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Theorem in computability theory
Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. The statement of Post's theorem
Post's_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Theorem about Turing reductions
middle of the 1950s. It is a more general view of the Kleene–Post theorem. The Kleene–Post theorem states that there exist incomparable languages A and B that
Friedberg–Muchnik_theorem
Theorem that arithmetical truth cannot be defined in arithmetic
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
American mathematician and logician (1897 – 1954)
to Gödel in 1938: I would have discovered Gödel's theorem in 1921—if I had been Gödel. In 1936, Post developed, independently of Alan Turing, a mathematical
Emil_Leon_Post
Study of computable functions and Turing degrees
precise by Post's theorem. A weaker relationship was demonstrated by Kurt Gödel in the proofs of his completeness theorem and incompleteness theorems. Gödel's
Computability_theory
Hierarchy of complexity classes for formulas defining sets
Thus the hierarchy does not collapse. This is a direct consequence of Post's theorem. The inclusions Δ n 0 ⊊ Π n 0 {\displaystyle \Delta _{n}^{0}\subsetneq
Arithmetical_hierarchy
Set of all true first-order statements about the arithmetic of natural numbers
canonical Gödel number of the sentence θ. Post's theorem is a sharper version of the undefinability theorem that shows a relationship between the definability
True_arithmetic
Theorem in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_theorem
Operation in computability theory
the problem X. That is, the problem X′ is not Turing-reducible to X. Post's theorem establishes a relationship between the Turing jump operator and the
Turing_jump
Theorem in quantum mechanics
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from
Gleason's_theorem
Theorem in group theory
mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality
Grushko_theorem
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
Counterintuitive result in probability
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
Infinite_monkey_theorem
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Principle in quantum information theory
In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts
No-communication_theorem
British mathematician who proved Fermat's Last Theorem
specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal
Andrew_Wiles
Concept in computability theory
the results of the computation if the program does halt. As with the smn theorem, the original notation used by Kleene has become standard terminology for
Kleene's_T_predicate
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Theorem in game theory
render largely obsolete my 2015 blog post Common Knowledge and Aumann’s Agreement Theorem, one of the most popular posts in this blog’s history. But I’m willing
Aumann's_agreement_theorem
Plurality voting system
First-past-the-post (FPTP) — also called choose-one, first-preference plurality (FPP), or simply plurality — is a single-winner voting rule. Each voter
First-past-the-post_voting
Condition under which an odd prime is a sum of two squares
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Type of number sequence
is countable, so f is zero almost everywhere. In fact, the de Bruijn–Post Theorem states the converse of the above criterion: If f is a function such that
Equidistributed_sequence
Theorem relating continuity to graphs
closed graphs are necessarily continuous. A blog post by T. Tao lists several closed graph theorems throughout mathematics. If f : X → Y {\displaystyle
Closed_graph_theorem
Mathematical theorem
In real analysis, a branch of mathematics, Bernstein's theorem, named after Sergei Bernstein, states that every real-valued function on the half-line
Bernstein's theorem on monotone functions
Bernstein's_theorem_on_monotone_functions
Theorem pertaining to the ontology of quantum mechanics
Pusey–Barrett–Rudolph (PBR) theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named)
Pusey–Barrett–Rudolph_theorem
Theorem on operator interpolation
analysis, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation
Riesz–Thorin_theorem
Key results in general relativity on gravitational singularities
The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Method of comparing problems by transforming one into another in computability theory
extra predicate for B {\displaystyle B} . Equivalently, according to Post's theorem, A is arithmetical in B {\displaystyle B} if and only if A {\displaystyle
Reduction (computability theory)
Reduction_(computability_theory)
Formal language
context-sensitive and recursive languages are recursively enumerable. Post's theorem shows that RE, together with its complement co-RE, correspond to the
Recursively enumerable language
Recursively_enumerable_language
Mathematical treatise by Euclid
These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many
Euclid's_Elements
Russian mathematician (born 1966)
Polikanova, he established a measure-theoretic formulation of Helly's theorem.[PP86] In 1987, the year he began graduate studies, he published an article
Grigori_Perelman
Measure of unsolvability
an infinite sequence ai of degrees such that a′i+1 ≤ ai for each i. Post's theorem establishes a close correspondence between the arithmetical hierarchy
Turing_degree
Theorem in physical cosmology
The Borde–Guth–Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout
