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Conjecture in knot theory relating quantum invariants and hyperbolic geometry
In the branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry
Volume_conjecture
Upper bound on the volume of a convex body containing one lattice point
In the geometry of numbers, Ehrhart's volume conjecture gives an upper bound on the volume of a convex body containing only one lattice point in its interior
Ehrhart's_volume_conjecture
Family of quantum invariants
odd r {\displaystyle r} , in 2018 Q. Chen and T. Yang suggested the volume conjecture for the RT-invariants, which essentially says that the RT-invariants
Reshetikhin–Turaev_invariant
Mathematical invariant of a knot or link
infinity, the limit value would give the hyperbolic volume of the knot complement. (See Volume conjecture.) In 2000 Mikhail Khovanov constructed a certain
Jones_polynomial
Three dimensional analogue of uniformization conjecture
In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric
Geometrization_conjecture
2000, six remain unsolved to date: Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Theorem in geometric topology
In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about
Poincaré_conjecture
Math theorem about sphere packing
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional
Kepler_conjecture
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
Even integers as sums of two primes
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural
Goldbach's_conjecture
Russian mathematician (born 1966)
analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem
Grigori_Perelman
Conjecture in number theory
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and
Abc_conjecture
Number associated with symmetric convex bodies
Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke–Santaló inequality. The still-unsolved Mahler conjecture states that
Mahler_volume
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
Statement in complex analysis; formerly the Bieberbach conjecture
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order
De_Branges's_theorem
Unsolved problem in topology
Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965
Novikov_conjecture
Number, approximately 3.14
{e^{n+1}}{\sqrt {2\pi n}}}.} Ehrhart's volume conjecture predicts that this is the (optimal) upper bound on the volume of a convex body containing only one
Pi
Theorem on the minimal volume of cells in the Voronoi decomposition of packed spheres
spheres. He conjectured in 1943 that the minimal volume of any cell in the resulting Voronoi decomposition was at least as large as the volume of a regular
Dodecahedral_conjecture
Disproved mathematical conjecture
In mathematics, the Mertens conjecture is the statement that the Mertens function M ( n ) {\displaystyle M(n)} is bounded by ± n {\displaystyle \pm {\sqrt
Mertens_conjecture
Chinese mathematician (born 1991)
preprint "Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions" claiming to solve the Kakeya conjecture in three
Hong_Wang
Mathematical space
the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter
3-manifold
Conjecture about the roots of polynomials
In mathematics, Sendov's conjecture, sometimes also called Ilieff's conjecture, concerns the relationship between the locations of roots and critical
Sendov's_conjecture
conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin–Mumford conjecture in
Bogomolov_conjecture
This fact and useful properties of alternating knots, such as the Tait conjectures, was what enabled early knot tabulators, such as Tait, to construct tables
Alternating_knot
Numerous conjectures by mathematician Irving Kaplansky
zero-divisor conjecture implies the idempotent conjecture and is implied by the unit conjecture. As of 2021, the zero divisor and idempotent conjectures are open
Kaplansky's_conjectures
Shape containing unit line segments in all directions
"A Tower of Conjectures That Rests Upon a Needle". Quanta Magazine. Retrieved 2025-07-20. Hong Wang; Joshua Zahl (2025-02-24). "Volume estimates for
Kakeya_set
Can every bounded subset of Rn be partitioned into (n+1) smaller diameter sets?
problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk. In
Borsuk's_conjecture
Mathematical foam of equal-volume bubbles
enclosing a single volume was not proven until the 19th century, and the next simplest such problem, the double bubble conjecture on enclosing two volumes
Weaire–Phelan_structure
Conjecture in number theory
In mathematics, Serre's modularity conjecture, introduced by Jean-Pierre Serre (1975, 1987), states that an odd, irreducible, two-dimensional Galois representation
Serre's_modularity_conjecture
Japanese mathematician
geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. Mochizuki
Shinichi_Mochizuki
Mathematical conjecture
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential
Arnold_conjecture
Mathematical conjecture about the Riemann zeta function
In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint
Hilbert–Pólya_conjecture
On smallest surface enclosing two volumes
honeycomb, but this conjecture was disproved by the discovery of the Weaire–Phelan structure, a partition of space into equal volume cells of two different
Double_bubble_theorem
Mathematical conjecture about elliptic curves
In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational
Sato–Tate_conjecture
3-dimensional geometric figure
formulated the bellows conjecture stating that the volume of a flexible polyhedron is invariant under flexing. This conjecture was proved for polyhedra
Flexible_polyhedron
Mathematical problem
Fuglede's conjecture is a problem in mathematics proposed by Bent Fuglede in 1974, and resolved in the negative for most dimensions by Terence Tao in 2004
Fuglede's_conjecture
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
Chern's conjecture for affinely flat manifolds was proposed by Shiing-Shen Chern in 1955 in the field of affine geometry. As of 2025, it remains an unsolved
Chern's conjecture (affine geometry)
Chern's_conjecture_(affine_geometry)
French mathematician (1906–2000)
(aged 93–94) Strasbourg Alma mater University of Strasbourg Known for Ehrhart polynomial Ehrhart's volume conjecture Scientific career Fields Mathematics
Eugène_Ehrhart
Theoretical Physics
Shinsei Ryu and Tadashi Takayanagi published, in 2006, a conjecture within holography that posits a quantitative relationship between the entanglement
Ryu–Takayanagi_conjecture
Mathematical theorem
correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical statistics
Gaussian correlation inequality
Gaussian_correlation_inequality
Mathematical conjectures in class field theory
In mathematics, the local Langlands conjectures, introduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between
Local_Langlands_conjectures
Conjecture unifying entanglement and wormholes
ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole
ER_=_EPR
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
In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston (1982) as the eleventh problem out of his twenty-four
Ending_lamination_theorem
Every symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
it was conjectured to be PPP-complete. Danzer set Pick's theorem Dirichlet's unit theorem Minkowski's second theorem Ehrhart's volume conjecture Olds,
Minkowski's_theorem
Two unsolved conjectures in algebraic number theory
first conjecture was proposed in 1976 and concerns Iwasawa invariants. This conjecture is related to Vandiver's conjecture, Leopoldt's conjecture, Birch–Tate
Greenberg's_conjectures
Set of points equidistant from a center
position vector scaled by 1/r. In Riemannian geometry, the filling area conjecture states that the hemisphere is the optimal (least area) isometric filling
Sphere
Type of graph vertex labeling
but weaker conjecture known as "Ringel's conjecture" was partially proven in 2020. Kotzig once called the effort to prove the conjecture a "disease"
Graceful_labeling
In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of
Homological conjectures in commutative algebra
Homological_conjectures_in_commutative_algebra
Manifold of dimension 3 equipped with a hyperbolic metric
3-manifolds of finite volume have a particular importance in 3-dimensional topology as follows from Thurston's geometrisation conjecture proved by Perelman
Hyperbolic_3-manifold
Proposition in group theory
Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was posed by
Hanna_Neumann_conjecture
Riemannian metrics, complex manifolds
the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on
Calabi_conjecture
In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential
Grothendieck–Katz p-curvature conjecture
Grothendieck–Katz_p-curvature_conjecture
Curves of genus > 1 over the rationals have only finitely many rational points
This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized
Faltings'_theorem
Conjecture in algebraic geometry
In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by
Witten_conjecture
In mathematics, when is n!+1 a square
follow from the abc conjecture that there are only finitely many Brown numbers. More generally, it would also follow from the abc conjecture that n ! + A =
Brocard's_problem
Whether a manifold which is a homotopy sphere is a sphere
In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold that is a homotopy sphere is a sphere. More precisely
Generalized Poincaré conjecture
Generalized_Poincaré_conjecture
Jungian concept of the meaningfulness of acausal coincidences
Interpretation of Nature and the Psyche. This culminated in the Pauli–Jung conjecture. Jung and Pauli's view was that, just as causal connections can provide
Synchronicity
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts
Tait_conjectures
Problem in graph theory
path? More unsolved problems in mathematics In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in graphs. It says:
Lovász_conjecture
In mathematics, the Cartan–Hadamard conjecture is a fundamental problem in Riemannian geometry and geometric measure theory which states that the classical
Cartan–Hadamard_conjecture
Physical theorem
In physics, the Painlevé conjecture is a theorem about singularities among the solutions to the n-body problem: there are noncollision singularities for n ≥ 4
Painlevé_conjecture
Ugandan Social Media influencer / blogger born 1995 in mbarara town
Chern's conjecture for hypersurfaces in spheres, unsolved as of 2018, is a conjecture proposed by Chern in the field of differential geometry. It originates
Chern's conjecture for hypersurfaces in spheres
Chern's_conjecture_for_hypersurfaces_in_spheres
Theory in number theory
maps between the curves. A first version of Grothendieck's anabelian conjecture was solved by Hiroaki Nakamura and Akio Tamagawa (for affine curves),
