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Conjecture about the behaviour of the Fourier transform on curved hypersurfaces
In harmonic analysis, the restriction conjecture, also known as the Fourier restriction conjecture, is a conjecture about the behaviour of the Fourier
Restriction_conjecture
Chinese mathematician (born 1991)
her contributions to Fourier restriction, Falconer's conjecture, Furstenberg sets in the plane, and the Kakeya conjecture. She is the third woman and the
Hong_Wang
Shape containing unit line segments in all directions
dimensions. The Kakeya conjecture is closely related to the restriction conjecture, Bochner-Riesz conjecture and the local smoothing conjecture. In February 2025
Kakeya_set
Mathematical conjecture
varieties. A special case of the conjecture was stated by Yves André in 1989, and a more general statement (albeit with a restriction on the type of the Shimura
André–Oort_conjecture
Open problem on 3x+1 and x/2 functions
problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple
Collatz_conjecture
Aharoni-Korman conjecture also known as the fishbone conjecture Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Bunkbed conjecture Chinese
List_of_conjectures
Mathematics award
in dense sets." Hong Wang – "For advances on the restriction conjecture, the local smoothing conjecture, and related problems." Yilin Wang – "For innovative
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Conjecture in the representation theory of Lie groups
In mathematics, the Gan–Gross–Prasad conjecture is a restriction problem in the representation theory of real or p-adic Lie groups posed by Gan Wee Teck
Gan–Gross–Prasad_conjecture
American mathematician
Maryland, focusing on Fourier restriction theory. While studying under Zhang, Cairo began working on the Mizohata–Takeuchi conjecture, which had remained unresolved
Hannah_Cairo
Seven mathematical problems with a US$1 million prize for each solution
unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem
Millennium_Prize_Problems
Unproven conjecture in graph theory
unsolved problems in mathematics In graph theory, the unproven Erdős–Gyárfás conjecture, made in 1995 by mathematician Paul Erdős and his collaborator András
Erdős–Gyárfás_conjecture
Australian and American mathematician (born 1975)
resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks
Terence_Tao
Restriction of scalars
In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic
Weil_restriction
Open conjecture that no real circulant Hadamard matrix has order greater than 4
and combinatorics, Ryser's conjecture on circulant Hadamard matrices, also called the circulant Hadamard matrix conjecture, states that no real circulant
Ryser's conjecture on circulant Hadamard matrices
Ryser's_conjecture_on_circulant_Hadamard_matrices
In mathematics, the Atiyah conjecture is a collective term for a number of statements about restrictions on possible values of l 2 {\displaystyle l^{2}}
Atiyah_conjecture
Fontaine–Mazur conjecture: actually numerous conjectures, all proposed by Jean-Marc Fontaine and Barry Mazur. Gan–Gross–Prasad conjecture: a restriction problem
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Conjecture in algebraic geometry
In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a simply connected
Weil's conjecture on Tamagawa numbers
Weil's_conjecture_on_Tamagawa_numbers
French mathematician (1906-1998)
Weil conjecture, around 1967, which later under pressure from Serge Lang (resp. of Jean-Pierre Serre) became known as the Taniyama–Shimura conjecture (resp
André_Weil
Mathematical problem
an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning the sizes of the smaller squares
Squaring_the_square
In mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group G in
Blattner's_conjecture
American mathematician (1943–2024)
of results and ideas for using it to prove the Poincaré conjecture and geometrization conjecture from the field of geometric topology. Hamilton's work on
Richard_S._Hamilton
1929 mathematical conjecture
Diophantine approximation, a subfield of number theory, the Oppenheim conjecture concerns representations of numbers by real quadratic forms in several
Oppenheim_conjecture
Chinese-American mathematician (born 1949)
recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered
Shing-Tung_Yau
Technology to control access to copyrighted works and prevent unauthorized copying
different authors on DRM. Arun Sundararajan uses the following digital rights conjecture, that "digital rights increases the incidence of digital piracy, and that
Digital_rights_management
Directed graph with no directed cycles
Press, p. 19, ISBN 978-0-12-324245-7. Weisstein, Eric W., "Weisstein's Conjecture", MathWorld{{cite web}}: CS1 maint: overridden setting (link) McKay, B
Directed_acyclic_graph
Type of Dirichlet series associated to number field extensions
and have vital meaning for number theory. The Artin conjecture also called Artin holomorphy conjecture states that L ( s , ρ , L / K ) {\displaystyle L(s
Artin_L-function
Planar maps require at most four colors
