List of conjectures
From Wikipedia, the free encyclopedia
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,
also
for problems not subject to conventional proof nor disproof.
Contents |
[edit] Proved (now theorems)
The theorems may not be their official names.
- Adams conjecture (J-homomorphism)
- Bieberbach conjecture (De Branges' theorem)
- Blattner's conjecture (Blattner formula)
- Burnside conjecture (Feit-Thompson theorem)
- Catalan's conjecture (Mihăilescu's theorem)
- Conway-Norton conjecture (Monstrous moonshine)
- Dinitz conjecture (Galvin's theorem)
- Dodecahedral conjecture (Hales-McLaughlin theorem)
- Epsilon conjecture (Ribet's theorem)
- Fermat's Last Theorem
- 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 conjecture on the cusp form Δ (proved by the proof of the Weil conjectures)
- Segal's Burnside ring conjecture (Carlsson theorem)
- Serre's conjecture (Quillen-Suslin theorem)
- Seymour's conjecture
- Smith conjecture (Gordon's theorem)
- Stanley-Wilf conjecture (Tardos-Marcus 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 (Taniyama–Shimura theorem)
- Wagner's conjecture (Robertson-Seymour theorem)
- Weil conjectures (Deligne's theorems)
[edit] Disproved
- Borsuk's conjecture
- Euler's conjecture
- Ganea conjecture
- Generalized Smith conjecture
- Hauptvermutung
- Intersection graph conjecture
- Kouchnirenko's conjecture
- Mertens conjecture
- Pólya conjecture
- Ragsdale conjecture
- Tait's conjecture
- Von Neumann conjecture
- Weyl-Berry conjecture
[edit] 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
[edit] 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
- Catalan-Dickson conjecture on aliquot sequences
- Collatz conjecture
- Cramér's conjecture
- Deligne conjecture disambiguation
- Eilenberg-Ganea conjecture
- Elliott-Halberstam conjecture
- Erdős-Burr conjecture
- Erdős-Gyárfás conjecture
- Farrell-Jones conjecture
- Frankl conjecture
- Gilbreath conjecture
- Goldbach's conjecture
- Goldbach's weak conjecture
- Grimm's conjecture
- Grothendieck–Katz p-curvature conjecture
- Hadamard conjecture
- Hedetniemi's 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
- Density hypothesis
- Lindelöf hypothesis
- Hilbert-Pólya conjecture on the Riemann hypothesis
- Ringel-Kotzig_conjecture
- Schanuel'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
- Weight-monodromy conjecture
- Whitehead conjecture
