jordan: The Jordan curve theorem states that every simple closed curve has a well-defined...

proved theorems related to the law of large numbers, using a probabilistic interpretation of Birkhoff's ergodic theorem. Then he used these theorems to give...

1103/PhysRevLett.26.331. Bhattacharya, Sourav; Lahiri, Amitabha (2007). "No hair theorems for positive Λ". Physical Review Letters. 99 (20) 201101. arXiv:gr-qc/0702006...

topological minor. Wagner published both theorems in 1937, subsequent to the 1930 publication of Kuratowski's theorem, according to which a graph is planar...

extension may not be unique. Closed graph theorem (functional analysis) – Theorems connecting continuity to closure of graphs Continuous linear operator –...

the second the relations). The theorems are among the most important results of invariant theory. Classically the theorems are proved over the complex numbers...

whilst writing Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, which was later translated into Polish, Spanish,...

several theorems of Helmut Hasse that are sometimes called Hasse's theorem: Hasse norm theorem Hasse's theorem on elliptic curves Hasse–Arf theorem Hasse–Minkowski...

the basis of two classical and important theorems, the Fredholm alternative and the Hilbert–Schmidt theorem. The result is named after the Swedish mathematician...

In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number...

 273–274; Gilbarg & Trudinger 2001, Theorem 2.9; Protter & Weinberger 1984, Section 2.10. Gilbarg & Trudinger 2001, Theorems 2.7 and 2.8. Sources Courant, R...

exceptions involving parallel lines. Desargues's theorem is therefore one of the simplest geometric theorems whose natural home is in projective rather than...

to 1. There are many other jury theorems, relaxing some or all of these assumptions. The premise of all jury theorems is that there is an objective truth...

abstracts away from the details of encodings used in Gödel's incompleteness theorems by expressing the provability of ϕ {\displaystyle \phi } in the given system...

recursive functions. The theorem has been used in proofs of Gödel's incompleteness theorems. One would first prove the theorems for all theories that with...

formal language theory, the Chomsky–Schützenberger theorem may refer to either of two different theorems derived by Noam Chomsky and Marcel-Paul Schützenberger...

In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate...

geometry, including some of the fundamental theorems of functional analysis. Versions of the Baire category theorem were first proved independently in 1897...

generalization of Burnside's theorem that any group whose order is of the form paqb for primes p and q is solvable, because Sylow's theorem implies that all Hall...

natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k {\displaystyle...

four major theorems which are sometimes called the four pillars of functional analysis: the Hahn–Banach theorem the open mapping theorem the closed graph...

Two other theorems of Helly and Radon are closely related to Carathéodory's theorem: the latter theorem can be used to prove the former theorems and vice...

the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is generally effective, but there may be no method...

common in abstract algebra, where they often take the form of “structure theorems,” expressing the structure of an object in a simple form. These results...

mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often...

"lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures...

orders the two theorems differ, and (as Mirsky observes) Dilworth's theorem is more difficult to prove. Mirsky's theorem and Dilworth's theorem are also related...

In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping...

properties can be derived from these, and they are sufficient for proving theorems in mathematics. Similarly, set membership can be understood solely through...

Zariski (1958) proved that Castelnuovo's theorem also holds over fields of positive characteristic. Castelnuovo's theorem also implies that any unirational complex...

electronic devices and systems. A number of fundamental electrical laws and theorems apply to all electrical networks. These include: Faraday's law of induction:...

equilibrium Lyapunov central limit theorem, variant of the central limit theorem Lyapunov vector-measure theorem, theorem in measure theory that the range...

doi:10.3390/sym13050853 Champeney, D.C. (1987), A Handbook of Fourier Theorems, Cambridge University Press, Bibcode:1987hft..book.....C Chandrasekharan...

In fluid dynamics, Squire's theorem states that of all the perturbations that may be applied to a shear flow (i.e. a velocity field of the form U = (...

of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations...

dots and dividers) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems, such as how many...

