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Quantum physics theorem on causality
The free will theorem of John H. Conway and Simon B. Kochen states that if we have free will in the sense that our choices are not a function of the past
Free_will_theorem
Mathematical folklore
the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such thing as a free lunch".
No_free_lunch_theorem
Average solution cost is the same with any method
In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational
No free lunch in search and optimization
No_free_lunch_in_search_and_optimization
Ability to make choices voluntarily
freedom of will by Augustine of Hippo Free will theorem Locus of control Problem of mental causation Prospection Superdeterminism True Will Voluntarism
Free_will
English mathematician (1937–2020)
and Simon B. Kochen, another Princeton mathematician, proved the free will theorem, a version of the "no hidden variables" principle of quantum mechanics
John_Horton_Conway
Theorem in physics
by John Conway and Simon Kochen under the name of the free will theorem. The Conway–Kochen theorem uses a pair of entangled qutrits and a Kochen–Specker
Bell's_theorem
Kuratowski's free set theorem, named after Kazimierz Kuratowski, is a result of set theory, an area of mathematics. It was largely forgotten for decades
Kuratowski's_free_set_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Canadian mathematician (born 1934)
and John Horton Conway proved the free will theorem. The theorem states that if we have a certain amount of free will, then, subject to certain assumptions
Simon_B._Kochen
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
Topics referred to by the same term
Huoranszki FreeWill, software company for charitable donations Free will in theology Free will theorem Freedom of choice Karma Neuroscience of free will Theodicy
Free_Will_(disambiguation)
American mathematician, physicist and computer scientist
awards. His name is particularly associated with a theorem in computer science known as "no free lunch". David Wolpert took a B.A. in physics at Princeton
David_Wolpert
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem, or the sampling theorem, is a theorem in the field of signal processing which serves as a fundamental bridge between
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Subset of evolutionary computation
following theoretical principles apply to all or almost all EAs. The no free lunch theorem of optimization states that all optimization strategies are equally
Evolutionary_algorithm
Theorem in algebra
Muller–Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by
Muller–Schupp_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
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
Class of theories in quantum mechanics
Broglie–Bohm theory Many-worlds interpretation Quantum entanglement Free will theorem Larsson, Jan-Åke (2014). "Loopholes in Bell inequality tests of local
Superdeterminism
Proof assistant and programming language
foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source software project hosted on
Lean_(proof_assistant)
Short story by Ted Chiang
warn the reader, urging them to pretend that free will exists. Free will and determinism Free will theorem Locus of control Problem of mental causation
What's_Expected_of_Us
Necessary and sufficient conditions for a market to be arbitrage free and complete
Second Fundamental Theorem of Asset Pricing: An arbitrage-free market (S,B) consisting of a collection of stocks S and a risk-free bond B is complete
Fundamental theorem of asset pricing
Fundamental_theorem_of_asset_pricing
Form of predeterminism
director of the universe as per an argument similar to free will theorem) have free will to choose their actions, holding that God, whilst knowing their
Theological_determinism
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Adage of the impossibility of getting something for nothing
in machine learning) which are unavoidable according to the "No free lunch" theorem. That is, any model that claims to offer superior flexibility in
No_such_thing_as_a_free_lunch
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
Basis_theorem_(computability)
Theorem in group theory
Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product
Grushko_theorem
Term in metaphysics
naturalistic worldview. Actual idealism Bayesian inference Benjamin Libet Free will theorem Ilya Prigogine Many-worlds interpretation Newcomb's paradox Philosophical
Libertarianism_(metaphysics)
Theorem in computability theory
recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first
Kleene's_recursion_theorem
Mathematics concept
Nielsen–Schreier theorem. Otto Schreier published an algebraic proof of this result in 1927, and Kurt Reidemeister included a comprehensive treatment of free groups
Free_group
Property of artificial neural networks
In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate
Universal approximation theorem
Universal_approximation_theorem
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
Transformations induced by a mathematical group
action of any group on itself by left multiplication is free. This observation implies Cayley's theorem that any group can be embedded in a symmetric group
Group_action
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f {\displaystyle
Brouwer_fixed-point_theorem
Statement on equilibrium in electromagnetism
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic
Earnshaw's_theorem
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Theorem for proving more complex theorems
also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however
Lemma_(mathematics)
Contradiction of free will and determinism
free will theorem of John H. Conway and Simon B. Kochen further establishes that if we have free will, then quantum particles also possess free will.