Borde–Guth–Vilenkin_theorem
Automated theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover
List of mathematical logic topics
List_of_mathematical_logic_topics
Branch of mathematical logic
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
Reverse_mathematics
American actress, mathematics writer, and education advocate (born 1975)
(August 20, 2007). "Blog post by mathematician, and a former instructor of McKellar's, complimenting her book and explaining the theorem". Chang, Kenneth (July
Danica_McKellar
Limit of a uniformly computable sequence of functions
_{2}^{0}} sets are just the sets computable from 0 ′ {\displaystyle 0'} by Post's theorem, the limit lemma also entails that the limit computable sets are the
Computation_in_the_limit
recherche en informatique fondamentale. Retrieved 2025-10-07. Kleene's theorem is usually considered as the starting point of automata theory. Kahrs,
List of pioneers in computer science
List_of_pioneers_in_computer_science
Statement of spherically symmetric spacetimes
In general relativity, Birkhoff–Jebsen's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically
Birkhoff's theorem (relativity)
Birkhoff's_theorem_(relativity)
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
In algebra, the first and second fundamental theorems of invariant theory concern the generators and relations of the ring of invariants in the ring of
First and second fundamental theorems of invariant theory
First_and_second_fundamental_theorems_of_invariant_theory
Overview of and topical guide to logic
Cantor's theorem Church's theorem Church's thesis Effective method Formal system Gödel's completeness theorem Gödel's first incompleteness theorem Gödel's
Outline_of_logic
Ancient Greek mathematician (fl. 300 BC)
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
Euclid
Theorem of quantum information theory
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot
No-hiding_theorem
Fundamental combinatorial result of Ramsey theory
In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, named after Alfred W. Hales and Robert I. Jewett, that
Hales–Jewett_theorem
Problem in computer science
Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram
Halting_problem
American philosopher and logician (1940–2022)
application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable
Saul_Kripke
Black holes are characterized only by mass, charge, and spin
The no-hair theorem, also known as the black hole uniqueness theorem, states that all stationary black hole solutions of the Einstein–Maxwell equations
No-hair_theorem
German mathematician (1905–1980)
Königsberg in 1934, and subsequently held posts in a number of universities until 1974. Sperner's theorem, from 1928, says that the size of an antichain
Emanuel_Sperner
Quantum error correction schemes can suppress the logical error rate arbitrarily low
In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain
Threshold_theorem
The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex
2D_Z-transform
Brothers Grimm (2005), The Imaginarium of Doctor Parnassus (2009), The Zero Theorem (2013) John Gilling Sid James Escape by Night (1953), Interpol (1957),
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Theorem in theoretical physics
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Theorem in theoretical computer science
database theory, the PACELC design principle is an extension to the CAP theorem. It states that in case of network partitioning (P) in a distributed computer
PACELC_design_principle
Impossible task in computing
impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it
Entscheidungsproblem
Formal semantics for non-classical logic systems
application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable
Kripke_semantics
Theorem in geometric topology
conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds
Poincaré_conjecture
Theorem in statistical mathematics
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently
Fluctuation_theorem
Computational quantum mechanical modelling method to investigate electronic structure
Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence
Density_functional_theory
Mathematics award
first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts
Fields_Medal
1995 film by Terry Gilliam
Theorem in 2013, claims were made that Gilliam had meant it as part of a trilogy. A 2013 review for The Guardian said, "Calling it [The Zero Theorem]
12_Monkeys
Establish relationships between homology and cohomology theories
In algebraic topology, universal coefficient theorems (UCT) establish relationships between homology groups (or cohomology groups) with different coefficients
Universal_coefficient_theorem
Foundational theorem of quantum information processing
In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary
No-deleting_theorem
Category of mathematical proof
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as
Proof_of_impossibility
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems
Mathematics
developed the theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws. Enheduanna
List of women in the Heritage Floor
List_of_women_in_the_Heritage_Floor
Theorem of quantum information processing
no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning
No-broadcasting_theorem
Polish mathematician (1932–2015)
iconic problems posed by Hugo Steinhaus: the three-gap theorem and the non-tetratorus theorem. Stanisław (Stash) Świerczkowski was born in Toruń, Poland
Stanisław_Świerczkowski
