List of conjectures.html



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)
• quantum unique ergodicity conjecture, (2008)
• 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

• Open Problem Garden