short: every planar graph is four-colorable. As far as is known, the conjecture was first proposed on October 23, 1852, when Francis Guthrie, while trying
Four_color_theorem
Number theory conjecture
theory. It is a very broad generalization of widely open conjectures such as the twin prime conjecture. The hypothesis is named after Andrzej Schinzel. The
Schinzel's_hypothesis_H
Mathematics concept
algebra of the Galois image. This conjecture is known only in particular cases. Through generalisations of this conjecture, the Mumford–Tate group has been
Mumford–Tate_group
Principle suggesting that time travel paradoxes are inherently impossible
self-consistency principle, also known as the Novikov self-consistency conjecture and Larry Niven's law of conservation of history, is a principle developed
Novikov self-consistency principle
Novikov_self-consistency_principle
Field of algebraic geometry
a general linear series of degree d. The Maximal Rank Conjecture asserts that the restriction maps H 0 ( O P r ( m ) ) → H 0 ( O C ( m ) ) {\displaystyle
Brill–Noether_theory
On the approximate structure of sets whose sumset is small
Manners, Freddie; Tao, Terence (2023). "On a conjecture of Marton". arXiv:2311.05762 [math.NT]. "On a conjecture of Marton". What's new. 2023-11-13. Retrieved
Freiman's_theorem
Riemannian manifold with SU(n) holonomy
superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to
Calabi–Yau_manifold
3-regular graph with no 3-edge-coloring
problems in graph theory (such as the cycle double cover conjecture and the 5-flow conjecture), one encounters an interesting but somewhat mysterious variety
Snark_(graph_theory)
Taniyama–Shimura–Weil conjecture, now proved as the modularity theorem Weil algebra Weil–Brezin Map Weil–Châtelet group Weil cohomology Weil conjecture (disambiguation)
List of things named after André Weil
List_of_things_named_after_André_Weil
notation represents restriction to the set X {\textstyle X} . Fourier transform § Restriction problems Mizohata–Takeuchi conjecture Bennett, Jonathan;
Fourier_extension_operator
Sumset of a field subject to a specific polynomial restriction
theorem generalises this to general abelian groups. The Erdős–Heilbronn conjecture posed by Paul Erdős and Hans Heilbronn in 1964 states that | 2 ∧ A | ≥
Restricted_sumset
Elliptic curves
Gauss–Manin connection may give some important hints for Vojta's conjecture, ABC conjecture and so on; in 2012, he published his Inter-universal Teichmuller
Hodge–Arakelov_theory
Mathematics award
analysis, leading to the proof of the Furstenberg set conjecture in the plane and the Kakeya conjecture in three dimensions." 2025 not awarded 2024 Paul Nelson
Clay_Research_Award
Malaysian mathematician (born 1972)
central critical L-values, and restriction problems in the representation theory of classical groups". Sur les conjectures de Gross et Prasad. Paris: Astérisque
Gan_Wee_Teck
Conjecture in symplectic geometry
In mathematics, and especially symplectic geometry, the Thomas–Yau conjecture asks for the existence of a stability condition, similar to those which appear
Thomas–Yau_conjecture
Mathematics award
was found in 1993. In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal, stating "I'm not interested in money or fame;
Fields_Medal
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a
Carathéodory_conjecture
Mathematics award
particular, for substantial contributions to the Fourier restriction problem, the Kakeya conjecture, and geometric measure theory". List of awards honoring
Sadosky_Prize
Mathematical problem in number theory
greater than or equal to zero. This question later became known as Bachet's conjecture, after the 1621 translation of Diophantus by Claude Gaspard Bachet de
Waring's_problem
Polynomial of the elements of a matrix
by the matrix for which all entries are equal to 1/n. Proofs of this conjecture were published in 1980 by B. Gyires and in 1981 by G. P. Egorychev and
Permanent_(mathematics)
Mathematical problem in spectral theory
\omega _{d}} is the volume of the d-dimensional unit ball. Weyl also conjectured that the next term in the approximation below would give the perimeter
Hearing_the_shape_of_a_drum
Way to divide polygon into smaller parts
action by isometries. This conjecture was partially solved by Grigori Perelman in his proof of the geometrization conjecture, which states (in part) that
Finite_subdivision_rule
Mathematical concept
vector field is the restriction to the submanifold of the Hamiltonian vector field associated to the energy function. (The restriction yields a vector field
Reeb_vector_field
2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order must be a square number. The excess, denoted E(H ), of
Regular_Hadamard_matrix
\alpha \,\varphi } Restriction 1: β {\displaystyle \beta } is a variable which does not occur in φ {\displaystyle \varphi } . Restriction 2: β {\displaystyle
List_of_rules_of_inference
Concerned with the notion of stability in model theory
theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted in the proof of Morley's
Stable_theory
Number of planar subgraphs to cover a graph