Q}{\therefore \neg (P\lor Q)}}} and expressed as truth-functional tautologies or theorems of propositional logic: ¬ ( P ∧ Q ) ↔ ( ¬ P ∨ ¬ Q ) , ¬ ( P ∨ Q ) ↔ ( ¬...

the first 52 theorems in chapter two of Whitehead and Bertrand Russell's Principia Mathematica, and found a new and shorter proof for Theorem 2.85. In 1955...

dissipated to almost nothing by comparison. The impact of the known anti-dynamo theorems is that successful dynamos do not possess a high degree of symmetry. Dynamo...

Discrepancy theory is based on the following classic theorems: Geometric discrepancy theory The theorem of van Aardenne-Ehrenfest Arithmetic progressions...

corresponding theorems which generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce...

Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex...

Fixed-Point Theorems. New York: Springer. ISBN 0-387-96499-1. Dennis, John E.; Schnabel, Robert B. (1983). "The Kantorovich and Contractive Mapping Theorems". Numerical...

In graph theory, approximate max-flow min-cut theorems concern the relationship between the maximum flow rate (max-flow) and the minimum cut (min-cut)...

generalized Van Kampen theorems (HD-GVKT)". 15 October 2024. Archived from the original on August 1, 2009. Lee 2011, p. 253, Theorem 10.3. Greenberg & Harper...

and to applications of several theorems of such kind for various summability methods. The statement of these theorems has a standard structure: if a series...

The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator:...

Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. It...

In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It was first...

Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis...

volumes rather than derivatives and tangents (see The Method of Mechanical Theorems). The use of infinitesimals to compute rates of change was developed significantly...

(for example, the Paris–Harrington theorem) provable using second order but not first-order methods, but such theorems are rare to date. Erdős and Selberg's...

In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about...

Hurwitz's theorem can refer to several theorems named after Adolf Hurwitz: Hurwitz's theorem (complex analysis) Riemann–Hurwitz formula in algebraic geometry...

Brandao, Fernando G.S.L.; Harrow, Aram W. (2013-01-01). "Quantum de finetti theorems under local measurements with applications". Proceedings of the forty-fifth...

In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to...

Borsuk–Ulam theorem. Therefore, these two theorems are equivalent. There are several fixed-point theorems which come in three equivalent variants: an...

with the classical equation. It was established above that the Ehrenfest theorems are consequences of the Schrödinger equation. However, the converse is...

originally considered by Kimeldorf and Wahba) have representer theorems. Representer theorems are useful from a practical standpoint because they dramatically...

Descartes' theorem states that, for every four mutually tangent circles, the radii of the circles satisfy a certain quadratic equation. Descartes' theorem may...

Zero Theorem, Zero Conjecture, Zero Law or similar, may mean: X&Y, Coldplay's third album, once rumored to be titled Zero Theory The Zero Theorem, a science...

succeeded in replacing theorems of classical geometry with computations via invariants of transformation groups. Since that time, new theorems of classical geometry...

Igor (April 20, 2010), "Theorems 21.22–21.24, p. 203", Lectures on Discrete and Polyhedral Geometry Weisstein, Eric W., "Tennis Ball Theorem", MathWorld...

Problems and Theorems in Analysis (German: Aufgaben und Lehrsätze aus der Analysis) is a two-volume problem book in analysis by George Pólya and Gábor...

standard model, so a model where Goodstein's theorem fails must be non-standard. Gödel's incompleteness theorems also imply the existence of non-standard...

The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no...

In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative...

automatically satisfied under an assumption on Ricci curvature. These theorems have been widely used in the fields of geometric group theory and Riemannian...

became known as the modularity theorem. Several theorems in number theory similar to FLT follow from the modularity theorem. For example: no cube can be...

in a circle. As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle...

York. (Multiplication theorems are individually listed chapter by chapter) C. Truesdell, "On the Addition and Multiplication Theorems for the Special Functions"...

to the individual forces. Using this theorem, as well as Ohm's law, Helmholtz proved the following three theorems about the relation between the internal...

