This is a list of mathematical conjectures, by Wikipedia page. They are divided into four sections, according to their status in 2005. In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. ...

See also:

• Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators
• Unsolved problems in mathematics
• List of unsolved problems
• Millennium Prize Problems

and, for proved results, The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects. ... Paul Erdős, pictured in lecture, late in life. ... Unsolved problems in : Note: Use the unsolved tag: {{unsolved|F|X}}, where F is any field in the sciences: and X is a concise explanation with or without links. ... This is a list of lists of unsolved problems in various subjects: Unsolved problems in biology Unsolved problems in chemistry Unsolved problems in cognitive science Unsolved problems in computer science Unsolved problems in economics Unsolved problems in Egyptology Unsolved problems in governance Unsolved problems in mathematics Unsolved problems in medicine... The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts, and dedicated to increasing and disseminating mathematical knowledge. ...

• List of theorems, list of lemmas;

also This is a list of theorems, by Wikipedia page. ... This is a list of lemmas (i. ...

• List of statements undecidable in ZFC

for problems not subject to conventional proof nor disproof. The following is a list of mathematical statements that are undecidable in ZFC (the Zermelo-Fraenkel axioms plus the axiom of choice), assuming that ZFC is consistent. ...

Proved (now theorems)

• Adams conjecture
• Bieberbach conjecture (now known as De Branges' theorem)
• Blattner's conjecture (now often known as the Blattner formula)
• Conway-Norton conjecture (now known as Monstrous moonshine)
• Dinitz conjecture
• Epsilon conjecture (an intermediate on the way to Fermat's last theorem)
• Fermat's last theorem
• Gradient conjecture
• Heawood conjecture
• Kummer's conjecture on cubic Gauss sums
• Mahler-Manin conjecture
• Manin-Mumford conjecture (now Raynaud's theorem)
• Mordell conjecture (now known as Faltings' theorem)
• Mumford conjecture (now Haboush's theorem)
• Oppenheim conjecture
• Ramanujan conjecture on the cusp form Δ
• Segal's Burnside ring conjecture
• Serre's conjecture (now known as the Quillen-Suslin theorem)
• Smith conjecture
• Star height problem
• Sullivan conjecture
• Taniyama-Shimura conjecture
• Wagner's conjecture (now known as the Robertson-Seymour theorem)
• Weil conjectures

In mathematics, the J-homomorphism is a mapping from the homotopy groups of the special orthogonal groups to the homotopy groups of spheres, defined by George Whitehead. ... In complex analysis, de Branges theorem, formerly the Bieberbach conjecture, states a necessary condition on an analytic function to map the unit disk injectively to itself. ... In complex analysis, de Branges theorem, named after Louis de Branges, formerly called the Bieberbach conjecture, after Ludwig Bieberbach, states a necessary condition on an analytic function to map the unit disk injectively to the complex plane. ... In mathematics, Blattners conjecture was a description of the discrete series representations of a general semisimple group G in terms of their restricted representations to a maximal compact subgroup K (their so-called K-types), formulated by R. J. Blattner. ... In mathematics, monstrous moonshine is a term devised by John Horton Conway and Simon P. Norton in 1979, used to describe the (then totally unexpected) connection between the monster group M and modular functions (particularly, the j function). ... In mathematics, monstrous moonshine is a term devised by John Conway and Simon P. Norton in 1979, used to describe the (then totally unexpected) connection between the monster group M and modular functions (particularly, the j function). ... In combinatorics, the Dinitz conjecture was a problem on the extension of arrays to partial Latin squares, posed in 1979 by Jeff Dinitz, and proven in 1994 by Fred Galvin. ... Pierre de Fermat Fermats last theorem (sometimes abbreviated as FLT and also called Fermats great theorem) is one of the most famous theorems in the history of mathematics. ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats last theorem (edition of 1670). ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats last theorem (edition of 1670). ... The gradient conjecture, due to René Thom, was proved in 2000 by K. Kurdyka, T. Mostowski and A. Parusinski. ... The Heawood conjecture in graph theory was an expected formula to give the correct upper bound for the number of colors which are sufficient for graph coloring on a surface of a given genus. ... In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. ... In number theory, the Mordell conjecture stated a basic result regarding the rational number solutions to Diophantine equations. ... In number theory, the Mordell conjecture stated a basic result regarding the rational number solutions to Diophantine equations. ... In mathematics, 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-vector space V, given v in V that is fixed by the action of G, there is a G-invariant F on... In mathematics, the Ramanujan conjecture states that the Fourier coefficients τ(n) of the cusp form Δ(z) of weight 12, defined in modular form theory, satisfy τ(p) ≤ 2p11/2, when p is a prime number. ... In number theory, a cusp form is a particular kind of modular form, distinguished in the case of modular forms for the modular group by the vanishing in the Fourier series expansion of the constant coefficient a0. ... In mathematics, the Quillen–Suslin theorem is a theorem in abstract algebra about the relationship between free modules and projective modules. ... The Quillen-Suslin theorem is a theorem in abstract algebra about the relationship between free modules and projective modules. ... In mathematics, the Smith conjecture was a problem open for many years, and proved at the end of the 1970s. ... The star-height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions with a limited nesting depth of Kleene stars. ... The Taniyama-Shimura theorem establishes an important connection between elliptic curves, which are objects from algebraic geometry, and modular forms, which are certain periodic holomorphic functions investigated in number theory. ... ... In graph theory, the Robertson-Seymour theorem states that every downwardly closed set of (isomorphism classes of) finite graphs is precisely the set of all (isomorphism classes of) graphs that lack a certain set of finitely many forbidden minors. ... In mathematics, the Weil conjectures, which had become theorems by 1975, were some highly-influential proposals from the late 1940s by Andre Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. ...