biplanar graphs, posed in 1959 by Gerhard Ringel, and on a related 1962 conjecture of Frank Harary: Every graph on nine points or its complementary graph
Thickness_(graph_theory)
Prime pair of the form (p, 2p+1)
this and the twin prime conjecture; they include Dickson's conjecture, Schinzel's hypothesis H, and the Bateman–Horn conjecture. A heuristic estimate for
Safe and Sophie Germain primes
Safe_and_Sophie_Germain_primes
Area of combinatorics
are asked to mark as large a subset as possible of this set under the restriction that the sum of any two marked integers cannot be marked. It appears
Extremal_combinatorics
algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question of proving that "when something
Purity_(algebraic_geometry)
Key result in general relativity
Richard; Yau, Shing-Tung (1979). "On the proof of the positive mass conjecture in general relativity". Communications in Mathematical Physics. 65 (1):
Positive_energy_theorem
Theorem about admissible crystal symmetries
Kilminster, Devin (March 2003), "The crystallographic restriction, permutations, and Goldbach's conjecture" (PDF), American Mathematical Monthly, 110 (3): 202–209
Crystallographic restriction theorem
Crystallographic_restriction_theorem
Prime number p where p+2 is prime or semiprime
primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime
Chen_prime
The only quadratic pairing functions are the Cantor polynomials
{\displaystyle P} is a real quadratic polynomial in two variables whose restriction to N 2 {\displaystyle \mathbb {N} ^{2}} is a bijection from N 2 {\displaystyle
Fueter–Pólya_theorem
Indian mathematician (born 1960)
1–109, ISBN 978-2-85629-348-5, MR 3202556 "Restriction of Hermitian Maas Lifts and the Gross-Prasad Conjecture" (PDF). 2003. Retrieved 11 March 2017. "American
Dipendra_Prasad
Class of integer
whose integer solutions are sought Euler's sum of powers conjecture – Disproved conjecture in number theory Generalized taxicab number – Smallest number
Taxicab_number
Platonic philosophical analogy
succession as corresponding to increasing levels of reality and truth from conjecture (εἰκασία) to belief (πίστις) to thought (διάνοια) and finally to understanding
Analogy_of_the_divided_line
Number of independent rational basis points with infinite order
Katz–Sarnak conjectured that in a suitable asymptotic sense (see below), the rank of elliptic curves should be 1/2 on average. An even stronger conjecture is that
Rank_of_an_elliptic_curve
Set of objects whose state must satisfy limits
notably for all CSPs over finite domains. This finite-domain dichotomy conjecture was first formulated by Tomás Feder and Moshe Vardi, and finally proven
Constraint satisfaction problem
Constraint_satisfaction_problem
Mathematical concept
variety is described by the André–Oort conjecture. Conditional results have been obtained on this conjecture, assuming a generalized Riemann hypothesis
Shimura_variety
concerning the cohomology of algebraic varieties. It was originally conjectured by Gelfand and MacPherson. The first case of the decomposition theorem
Decomposition theorem of Beilinson, Bernstein and Deligne
Decomposition_theorem_of_Beilinson,_Bernstein_and_Deligne
Number of partitions of an integer
are partition congruences modulo every integer coprime to 6. Newman's conjecture is an unsolved problem regarding the congruences of the partition function
Partition function (number theory)
Partition_function_(number_theory)
Hypothetical FTL transportation by warping space
brings up the chronology protection conjecture and writes: "The conjecture has not been proven (it wouldn't be a conjecture if it had), but there are good
Alcubierre_drive
differential geometric approach which is based on his resolution of the Calabi conjecture. Since c 2 ( X ) = e ( X ) {\displaystyle c_{2}(X)=e(X)} is the topological
Bogomolov–Miyaoka–Yau inequality
Bogomolov–Miyaoka–Yau_inequality
Gauge theory providing unifying formalism for integrable systems
systems is the anti-self-dual Yang–Mills (ASDYM) system. Ward's conjecture is the conjecture that in fact all integrable ODEs or PDEs come from ASDYM. A connection
Four-dimensional Chern–Simons theory
Four-dimensional_Chern–Simons_theory
Japanese anime television series
which she blames and angrily confronts Natsuki the next morning. Natsuki conjectures that someone wants Chiaki dead, and recommends offering three hairs at
Yamishibai: Japanese Ghost Stories
Yamishibai:_Japanese_Ghost_Stories
1932 Japanese film
Overall, much of the discourse surrounding the film is based on hearsay and conjecture, and discussing the work in detail through literature alone has been criticized
Suzumi-bune
English mathematician (born 1957)
together with Xiuxiong Chen and Song Sun, for proving a long-standing conjecture on Fano manifolds, which states "that a Fano manifold admits a Kähler–Einstein
Simon_Donaldson
Religious nonconformism in Britain, 16th–19th centuries
to Nonconformist Protestants rather than to Catholics, to whom some restrictions applied into the 1920s, through the Act of Settlement 1701, despite the
Recusancy