Anabelian_geometry
List of unsolved computational problems
functions exist? Is public-key cryptography possible? Log-rank conjecture Hartmanis–Stearns conjecture Can integer factorization be done in polynomial time on
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Geometry problem on tiling by hypercubes
In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes
Keller's_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
who published a list of 92 non-uniform Johnson polyhedra in 1966. His conjecture that the list was complete and no other examples existed was proven by
List_of_Johnson_solids
In differential geometry, Mikhail Gromov's filling area conjecture asserts that the hemisphere has minimum area among the orientable surfaces that fill
Filling_area_conjecture
Conjecture in geometry
In geometry, the Egan conjecture gives a sufficient and necessary condition for the radii of two spheres and the distance of their centers, so that a simplex
Egan_conjecture
Normalized hyperbolic volume of the complement of a hyperbolic knot
first studied by William Thurston in connection with his geometrization conjecture. A hyperbolic link is a link in the 3-sphere whose complement (the space
Hyperbolic_volume
Greek American mathematician
of the Jones polynomial to Hyperbolic volumes of knots and on the Volume conjecture for Quantum invariants of 3-manifolds and the theory of Skein modules
Efstratia_Kalfagianni
On dissections between polyhedra
Hilbert conjectured that this was not always possible. His student Max Dehn confirmed the conjecture with a counterexample. The formula for the volume of a
Hilbert's_third_problem
In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime p does not divide the class number hK of the maximal real subfield
Kummer–Vandiver_conjecture
Thurston–Bennequin number Tricolorability Unknotting number Unknotting problem Volume conjecture Schubert's theorem Conway's theorem Alexander's theorem List of mathematical
List_of_knot_theory_topics
Class of mathematical knot with special properties
Gordon conjectured these were the only knots admitting lens space surgeries. This is now known as the Berge conjecture. The Berge conjecture states that
Berge_knot
Maths conjecture
In geometry, more specifically in polytope theory, Kalai's 3d conjecture is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes
Kalai's_3^d_conjecture
for her solution of the generic case of Green's conjecture in two papers. The case of Green's conjecture for generic curves had attracted a huge amount
Clifford's theorem on special divisors
Clifford's_theorem_on_special_divisors
and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality. Diophantine geometry
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Brazilian mathematician
with André Neves, he proved the Willmore conjecture. Since then, among proving other important conjectures, Marques and Neves greatly extended Almgren–Pitts
Fernando_Codá_Marques
competitors may react if it varies its output or price. The firm forms a conjecture about the variation in the other firm's output that will accompany any
Conjectural_variation
Mathematical conjecture on the Riemann zeta function
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf about the rate of growth of the Riemann zeta function
Lindelöf_hypothesis
Type of mathematical knot
the slice-ribbon conjecture, asks if the converse is true: is every (smoothly) slice knot ribbon? Lisca (2007) showed that the conjecture is true for knots
Ribbon_knot
Disproven conjecture for a primality test
In number theory, the Chinese hypothesis is a disproven conjecture stating that an integer n is prime if and only if it satisfies the condition that 2
Chinese_hypothesis
Cuboid whose edges and face diagonals have integer lengths
all of these three conjectures are true, then no perfect cuboids exist. They are neither proved nor disproved. Cuboid conjecture 1. For any two positive
Euler_brick
Partial differential equation
Thurston's geometrization conjecture, Hamilton produced a number of results in the 1990s which were directed towards the conjecture's resolution. In 2002 and
Ricci_flow
Number of form 2^(2^p-1)-1 with prime exponent
numbers. Volume 1: Divisibility and primality (1919). Published by Washington, Carnegie Institution of Washington. New Mersenne Conjecture Dickson, L
Double_Mersenne_number
Study of algorithms for performing number theoretic computations
investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the
Computational_number_theory
Pseudometric of complex manifolds
Voisin (2003), Lemma 1.51. Campana (2004), Conjecture 9.2, Lang (1986), Conjecture 5.8. Campana (2004), Conjecture 9.20. Kobayashi (1998), Theorem 3.5.31
Kobayashi_metric
Mathematics concept
Specifically, the Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. The Hadamard conjecture has also been attributed
Hadamard_matrix
Mathematical theory
spheres has a longer history of investigation, from which the Kepler conjecture is most well-known. Atoms in crystal structures can be simplistically
Finite_sphere_packing
Type of Riemannian manifold with constant Jacobi operator spectrum
symmetric spaces? More unsolved problems in mathematics The Osserman conjecture asks whether every Osserman manifold is either a flat manifold or locally
Osserman_manifold
Berger spheres show that the minimal volume of the three-dimensional sphere is also zero. Gromov has conjectured that every closed simply connected odd-dimensional
Minimal_volume
Partition of a graph into spanning subgraphs
Unsolved problem in mathematics Conjecture: If n is odd and k ≥ n, then G is 1-factorable. If n is even and k ≥ n − 1 then G is 1-factorable. More unsolved
Graph_factorization
Self-adjusting binary search tree
knowledge of the pattern. According to the unproven dynamic optimality conjecture, their performance on all access patterns is within a constant factor
Splay_tree
Theory in the philosophy of mind
Atmanspacher, Harald. The Pauli–Jung Conjecture and Its Relatives: A Formally Augmented Outline. Open Philosophy, Volume 3 Issue 1. De Gruyter | Published
Double-aspect_theory
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a
Carathéodory_conjecture
In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert
Seifert_conjecture
Thesis on the nature of computability
thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis. Soare, Robert I. (2009-09-01)
Church–Turing_thesis
VOLUME CONJECTURE
VOLUME CONJECTURE
Boy/Male
Indian, Sanskrit
Column; Pillar
Girl/Female
American, British, English, Italian
Of High Value
Male
Scottish
Scottish form of Latin Columba, COLUMB means "dove."