Using the narrow definition of theorem, for sentences provable from no premises, weak soundness says that all theorems are tautologies. Strong soundness...

In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite...

The parametricity theorem was originally stated by John C. Reynolds, who called it the abstraction theorem. In his paper "Theorems for free!", Philip...

image of the homomorphism. The homomorphism theorem is used to prove the isomorphism theorems. Similar theorems are valid for vector spaces, modules, and...

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete...

oversights throughout the text, including missing hypotheses in theorems, inaccurately stated theorems, and proofs that fail to handle all cases. A more recent...

by its theorems. Two formal systems F S {\displaystyle {\mathcal {FS}}} and F S ′ {\displaystyle {\mathcal {FS'}}} may have all the same theorems and yet...

Carnot's theorem or Carnot's principle may refer to: In geometry: Carnot's theorem (inradius, circumradius), describing a property of the incircle and...

about reality. The PBR theorem may also be compared with other no-go theorems like Bell's theorem and the Bell–Kochen–Specker theorem, which, respectively...

The Bernstein–Kushnirenko theorem, also called Bernstein–Khovanskii–Kushnirenko theorem (BKK theorem), states that the number of nonzero complex solutions...

The Wigner–Araki–Yanase theorem, also known as the WAY theorem, is a result in quantum physics establishing that the presence of a conservation law limits...

and vector calculus, such as the divergence theorem, magnetic flux, and its generalization, Stokes' theorem. Let us notice that we defined the surface...

Wiener's theorem is any of several theorems named after Norbert Wiener: Paley–Wiener theorem Wiener's 1/ƒ theorem about functions with absolutely convergent...

altitude figures prominently in many important theorems and their proofs. For example, besides those theorems listed below, the altitude plays a central role...

Kharitonov's theorem is a result used in control theory to assess the stability of a dynamical system when the physical parameters of the system are not...

questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the...

than a given natural number is computable. c.f. Gödel's incompleteness theorems; "On formally undecidable propositions of Principia Mathematica and related...

with topology, and obtained the first proof of the full Nielsen–Schreier theorem. Otto Schreier published an algebraic proof of this result in 1927, and...

In commutative algebra, Grothendieck local duality is a duality theorem for cohomology of modules over local rings, analogous to Serre duality of coherent...

Sylow theorems Transcendence of e and π (as corollaries of Lindemann–Weierstrass) Tychonoff's theorem (to do) Ultrafilter lemma Ultraparallel theorem Urysohn's...

See also Gap theorem (disambiguation) for other gap theorems in mathematics. In computational complexity theory, the gap theorem, also known as the Borodin–Trakhtenbrot...

Wojciech H. Zurek as well as Dennis Dieks the same year). The aforementioned theorems do not preclude the state of one system becoming entangled with the state...

branch of mathematics, Weinstein's neighbourhood theorem refers to a few distinct but related theorems, involving the neighbourhoods of submanifolds in...

In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may...

Thue's theorem may refer to the following mathematical theorems named after Axel Thue: Thue equation has finitely many solutions in integers. Thue's lemma...

differ only in sign. By re-writing each in terms of cross-ratios, the two theorems may be seen as projective duals. A proof given by John Wellesley Russell...

approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [...

in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping f : M → N {\displaystyle f\colon M\rightarrow...

In mathematics, Joyal's theorem is a theorem in homotopy theory that provides necessary and sufficient conditions for the solvability of a certain lifting...

Göttingen in 1915, she proved the two Noether's theorems, "one of the most important mathematical theorems ever proved in guiding the development of modern...

In the mathematical field of functional analysis, the Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian)...

complete metric space). The Hahn–Banach theorem is one of the fundamental theorems of functional analysis. Further theorems related to Banach are: Banach–Tarski...