Any individual whose preferences satisfy four axioms has a utility function
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that
Von Neumann–Morgenstern utility theorem
Von_Neumann–Morgenstern_utility_theorem
Chinese-born American mathematician
age of nine, he found a proof of the Pythagorean theorem. He first learned about Fermat's Last Theorem and Goldbach's conjecture when he was 10. During
Yitang_Zhang
1968 film by Pier Paolo Pasolini
Teorema (English: "Theorem") is a 1968 Italian allegorical art film written and directed by Pier Paolo Pasolini. The film centers on an upper-class Milanese
Teorema
American-born British mathematician (1888-1972)
also built up the department, offering posts to a number of outstanding mathematicians who had been forced from posts on the continent of Europe. He brought
Louis_J._Mordell
1995 US criminal trial
disclosed the hoax. The trial provided an example of incorrect use of Bayes theorem in the courtroom that is used in statistics courses around the world. O
Murder_trial_of_O._J._Simpson
Logical paradox in decision-making theory
strategy of a façade, which does not meet the legal criteria for a ban. Several post-war European democracies have translated the paradox of tolerance into legal
Paradox_of_tolerance
Australian and American mathematician (born 1975)
and Sciences. Among his contributions to mathematics is the Green–Tao theorem on prime numbers, which he proved in 2004 in collaboration with Ben Green
Terence_Tao
Swiss mathematician (1707–1783)
properties of this function, he generalized Fermat's little theorem to what is now known as Euler's theorem. He contributed significantly to the theory of perfect
Leonhard_Euler
German-born theoretical physicist (1879–1955)
rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said that only
Albert_Einstein
Theorem in general relativity
Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime
Lovelock's_theorem
Polish mathematician (1892–1945)
Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, Banach-Saks property, and the Banach fixed-point theorem. Stefan
Stefan_Banach
On the approximate structure of sets whose sumset is small
In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose
Freiman's_theorem
Number in {..., –2, –1, 0, 1, 2, ...}
products of primes in an essentially unique way. This is the fundamental theorem of arithmetic. Z {\displaystyle \mathbb {Z} } is a totally ordered
Integer
American columnist, author and lecturer (born 1946)
Last Theorem, Savant published the book The World's Most Famous Math Problem (October 1993), which surveys the history of Fermat's Last Theorem as well
Marilyn_vos_Savant
Hypothesis about intelligent agents
Doom The Human Race Within A Century, Oxford Professor Says". Huffington Post. Archived from the original on 2018-02-25. Retrieved 2018-11-30. Ford, Paul
Instrumental_convergence
Economic theorem
The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel [es], and Hugo F
Sonnenschein–Mantel–Debreu theorem
Sonnenschein–Mantel–Debreu_theorem
Technical treatment of Boolean algebras
set contained an operation lacking that property. (The converse of Post's theorem, extending "if" to "if and only if," is the easy observation that a
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Formula for the "volume" of an n-simplex
determinant, which became known as Menger's theorem (unrelated to the theorem of that name in graph theory). The theorem states: For a finite set of points
Cayley–Menger_determinant
Cryptography secured against quantum computers
current algorithms will be vulnerable to quantum computing attacks. Mosca's theorem provides the risk analysis framework that helps organizations identify
Post-quantum_cryptography
Bound on the number of incidences between points and lines in the plane
The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean
Szemerédi–Trotter_theorem
Austrian, German, and American actor (born 1956)
named Dr. King Schultz. Waltz also starred in Carnage (2011), The Zero Theorem (2013), Big Eyes (2014), Downsizing (2017), Alita: Battle Angel (2019)
Christoph_Waltz
Mathematical result on arithmetic properties of binomial coefficients
The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by Henry W. Gould in 1972. The
Star_of_David_theorem
Election that narrows the field of candidates before an election for office
spectrum. In the general election, under the assumptions of the median voter theorem, the candidate must move more towards the center in hopes of capturing
Primary_election
Scottish physicist and mathematician (1831–1879)
unsuccessful in applying for Forbes's recently vacated chair at Edinburgh, the post instead going to Tait. Maxwell was granted the Chair of Natural Philosophy
James_Clerk_Maxwell
In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation
Weyl's theorem on complete reducibility
Weyl's_theorem_on_complete_reducibility
American mathematician (1923–1992)
after a brief illness. He was 69 years old. Gorenstein–Harada theorem Gorenstein–Walter theorem Peterson–Gorenstein–Zierler algorithm Saxon, Wolfgang (August
Daniel_Gorenstein
Canadian cryptographer (born c. 1970)
also at the University of Oxford. In the field of cryptography, Mosca's theorem addresses the question of how soon an organization needs to act in order
Michele_Mosca
Theorem that the sum of the reciprocals of the twin primes converges
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite
Brun's_theorem
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