Boy/Male
Indian
Value, Price
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Boy/Male
Arabic
Value
Female
Yiddish
(בְּלוּמֶע) Variant form of Yiddish Bluma, BLUME means "flower."
Male
Irish
Irish form of Latin Columba, COLUM means "dove."
Boy/Male
African
placed in God's hands'.
Boy/Male
Hindu, Indian
Value
Boy/Male
Indian
Heart of God; Volume; Shlok
Boy/Male
Muslim
Value, Price
Girl/Female
Arabic
Value; Price
Boy/Male
Irish Gaelic Greek
a Latin name meaning dove.
Boy/Male
Arabic, Australian, Muslim
Column; Pillar
Girl/Female
Muslim/Islamic
Value Worth
Surname or Lastname
English
English : metonymic occupational name for a dealer in feathers, from Middle English, Old French plume ‘feather’ (Latin pluma).English and North German : variant of Plum.Catalan (Plumé) : variant of plomer, occupational name for a worker in lead, from a derivative of plom ‘lead’.
Surname or Lastname
English (mainly Lancashire) and Scottish
English (mainly Lancashire) and Scottish : topographic name for someone who lived by a holly tree, from Middle English holm, a divergent development of Old English hole(g)n; the main development was towards modern English holly (see Hollis).English and Scottish : topographic name or habitational name from northern Middle English holm ‘island’, Old Norse holmr (see Holm 1).Danish and Swedish : variant of Holm 1.Norwegian : habitational name from any of several farmsteads, so named from the dative singular of Old Norse holmr ‘islet’, ‘low flat land beside a river’.
Girl/Female
Indian, Kannada
Love
Girl/Female
American, British, English
Of High Value
VOLUME CONJECTURE
VOLUME CONJECTURE
Surname or Lastname
English
English : of uncertain origin; it may be from the thieves’ slang term kinchin ‘child’, which is probably a derivative of German Kindchen, diminutive of Kind ‘child’.Americanized form of Kindchen or more probably of Rhenish Kindgen (pronounced ‘kintshen’), both diminutives of Kind.
Girl/Female
Tamil
Bird of queen
Male
Romanian
Pet form of Romanian Ioan, IONEL means "God is gracious."
Boy/Male
English American Latin Hebrew
Right-hand son.
Male
Norse
Variant form of Old Norse Hallþórr, HALLDÓRR means "Thor's rock."
Boy/Male
Arabic
Fluency; Eloquence
Girl/Female
Indian
Bright eyes like a lamp
Boy/Male
Hindu, Indian
Earth
Boy/Male
Arabic, Muslim
Joy of Allah
Girl/Female
Muslim
Hope
VOLUME CONJECTURE
VOLUME CONJECTURE
VOLUME CONJECTURE
VOLUME CONJECTURE
VOLUME CONJECTURE
a.
Easily rolling or turning; easily set in motion; apt to roll; rotating; as, voluble particles of matter.
a.
Having volume, or bulk; massive; great.
v. t.
To absolve; as, to solute sin.
n.
Value.
n.
Any one of numerous species of large, handsome marine gastropods belonging to Voluta and allied genera.
v. t.
To form into, or incorporate with, a volume.
n.
Anything resembling, in form or position, a column in architecture; an upright body or mass; a shaft or obelisk; as, a column of air, of water, of mercury, etc.; the Column Vendome; the spinal column.
a.
Of or pertaining to volume or volumes.
pl.
of Voluta
a.
Soluble; as, a solute salt.
n.
Dimensions; compass; space occupied, as measured by cubic units, that is, cubic inches, feet, yards, etc.; mass; bulk; as, the volume of an elephant's body; a volume of gas.
n.
Any voluta.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
a.
Having the power or habit of turning or twining; as, the voluble stem of hop plants.
a.
Having the form of a volume, or roil; as, volumed mist.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
n.
Hence, a collection of printed sheets bound together, whether containing a single work, or a part of a work, or more than one work; a book; a tome; especially, that part of an extended work which is bound up together in one cover; as, a work in four volumes.
a.
Loose; free; liberal; as, a solute interpretation.
a.
Having a volute, or spiral scroll.
a.
Not adhering; loose; -- opposed to adnate; as, a solute stipule.