36.1.48. PMC 1063129. PMID 16588946. Border, Kim C. (1989). Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press...

algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ⁠ ( x...

of theorems and concepts in that field. Łoś–Tarski preservation theorem Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski's...

not necessarily components of Proth's theorem. These are secondary facts largely attributed to other theorems, which are trivially evaluated during any...

their own expectation. The two theorems differ in the presence of more than one opponent: whereas the fundamental theorem always applies heads-up (one opponent)...

proved the principal theorems for this transform, the inversion formula, the Plancherel theorem and the analog of the Paley–Wiener theorem. Sigurdur Helgason...

defined on the same space. Several of the Sobolev embedding theorems are continuous embedding theorems. Let X and Y be two normed vector spaces, with norms ||·||X...

Function Theorem. Modern Birkhauser Classics. Birkhauser. ISBN 0-8176-4285-4. de Oliveira, Oswaldo (2013). "The Implicit and Inverse Function Theorems: Easy...

no-go theorems to show that spacetime symmetries and internal symmetries could not be combined in any but a trivial way. The first notable theorem was proved...

The Complete class theorems is a class of theorems in decision theory. They establish that all admissible decision rules are equivalent to the Bayesian...

Hirschhorn, Michael D. (2000). "Partial Fractions and Four Classical Theorems of Number Theory". The American Mathematical Monthly. 107 (3): 260–264...

The Ryll-Nardzewski theorem yields the existence of a Haar measure on compact groups. Fixed-point theorems Fixed-point theorems in infinite-dimensional...

Herbert A. Simon to "mimic human reasoning" in proving theorems and was demonstrated on fifty-two theorems from chapter two of Principia Mathematica, proving...

h-cobordism theorem showed that (simply connected) manifolds of dimension at least 5 are much easier than those of dimension 3 or 4. The proof of the theorem depends...

particularly in the following theorems of mathematical statistics. Completeness occurs in the Lehmann–Scheffé theorem, which states that given a complete...

commutation theorems of Murray and von Neumann; equally well the main results on Hilbert algebras can also be deduced directly from the commutation theorems for...

The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics...

Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram...

likelihood). Gödel's incompleteness theorem shows that no consistent, recursively enumerable theory (that is, one whose theorems form a recursively enumerable...

by Post's theorem. A weaker relationship was demonstrated by Kurt Gödel in the proofs of his completeness theorem and incompleteness theorems. Gödel's...

references). Fixed-point theorems Banach fixed-point theorem Kakutani fixed-point theorem F. F. Bonsall, Lectures on some fixed point theorems of functional analysis...

power of any prime dividing the group order. For solvable groups, Hall's theorems assert the existence of a subgroup of order equal to any unitary divisor...

infinity of natural numbers. Gödel's second incompleteness theorem (see Gödel's incompleteness theorems) places a severe limit on how weak a finitistic system...

{\textstyle L} . In general, theorems relating the properties of a lattice with properties of its dual are known as transference theorems. In this section we explain...

graph theorems hold Theorem 4 of Tao. NB: The Hausdorffness there is put to ensure the graph of a continuous map is closed. Vogt 2000, Theorem 1.8. Tao...

The low basis theorem is one of several basis theorems in computability theory, each of which show that, given an infinite subtree of the binary tree 2...

bandage completely. His research group designed the TPS, an automated theorem proving system for first-order and higher-order logic. A subsystem ETPS...

mathematics, specifically in algebraic number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting...

I. Pokhozhaev and is similar to the virial theorem. This relation is also known as G.H. Derrick's theorem. Similar identities can be derived for other...

Dilworth's theorem is equivalent to Kőnig's theorem on bipartite graph matching and several other related theorems including Hall's marriage theorem. To prove...

These models give rise to an influential theorem—the median voter theorem—attributed to Duncan Black. This theorem stipulates that within a broad range of...

Müntz–Szász theorem is a basic result of approximation theory, proved by Herman Müntz in 1914 and Otto Szász in 1916. Roughly speaking, the theorem shows to...