Incompatibilism
Important problem in lattice theory
with ℵ2 compact elements using a construction based on Kuratowski's free set theorem. We denote by Con A the congruence lattice of an algebra A, that is
Congruence_lattice_problem
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Attribute of machine learning models
worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity
Sample_complexity
Assumptions for inference in machine learning
process itself must have a bias. Algorithmic bias Cognitive bias No free lunch theorem No free lunch in search and optimization Mitchell, T. M. (1980), The need
Inductive_bias
Extremal graph theory bound on clique-free graph edges
r)} . Turán's theorem states that the Turán graph has the largest number of edges among all Kr+1-free n-vertex graphs. Turán's theorem, and the Turán
Turán's_theorem
Theorem on the orders of subgroups
In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
Putting things into categories
all given problems (a phenomenon that may be explained by the no-free-lunch theorem). Class (disambiguation) Classified (disambiguation) Classifier (disambiguation)
Classification
Statistical mechanics theorem relating non-equilibrium work to free energy differences
The Crooks fluctuation theorem (CFT), sometimes known as the Crooks equation, is an equation in statistical mechanics that relates the work done on a
Crooks_fluctuation_theorem
Topics referred to by the same term
Cantor's theorem in Wiktionary, the free dictionary. Cantor's theorem is a fundamental result in mathematical set theory. Cantor's theorem may also refer
Cantor's theorem (disambiguation)
Cantor's_theorem_(disambiguation)
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is
Classification of finite simple groups
Classification_of_finite_simple_groups
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Theorem that tells the maximum rate at which information can be transmitted
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified
Shannon–Hartley_theorem
Theorem that every subgroup of a free group is itself free
Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob Nielsen and Otto Schreier. A free group may be
Nielsen–Schreier_theorem
Mathematical theorem for algebraic structure of subgroups of free products
theory, the Kurosh subgroup theorem describes the algebraic structure of subgroups of free products of groups. The theorem was obtained by Alexander Kurosh
Kurosh_subgroup_theorem
Measure of algorithmic complexity
description will depend on the choice of description language; but the effect of changing languages is bounded (a result called the invariance theorem, see below)
Kolmogorov_complexity
Algebraic curve in mathematics
geometry) Modularity theorem Moduli stack of elliptic curves Nagell–Lutz theorem Riemann–Hurwitz formula Wiles's proof of Fermat's Last Theorem Sarli, J. (2012)
Elliptic_curve
Optimization technique
of finding the global optimum. Also worth mentioning are the no-free-lunch theorems, which state that there can be no metaheuristic that is better than
Metaheuristic
fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus
List of theorems called fundamental
List_of_theorems_called_fundamental
1993 physics textbook by Asher Peres
Kochen–Specker configuration from the book in order to prove their free will theorem. Peres' insistence in his textbook that the classical analogue of
Quantum Theory: Concepts and Methods
Quantum_Theory:_Concepts_and_Methods
Theorem in political science
voter theorem says that if voters and candidates are distributed along a one-dimensional political spectrum, any Condorcet consistent voting method will elect
Median_voter_theorem
Metaphysical theory
Rationality + Consciousness = Free Will. Oxford University Press. p. 121. ISBN 9780199845309. Hodgson relies upon the free will theorem 1 2 of scientists John
Causal_closure
Argument that classification is not really possible without some sort of bias
The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely
Ugly_duckling_theorem
Area of mathematical logic
It's a consequence of Gödel's completeness theorem (not to be confused with his incompleteness theorems) that a theory has a model if and only if it
Model_theory
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
Topics referred to by the same term
Chomsky–Schützenberger theorem may refer to either of two different theorems derived by Noam Chomsky and Marcel-Paul Schützenberger concerning context-free languages:
Chomsky–Schützenberger theorem
Chomsky–Schützenberger_theorem
Phrase used in computer science
Computer says no Data processing inequality FINO Model collapse No free lunch theorem Standard error Undefined behavior Demming, Anna (June 30, 2019). "Machine
Garbage_in,_garbage_out
Topic in group theory
. This is also known as the Krasner–Kaloujnine embedding theorem. The Krohn–Rhodes theorem involves what is basically the semigroup equivalent of this
Wreath_product
Theorem in general relativity
tensor. More precisely, the theorem states that a vacuum solution of the Einstein field equations will admit a shear-free null geodesic congruence if
Goldberg–Sachs_theorem
Commutative algebra theorem
Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between free modules
Quillen–Suslin_theorem
