Category: Conjectures that have been proved

Selberg's zeta function conjecture
In mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ(1/2 + it). It is known that the function has infinitely many ze
Hsiang–Lawson's conjecture
In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S3. The conjecture was featured by the Australian Mathematical Society Gazette a
Mariño–Vafa conjecture
No description available.
De Branges's theorem
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 for it to map the open unit disk of the comple
B-theorem
B-theorem is a mathematical finite group theory result formerly known as the B-conjecture. The theorem states that if is the centralizer of an involution of a finite group, then every component of is
Heawood conjecture
In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. For surfaces of genus
Abhyankar's conjecture
In abstract algebra, Abhyankar's conjecture is a 1957 conjecture of Shreeram Abhyankar, on the Galois groups of algebraic function fields of characteristic p. The soluble case was solved by Serre in 1
Bogomolov conjecture
In mathematics, the Bogomolov conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin-Mumford conjecture in arithmetic geometr
Scheinerman's conjecture
In mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Schein
Calabi's conjecture
No description available.
Witten conjecture
In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper Witten, and generalize
Epsilon conjecture
No description available.
Mordell's conjecture
No description available.
Dodecahedral conjecture
The dodecahedral conjecture in geometry is intimately related to sphere packing. László Fejes Tóth, a 20th-century Hungarian geometer, considered the Voronoi decomposition of any given packing of unit
Milnor conjecture (topology)
In knot theory, the Milnor conjecture says that the slice genus of the torus knot is It is in a similar vein to the Thom conjecture. It was first proved by gauge theoretic methods by Peter Kronheimer
Kepler conjecture
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no
Duffin–Schaeffer conjecture
The Duffin–Schaeffer conjecture was a conjecture (now a theorem) in mathematics, specifically, the Diophantine approximation proposed by R. J. Duffin and A. C. Schaeffer in 1941. It states that if is
Hajós's theorem
In group theory, Hajós's theorem states that if a finite abelian group is expressed as the Cartesian product of simplexes, that is, sets of the form where is the identity element, then at least one of
Dyson conjecture
In mathematics, the Dyson conjecture (Freeman Dyson ) is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson and Gunson. Andrews generalized it
Nirenberg's conjecture
In mathematics, Nirenberg's conjecture, now Osserman's theorem, states that if a neighborhood of the sphere is omitted by the Gauss map of a complete minimal surface, then the surface in question is a
Property P conjecture
In mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obt
Calabi conjecture
In the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on certain complex manifolds, made by Eugenio Cala
Soul conjecture
No description available.
Black hole stability conjecture
The black hole stability conjecture is the conjecture that a perturbed Kerr black hole will settled back down to a stable state. This has been an open problem in general relativity for some time. A 20
Serre's modularity conjecture
In mathematics, Serre's modularity conjecture, introduced by Jean-Pierre Serre , states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form.
Goldbach's weak conjecture
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that Every odd number greater than 5 can be expre
Crank conjecture
In mathematics, the crank conjecture was a conjecture about the existence of the crank of a partition that separates partitions of a number congruent to 6 mod 11 into 11 equal classes. The conjecture
Painlevé conjecture
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. The theorem was proven for n ≥ 5 in 1988
Mordell–Lang conjecture
No description available.
Willmore conjecture
In differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by F
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any i
Van der Waerden's conjecture
No description available.
Lieb conjecture
In quantum information theory, the Lieb conjecture is a theorem concerning the Wehrl entropy of quantum systems for which the classical phase space is a sphere. It states that no state of such a syste
Bachet's conjecture
No description available.
Milin conjecture
No description available.
Erdős–Graham problem
In combinatorial number theory, the Erdős–Graham problem is the problem of proving that, if the set of integers greater than one is partitioned into finitely many subsets, then one of the subsets can
Burr–Erdős conjecture
In mathematics, the Burr–Erdős conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erdős, and is one of many conjectures named af
Taniyama-Shimura conjecture
No description available.
Schreier conjecture
In finite group theory, the Schreier conjecture asserts that the outer automorphism group of every finite simple group is solvable. It was proposed by Otto Schreier in 1926, and is now known to be tru
Bloch–Kato conjecture
No description available.
Zimmer's conjecture
Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries." It was named after the mathematician Robert
Erdős–Heilbronn conjecture
No description available.
Lange's conjecture
In algebraic geometry, Lange's conjecture is a theorem about stability of vector bundles over curves, introduced by and proved by Montserrat Teixidor i Bigas and in 1999.
Carlitz–Wan conjecture
In mathematics, the Carlitz–Wan conjecture classifies the possible degrees of exceptional polynomials over a finite field Fq of q elements. A polynomial f(x) in Fq[x] of degree d is called exceptional
Stahl's theorem
In matrix analysis Stahl's theorem is a theorem proved in 2011 by Herbert Stahl concerning Laplace transforms for special matrix functions. It originated in 1975 as the Bessis-Moussa-Villani (BMV) con
Oppenheim conjecture
In Diophantine approximation, the Oppenheim conjecture concerns representations of numbers by real quadratic forms in several variables. It was formulated in 1929 by Alexander Oppenheim and later the
Quillen–Lichtenbaum conjecture
In mathematics, the Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by , p. 175), who was inspired by earlier conjectures of . and proved the
Tameness theorem
In mathematics, the tameness theorem states that every complete hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, in other words homeomorphic to the interior of a
Ahlfors measure conjecture
In mathematics, the Ahlfors conjecture, now a theorem, states that the limit set of a finitely-generated Kleinian group is either the whole Riemann sphere, or has measure 0. The conjecture was introdu
Marden tameness conjecture
No description available.