Toponogov's theorem (named after Victor Andreevich Toponogov) is a triangle comparison theorem. It is one of a family of comparison theorems that quantify...

In proving Fermat's Last Theorem, Wiles developed new tools for mathematicians to begin unifying disparate ideas and theorems. His former student Taylor...

holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes referred...

general theorems on rings rely heavily on the Noetherian property (for example, the Lasker–Noether theorem and the Krull intersection theorem). Noetherian...

known as the orbit–stabilizer theorem. If G is finite then the orbit–stabilizer theorem, together with Lagrange's theorem, gives | G ⋅ x | = [ G : G x...

studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces Disquisitiones Arithmeticae...

embedding theorems, Nash turned to research dealing directly with partial differential equations, where he discovered and proved the De Giorgi–Nash theorem, thereby...

Carleson's theorem is a fundamental result in mathematical analysis establishing the (Lebesgue) pointwise almost everywhere convergence of Fourier series...

In mathematics, Sharkovskii's theorem (also spelled Sharkovsky, Sharkovskiy, Šarkovskii or Sarkovskii), named after Oleksandr Mykolayovych Sharkovsky...

) Many of these results are sometimes called "Hadamard's theorem". Cartan–Hadamard theorem, a statement in Riemannian geometry concerning the structure...

coordinatewise. The isomorphism theorems, which encompass the isomorphism theorems of groups, rings, modules, etc. Birkhoff's HSP Theorem, which states that a class...

In geometry, the Petersen–Morley theorem states that, if a, b, c are three general skew lines in space, if a′, b′, c′ are the lines of shortest distance...

"K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems". arXiv:math/9908097. Lowrey, Parker; Schürg, Timo (2012-08-30)...

there are theorems that clearly presuppose that there is something in the domain of discourse. Consider the following classically valid theorems. 1. ∀ x...

an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing...

core type theory, induction and recursion principles are used to prove theorems about inductive types. In Agda, dependently typed pattern matching is used...

Myerson–Satterthwaite inefficiency theorem (Myerson and Satterthwaite, 1983), the Jehiel–Moldovanu impossibility theorems (Jehiel and Moldovanu, 2001), the...

Robinson's approach, a short proof of the intermediate value theorem (Bolzano's theorem) using infinitesimals is done by the following. Let f be a continuous...

In mathematics, the subspace theorem says that points of small height in projective space lie in a finite number of hyperplanes. It is a result obtained...

of analytic functions are analytic is an easy consequence of Morera's theorem. The set A ∞ ( Ω ) {\displaystyle A_{\infty }(\Omega )} of all bounded...

the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space...

The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space...

of a Hausdorff commutative topological group is closed. The isomorphism theorems from ordinary group theory are not always true in the topological setting...

is homotopy-equivalent to the original circle. A nerve theorem (or nerve lemma) is a theorem that gives sufficient conditions on C guaranteeing that...

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf...

The Method of Mechanical Theorems (Greek: Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving...

countably many finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but...

2307/2041008. ISSN 0002-9939. JSTOR 2041008. Caristi, James (1976). "Fixed point theorems for mappings satisfying inwardness conditions". Trans. Amer. Math. Soc...

theorem. Alternatively, the requirement that det(Dφ) ≠ 0 can be eliminated by applying Sard's theorem. For Lebesgue measurable functions, the theorem...

In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order...

limit states to define and check a structure's performance. Plastic limit theorems provide a way to calculate limit loads without having to solve the boundary...

topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications...

In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W....

L-functions of various twists of it are well-behaved. The first converse theorems were proved by Hamburger (1921) who characterized the Riemann zeta function...

consists of many stand-alone theorems, dealing with important special cases. Much of the work of proving these theorems was devoted to the analysis of...

theory that is used to refine various theorems related to perfect matching in graphs, such as Hall's marriage theorem. This was first studied by Øystein...