Mathematical proposition equivalent to the axiom of choice
the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space
Zorn's_lemma
Special type of lattice
both statements require the Boolean prime ideal theorem, a weak form of the axiom of choice. The free distributive lattice over a set of generators G
Distributive_lattice
Social choice theorem on superiority of majority voting
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function
May's_theorem
Hypothesis in neuroscience
0683. S2CID 28080508. Evans, Denis J. (2003). "A non-equilibrium free energy theorem for deterministic systems" (PDF). Molecular Physics. 101 (10): 1551–1554
Free_energy_principle
Theorem of physical impossibility
theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. This type of theorem imposes boundaries on
No-go_theorem
Commutative group (mathematics)
infinite rank, as it is a free abelian group with the set of the prime numbers as a basis (this results from the fundamental theorem of arithmetic). The center
Abelian_group
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
Group whose operation is composition of permutations
by Sn, and may be called the symmetric group on n letters. By Cayley's theorem, every group is isomorphic to some permutation group. The way in which
Permutation_group
Theorem in vector calculus
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
Stokes'_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
Every triangle-free planar graph is 3-colorable
Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. According to the four-color theorem, every
Grötzsch's_theorem
Software for solving satisfiability problems
Z3, also known as the Z3 Theorem Prover, is a satisfiability modulo theories (SMT) solver developed by Microsoft. Z3 was developed in the Research in
Z3_Theorem_Prover
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
Foundational law of electromagnetism relating electric field and charge distributions
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
Gauss's_law
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
selection theorem Knaster–Kuratowski–Mazurkiewicz lemma Kuratowski's free set theorem Knaster–Kuratowski fan Tarski–Kuratowski algorithm Kuratowski Prize
List of things named after Kazimierz Kuratowski
List_of_things_named_after_Kazimierz_Kuratowski
Planar maps require at most four colors
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Mathematical group based upon a finite number of elements
started with Camille Jordan's theorem that the projective special linear group PSL(2, q) is simple for q ≠ 2, 3. This theorem generalizes to projective groups
Finite_group
On graph coloring and neighborhood size
theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected
Brooks'_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Operation that combines groups
conditions given in the Seifert van-Kampen theorem, the free product of the fundamental groups of the spaces. Free products are also important in Bass–Serre
Free_product
Finite-domain model finder for pure first-order logic with equality
as part of an automated theorem proving system. The software is written mostly in the programming language Haskell. It is free and open-source software
Paradox_(theorem_prover)
Branch of mathematics that studies the properties of groups
their fundamental groups. A fundamental theorem of this area is that every subgroup of a free group is free. There are several natural questions arising
Group_theory
Group with subnormal series where all factors are abelian
radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0). This means associated to a polynomial
Solvable_group
Yes-or-no question that cannot ever be solved by a computer
are quite similar. In fact, a weaker form of the First Incompleteness Theorem is an easy consequence of the undecidability of the halting problem. This
Undecidable_problem
E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely
E_(theorem_prover)
On transforming a program by substituting constants for free variables
n theorem, written also as "smn-theorem" or "s-m-n theorem" (also called the translation lemma, parameter theorem, and the parameterization theorem) is
Smn_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making
Arrow's_impossibility_theorem
Approximation in plasma physics
force-free. Woltjer's theorem Chandrasekhar–Kendall function Magnetic helicity Wiegelmann, Thomas; Sakurai, Takashi (December 2021). "Solar force-free magnetic
Force-free_magnetic_field
On polynomial rings over fields
In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in
Hilbert's_syzygy_theorem
Group without normal subgroups other than the trivial group and itself
eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple groups, completed in 2004
Simple_group
Formal language generated by context-free grammar
context-free, one may employ the pumping lemma for context-free languages or a number of other methods, such as Ogden's lemma or Parikh's theorem. meaning
Context-free_language
Open platform for multi-objective optimization
folklore, the no free lunch theorem (sometimes pluralized) of David Wolpert and William G. Macready appears in the 1997 "No Free Lunch Theorems for Optimization
Kimeme
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