Kato's conjecture
Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of the University of California, Berkeley. Kato initially posed the problem in 1953. Kato asked whether the square roo
Poincaré conjecture
In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is th
Tait conjectures
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots,
Dinitz conjecture
In combinatorics, the Dinitz theorem (formerly known as Dinitz conjecture) is a statement about the extension of arrays to partial Latin squares, proposed in 1979 by Jeff Dinitz, and proved in 1994 by
Kemnitz's conjecture
In additive number theory, Kemnitz's conjecture states that every set of lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autum
Norm residue isomorphism theorem
In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time rep
Last geometric statement of Jacobi
In differential geometry the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi. According to this conjecture: Every caustic from any point on an ellipsoid other t
Haboush's theorem
In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-ve
Dwork conjecture
In mathematics, the Dwork unit root zeta function, named after Bernard Dwork, is the L-function attached to the p-adic Galois representation arising from the p-adic etale cohomology of an algebraic va
Erdős sumset conjecture
In additive combinatorics, the Erdős sumset conjecture is a conjecture which states that if a subset of the natural numbers has a positive upper density then there are two infinite subsets and of such
Nikiel's conjecture
In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by in 1986. The conject
Thurston elliptization conjecture
William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature.
Gras conjecture
In algebraic number theory, the Gras conjecture relates the p-parts of the Galois eigenspaces of an ideal class group to the group of global units modulo cyclotomic units. It was proved by as a coroll
Zucker conjecture
No description available.
Virtually Haken conjecture
In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is virtually Haken. Th
Thom conjecture
In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the genus–degree formula . The Thom conjecture, named after French mathematician René Thom, sta
Morita conjectures
The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. The conjectures, formulated by Kiiti Morita in 1976, asked 1. * If is normal for ev
Gudkov's conjecture
In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree obeys
Taniyama–Shimura conjecture
No description available.
Hanna Neumann conjecture
In the mathematical subject of group theory, the Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was pose
Catalan's conjecture
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu at Paderbor
Segal's conjecture
Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the sta
No description available.
Mordell conjecture
No description available.
Atiyah–Jones conjecture
In mathematics, the Atiyah–Jones conjecture is a conjecture about the homology of the moduli spaces of instantons. The original form of the conjecture considered instantons over a 4 dimensional sphere
Waring's prime number conjecture
In number theory, Waring's prime number conjecture is a conjecture related to Vinogradov's theorem, named after the English mathematician Edward Waring. It states that every odd number exceeding 3 is
Manin–Mumford conjecture
No description available.
Milnor conjecture
In mathematics, the Milnor conjecture was a proposal by John Milnor of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by means of the Galois (o
Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph theory. In 1974, tightened this to the conjectu
Ehrenpreis conjecture
In mathematics, the Ehrenpreis conjecture of Leon Ehrenpreis states that for any K greater than 1, any two closed Riemann surfaces of genus at least 2 have finite-degree covers which are K-quasiconfor
Spherical space form conjecture
In geometric topology, the spherical space form conjecture (now a theorem) states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere.
No description available.
Gray's conjecture
In mathematics, Gray's conjecture is a conjecture made by Brayton Gray in 1984 about maps between loop spaces of spheres. It was later proved by John Harper.
Sullivan conjecture
In mathematics, Sullivan conjecture or Sullivan's conjecture on maps from classifying spaces can refer to any of several results and conjectures prompted by homotopy theory work of Dennis Sullivan. A
Alspach's conjecture
Alspach's conjecture is a mathematical theorem that characterizes the disjoint cycle covers of complete graphs with prescribed cycle lengths. It is named after Brian Alspach, who posed it as a researc
Honeycomb conjecture
The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 b
Cameron–Erdős conjecture
In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in is The sum of two odd numbers is even, so a set of odd numbers is always s
Takeuti's conjecture
In mathematics, Takeuti's conjecture is the conjecture of Gaisi Takeuti that a sequent formalisation of second-order logic has cut-elimination (Takeuti 1953). It was settled positively: * By Tait, us
Modularity theorem
The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama-Weil conjecture or modularity conjecture for elliptic curves) states that elliptic curves over the field of rational n
Double bubble theorem
In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard do
Smale conjecture
The Smale conjecture, named after Stephen Smale, is the statement that the diffeomorphism group of the 3-sphere has the homotopy-type of its isometry group, the orthogonal group O(4). It was proved in
Toida's conjecture
In combinatorial mathematics, Toida's conjecture, due to in 1977, is a refinement of the disproven Ádám's conjecture from 1967.