List of conjectures

This is an incomplete list of mathematical conjectures. They are divided into four sections, according to their status in 2007.

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,

* List of theorems, list of lemmas;

also

* List of statements undecidable in ZFC

for problems not subject to conventional proof nor disproof.

Proved (now theorems)

The theorems may not be their official names.
* Adams conjecture (J-homomorphism)
* Bieberbach conjecture, 1916 (De Branges' theorem, 1984)
* Blattner's conjecture (Blattner formula)
* Burnside conjecture (Feit-Thompson theorem)
* Cameron–Erdős conjecture
* Catalan's conjecture, 1844 (Mihăilescu's theorem, 2002)
* Conway-Norton conjecture (Monstrous moonshine)
* Dinitz conjecture (Galvin's theorem)
* Deligne's conjecture on 1-motives
* Denjoy's conjecture
* Dodecahedral conjecture (Hales-McLaughlin theorem)
* Epsilon conjecture (Ribet's theorem)
* Fermat's Last Theorem (Andrew Wiles' proof in 1994)
* Frobenius conjecture (Iiyori and Yamaki)
* Gradient conjecture (Kurdyka-Mostowski-Parusinski theorem)
* Heawood conjecture (Ringel-Youngs' theorem)
* Kummer's conjecture on cubic Gauss sums (Kummer sum)
* Mahler-Manin conjecture
* Manin-Mumford conjecture (Raynaud's theorem)
* Milnor conjecture (Voevodsky's theorem)
* Mordell conjecture (Faltings' theorem)
* Mumford conjecture (Haboush's theorem)
* Oppenheim conjecture (Margulis' theorem)
* Ramanujan–Petersson conjecture (consequence of the proof of the Weil conjectures)
* Road coloring conjecture, 1970 (2008)
* Segal's Burnside ring conjecture (Carlsson theorem)
* Serre's conjecture (Quillen-Suslin theorem)
* Seymour's conjecture
* Smith conjecture (Gordon's theorem)
* Stanley-Wilf conjecture (Marcus-Tardos theorem)
* Star height problem (Hashiguchi theorem)
* Strong perfect graph conjecture (Chudnovsky-Robertson-Seymour-Thomas theorem)
* Sullivan conjecture
* Tameness conjecture (Agol or Calegari-Gabai theorem)
* Taniyama-Shimura conjecture (Modularity theorem)
* Wagner's conjecture (Robertson-Seymour theorem)
* Weil conjectures (Deligne's theorems)

Disproved (no longer conjectures)

* Borsuk's conjecture
* Euler's sum of powers conjecture
* Ganea conjecture
* Generalized Smith conjecture
* Hauptvermutung
* Intersection graph conjecture
* Kouchnirenko's conjecture
* Mertens conjecture
* Pólya conjecture, 1919 (1958)
* Ragsdale conjecture
* Tait's conjecture
* Von Neumann conjecture
* Weyl-Berry conjecture

Recent work

* Bloch-Kato conjecture
* Erdős–Straus conjecture
* Herzog-Schönheim conjecture
* Hilbert-Smith conjecture
* Kepler conjecture
* Nagata conjecture on automorphisms
* Poincaré conjecture
* Sato-Tate conjecture
* Thurston's conjecture

Open problems

* abc conjecture
* Andrews-Curtis conjecture
* Agoh-Giuga conjecture
* Andrica's 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
* Birkhoff conjecture
* Bloch-Beilinson conjectures
* Borel conjecture
* Bost conjecture
* Bunyakovsky conjecture
* Catalan-Dickson conjecture on aliquot sequences
* Carathéodory conjecture
* Catalan's Mersenne conjecture
* Cherlin-Zilber conjecture
* Collatz conjecture
* Cramér's conjecture
* Deligne conjecture disambiguation
* Eilenberg-Ganea conjecture
* Elliott-Halberstam conjecture
* Erdős-Burr conjecture
* Erdős-Gyárfás conjecture
* Farrell-Jones conjecture
* Filling area conjecture
* Frankl conjecture
* Gilbreath conjecture
* Goldbach's conjecture
* Goldbach's weak conjecture
* Goormaghtigh conjecture
* Grimm's conjecture
* Grothendieck–Katz p-curvature conjecture
* Hadamard conjecture
* Hedetniemi's conjecture
* Hirsch conjecture
* Hopf conjecture
* Hodge conjecture
* Homological conjectures in commutative algebra
* Jacobian conjecture
* Kaplansky conjecture
* Keating-Snaith conjecture
* Lawson's conjecture
* Lenstra-Pomerance-Wagstaff conjecture
* Lichtenbaum conjecture
* List coloring conjecture
* Littlewood conjecture
* Lovász 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
* Ringel-Kotzig_conjecture
* Schanuel's conjecture
* Scheinerman's conjecture
* Schinzel's hypothesis H
* Scholz conjecture
* Second Hardy-Littlewood conjecture
* Selfridge's conjecture
* Serre conjecture (number theory)
* Serre's multiplicity conjectures
* Singmaster's conjecture
* Tate conjecture
* Twin prime conjecture
* Vandiver's conjecture
* Waring's conjecture
* Weight-monodromy conjecture
* Weinstein conjecture
* Whitehead conjecture
* Zhou conjecture

External links

* [http://garden.irmacs.sfu.ca/ Open Problem Garden]