This is a list of conjectures, by Wikipedia page. They are divided into four sections, according to their status in 2004.

See also:

• Erdös conjecture, which lists conjectures of Paul Erdös 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)

• Adams conjecture
• Bieberbach conjecture
• Blattner's conjecture
• Conway-Norton conjecture
• Dinitz conjecture
• Epsilon conjecture
• Fermat's Last Theorem
• Gradient conjecture
• Kummer's conjecture on cubic Gauss sums
• Mahler-Manin conjecture
• Manin-Mumford conjecture
• Mordell conjecture
• Mumford conjecture
• Oppenheim conjecture
• Ramanujan conjecture on the cusp form Δ
• Segal's Burnside ring conjecture
• Serre's conjecture
• Smith conjecture
• Star height problem
• Sullivan conjecture
• Taniyama-Shimura conjecture
• Weil conjectures

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

Recent work

• Bloch-Kato conjecture
• Catalan's conjecture
• Hilbert-Smith conjecture
• Kepler conjecture
• Nagata conjecture
• Poincaré conjecture
• Strong perfect graph conjecture
• Thurston's conjecture

Open problems

• abc conjecture
• Andrews-Curtis conjecture
• Agoh-Giuga conjecture
• Artin conjecture
• 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
• Erdös-Gyárfás conjecture
• Farrell-Jones 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
• Milnor conjecture on quadratic forms
• Monodromy conjecture
• New Mersenne conjecture
• Novikov conjecture
• Petersen coloring conjecture
• Pierce-Birkhoff conjecture
• Pillai'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
• Serre's multiplicity conjectures
• Tate conjecture
• Twin prime conjecture
• Vandiver's conjecture
• Weight-monodromy conjecture