Disproved

• Euler's conjecture
• Ganea conjecture
• Generalized Smith conjecture
• Hauptvermutung
• Intersection graph conjecture
• Kouchnirenko's conjecture
• Mertens conjecture
• Ragsdale conjecture
• Tait's conjecture
• Von Neumann conjecture
• Weyl-Berry conjecture

Eulers conjecture is a conjecture related to Fermats last theorem which was proposed by Leonhard Euler in 1769. ... The Hauptvermutung of geometric topology (German for main conjecture), is the conjecture that topological manifolds and piecewise linear manifolds coincide. ... The Mertens conjecture is a statement about the behaviour of a certain function as its argument increases. ... Taits conjecture states that Every polyhedron has a Hamiltonian cycle (along the edges) through all its vertices. It was proposed in 1886 by P. G. Tait and disproved in 1946, when W. T. Tutte constructed a counterexample with 25 faces, 69 edges and 46 vertices. ... In mathematics, the von Neumann conjecture, disproved in recent years, stated that a topological group G is not amenable if and only if G contains a subgroup that is a free group on two generators. ... In mathematics, hearing the shape of a drum relates to a series of results that do just that, i. ...

Recent work

• Bloch-Kato conjecture
• Catalan's conjecture
• Erdős-Strauss conjecture
• Herzog-Schönheim conjecture
• Hilbert-Smith conjecture
• Kepler conjecture
• Milnor conjecture
• Nagata conjecture on automorphisms
• Poincaré conjecture
• Strong perfect graph conjecture
• Thurston's conjecture

Catalans conjecture is a simple conjecture in number theory that was proposed by the mathematician Eugène Charles Catalan. ... The Erdős-Strauss conjecture states that for all integers n ≥ 2 there exist integers a, b, and c such that This is the same as saying that any number of the form 4/n can be expressed as the sum of three unit fractions. ... Let be a group, and let be a finite system of left cosets of subgroups of . ... In mathematics, the Hilbert-Smith conjecture is concerned with the transformation groups of manifolds; and in particular with the limitations on topological groups G that can act effectively (faithfully) on a (topological) manifold M. Restricting to G which are locally compact and have a continuous, faithful group action on M... In mathematics, the Kepler conjecture is a conjecture about sphere packing in three dimensional Euclidean space. ... 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 coprime to 2, by means of the Galois (or equivalently étale) cohomology of F with coefficients in Z/2Z. It was proved... In mathematics, the Poincaré conjecture (see Henri Poincaré for pronunciation) is a conjecture about the characterisation of the three-dimensional sphere amongst 3-manifolds. ... In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the clique number of that subgraph. ... The geometrization conjecture, also known as Thurstons geometrization conjecture, concerns the geometric structure of compact 3-manifolds. ...

Open problems

• abc conjecture
• Andrews-Curtis conjecture
• Agoh-Giuga conjecture
• Artin conjectures
• Atiyah conjecture
• Bateman-Horn conjecture
• Baum-Connes conjecture
• Beal's conjecture
• Beilinson conjecture
• Berry-Tabor conjecture
• Birch and Swinnerton-Dyer conjecture
• Birch-Tate conjecture
• Bloch-Beilinson conjectures
• Borel conjecture
• Bost conjecture
• Collatz conjecture
• Cramér's conjecture
• Deligne conjecture disambiguation
• Eilenberg-Ganea conjecture
• Elliott-Halberstam conjecture
• Erdős-Burr conjecture
• Erdős-Gyárfás conjecture
• Farrell-Jones conjecture
• Fibonacci primes conjecture
• Frankl conjecture
• Gilbreath conjecture
• Goldbach's conjecture
• Goldbach's weak conjecture
• Hadamard conjecture
• Hodge conjecture
• Homological conjectures in commutative algebra
• Jacobian conjecture
• Lawson's conjecture
• Lenstra-Pomerance-Wagstaff conjecture
• Lichtenbaum conjecture
• List coloring conjecture
• Littlewood conjecture
• Marshall Hall's conjecture
• Mazur's conjectures
• Monodromy conjecture
• New Mersenne conjecture
• Novikov conjecture
• Petersen coloring conjecture
• Pierce-Birkhoff conjecture
• Pillai's conjecture
• De Polignac's conjecture
• Quillen-Lichtenbaum conjecture
• Reconstruction conjecture
• Riemann Hypotheses: see also Weil conjectures, above
  • Riemann hypothesis
    • Generalized Riemann hypothesis
    • Grand Riemann hypothesis
  • Density hypothesis
  • Lindelöf hypothesis
  • Hilbert-Pólya conjecture on the Riemann hypothesis
• Sato-Tate conjecture
• Schanuel's conjecture
• Schinzel's hypothesis H
• Scholz conjecture
• Second Hardy-Littlewood conjecture
• Selfridge's conjecture
• Serre's multiplicity conjectures
• Tate conjecture
• Twin prime conjecture
• Vandiver's conjecture
• Weight-monodromy conjecture