structural restriction, as it can be checked by looking only at the scopes of the constraints, ignoring domains and relations. This restriction is based
Complexity of constraint satisfaction
Complexity_of_constraint_satisfaction
Polynomial whose coefficients are all 1 or −1
{n+1}}} at every point of the circle. Littlewood conjectured that this was possible; the conjecture was proved in 2020 by Paul Balister, Béla Bollobás
Littlewood_polynomial
On solvability of Diophantine equations
finitely many components. This conjecture implies that the integers are not Diophantine over the rationals, and so if this conjecture is true, a negative answer
Hilbert's_tenth_problem
Belgian mathematician (1954–2018)
Together with Vitali Milman, he contributed to progress on Mahler’s conjecture in 1987. In 2000, he connected the Kakeya problem to arithmetic combinatorics
Jean_Bourgain
British-Lebanese mathematician (1929–2019)
related paper they showed that the Hodge conjecture for integral cohomology is false. The Hodge conjecture for rational cohomology is, as of 2008, a
Michael_Atiyah
Mathematical manifold theory
dimensions; this duality is now known as the Hodge star operator. He further conjectured that each cohomology class should have a distinguished representative
Hodge_theory
AI personality and codename
regulation on AI technology. Connor Leahy, CEO of the AI safety company Conjecture described Sydney as "the type of system that I expect will become existentially
Sydney_(Microsoft)
Inequality in differential geometry
{\gamma }}f\,\mathrm {dLength} _{\text{Euclidean}}.} Subject to the restriction that each of these lengths is at least L {\displaystyle L} , we want
Pu's_inequality
Mathematical Concept
degree d for large enough g. In this case all classes are tautological. Conjecture (Faber). (1) Large-degree tautological rings vanish: R d ( M g ) = 0 {\displaystyle
Tautological_ring
Type of natural number
Assuming the conjecture holds, this sequence of primes begins 2, 3, 2, 5, 2, 3, 7, 2 (sequence A073751 in the OEIS). Alaoglu and Erdős's conjecture would also
Colossally_abundant_number
Indian-American mathematician
with Patrick Brosnan, Belkale disproved Maxim Kontsevich's Spanning-Tree Conjecture (first published in 1997). Let G be a finite connected graph. The Kirchhoff
Prakash_Belkale
Invariant cycle theorem
In mathematics, the local invariant cycle theorem was originally a conjecture of Griffiths which states that, given a surjective proper map p {\displaystyle
Local_invariant_cycle_theorem
Area of discrete mathematics
conjecture Total coloring conjecture, also called Behzad's conjecture (unsolved) List coloring conjecture (unsolved) Hadwiger conjecture (graph theory) (unsolved)
Graph_theory
Theorem in mathematics
\mathbb {R} } -Banach space deduced from X {\displaystyle X} by any restriction scalar will be denoted X R ′ . {\displaystyle X_{\mathbb {R} }^{\prime
James's_theorem
Economic model
competitors' decisions. An essential assumption of this model is the "Cournot conjecture" that each firm aims to maximize profits, based on the expectation that
Cournot_competition
American mathematician
important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings
John_R._Stallings
Country in Eastern Europe and North Asia
Clay Millennium Prize Problems Award for his final proof of the Poincaré conjecture in 2002, as well as the Fields Medal in 2006. Alexander Popov was among
Russia
Form of differential geometry
filling area conjecture has been proved in a hyperelliptic setting (see reference by Bangert et al. below). The filling area conjecture asserts that among
Systolic_geometry
Problem in Lie group theory
was an acute one of making this precise: is there any difference if a restriction to smooth manifolds is imposed? The expected answer was in the negative
Hilbert's_fifth_problem
Control theory for nonlinear or time-variant systems
graphical restrictions on the graph of Φ(y) x y or also on the graph of dΦ/dy x Φ/y. There are counterexamples to Aizerman's and Kalman's conjectures such
Nonlinear_control
Theorem in Euclidean geometry
compass. Motivated by Mascheroni's result, in 1822 Jean Victor Poncelet conjectured a variation on the same theme. His work paved the way for the field of
Mohr–Mascheroni_theorem
appears in various contexts in elementary geometry. The Fermat–Catalan conjecture concerns a certain Diophantine equation, equating the sum of two terms
List_of_sums_of_reciprocals
Methodic assignment of colors to elements of a graph
In 1960, Claude Berge formulated another conjecture about graph coloring, the strong perfect graph conjecture, originally motivated by an information-theoretic
Graph_coloring
Statement in mathematical combinatorics
Paul Erdős conjectured that there exists a constant c such that every graph H on k vertices satisfies rind(H) ≤ 2ck. If this conjecture is true, it would
Ramsey's_theorem
Quantum mechanics thought experiment
subjective experience of surviving quantum suicide. It is sometimes conjectured to be applicable to real-world causes of death as well. As a thought
Quantum suicide and immortality
Quantum_suicide_and_immortality
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