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise...

no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture)...

In the mathematics of topological vector spaces, Minlos's theorem states that a cylindrical measure on the dual of a nuclear space is a Radon measure...

The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will...

but happens to be different from the volume at the start. Unlike most theorems in geometry, the mathematical proof of this result depends on the choice...

The somewhat weaker analogous theorems for time are the time hierarchy theorems. The foundation for the hierarchy theorems lies in the intuition that with...

Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval...

advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other...

mathematics, the Wiener–Wintner theorem, named after Norbert Wiener and Aurel Wintner, is a strengthening of the ergodic theorem, proved by Wiener and Wintner (1941)...

of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution...

In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain...

consequence of a conjectural quantum PCP theorem which would be easier to prove than a full quantum PCP theorem. A solution to the NLTS conjecture was initially...

physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022...

The theorem implies both the Hermite–Lindemann and Gelfond–Schneider theorems, and implies the transcendence of some values of elliptic functions and...

In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions...

Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued...

via induction over the derivations. algebraically, using amalgamation theorems for the variety of algebras representing the logic. via translation to...

localization functor from the ∞-category of presheaves of spaces on C to X. A theorem of Lurie states that an ∞-category is an ∞-topos if and only if it satisfies...

theory, a reflection theorem or Spiegelungssatz (German for reflection theorem – see Spiegel and Satz) is one of a collection of theorems linking the sizes...

to polytopes of dimension four. Mnëv, N. E. (1988), "The universality theorems on the classification problem of configuration varieties and convex polytopes...

theorems have been cited in support of various philosophies, including perspectivism, constructive empiricism and agential realism. Gleason's theorem...

calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds...

\mathbb {Z} ^{2}} ." Their results are termed the "Chayes–McKellar–Winn theorem". Later, when Chayes was asked to comment about the mathematical abilities...

^{s}(\mu ,a)} . The following theorem states that the times when the s-density exists are rather seldom. Marstrand's theorem: Let μ {\displaystyle \mu }...

Weber's theorem may refer to: Kronecker–Weber theorem Weber's theorem (algebraic curves) This disambiguation page lists mathematics articles associated...

ISSN 0002-9947, JSTOR 1990065 Hempel, Joachim A. (1980), "Precise bounds in the theorems of Schottky and Picard", Journal of the London Mathematical Society, 21...

proved within the given axiomatization. According to the incompleteness theorems, a powerful-enough consistent axiomatic theory is incomplete, meaning the...

restriction is continuous. Closed graph theorem (functional analysis) – Theorems connecting continuity to closure of graphs Densely defined operator – Linear...

where there is the potential for negotiation. Pigovian tax Fundamental theorems of welfare economics Economics Economic efficiency Market failure Externalities...

2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications. pp...

take the theorems of welfare economics as accurate descriptions of the real world. Therefore, the significance of the two welfare theorems of economics...

The Valiant–Vazirani theorem is a theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT,...

In mathematics, the Lévy–Steinitz theorem identifies the set of values to which sums of rearrangements of an infinite series of vectors in Rn can converge...

n } {\displaystyle i>\min\{m,n\}} ⁠. The geometric content of the SVD theorem can thus be summarized as follows: for every linear map ⁠ T : C n → C m...

a\rangle ),} where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup...

notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate...

The log sum inequality is used for proving theorems in information theory. Let a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} and b 1 , … , b n {\displaystyle...

deduced from the closed graph theorem). Often, the closed graph theorems are obtained as corollaries of the open mapping theorems in the following way. Let...

the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski (1949, theorem 3) and John Shepherdson (1953). Suppose that...

In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers α...

73: 115–138. Three-Distance Theorem at Theorem of the Day Alessandri, P., and Berthé, V. (1998). "Three distance theorems and combinatorics on words"...

Aubel's theorem and a square version of Napoleon's theorem. All three of these theorems are just a special case of Petr–Douglas–Neumann theorem. Given...