List of conjectures
This is a list of mathematical conjectures.
Open problems
- 1/3–2/3 conjecture
- abc conjecture (proof claimed by Shinichi Mochizuki)
- Andrews–Curtis conjecture
- Agoh–Giuga conjecture
- Andrica's conjecture
- Artin conjectures
- 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
- Bloch–Kato conjecture
- Bombieri-Lang conjecture
- Borel conjecture
- Bost conjecture
- Brocard's conjecture
- Brumer–Stark conjecture
- Bunyakovsky conjecture
- Catalan–Dickson conjecture on aliquot sequences
- Carathéodory conjecture
- Carmichael totient conjecture
- Casas-Alvero conjecture
- Catalan's Mersenne conjecture
- Cherlin–Zilber conjecture
- Collatz conjecture
- Cramér's conjecture
- Conway's thrackle conjecture
- Deligne conjecture disambiguation
- Eilenberg−Ganea conjecture
- Elliott–Halberstam conjecture
- Erdős–Burr conjecture
- Erdős–Faber–Lovász conjecture
- Erdős–Gyárfás conjecture
- Erdős–Straus conjecture
- Farrell–Jones conjecture
- Filling area conjecture
- Fortune's conjecture
- Frankl conjecture
- Gauss circle problem
- Gilbreath conjecture
- Giuga's conjecture
- Goldbach's conjecture
- Goldbach's weak conjecture (proof claimed by Harald Helfgott)
- Gold partition conjecture[1]
- Goormaghtigh conjecture
- Green's conjecture
- Grimm's conjecture
- Grothendieck–Katz p-curvature conjecture
- Guralnick–Thompson conjecture (Riemann surfaces)
- Hadamard conjecture
- Hedetniemi's conjecture
- Herzog–Schönheim conjecture
- Hilbert–Smith conjecture
- Hopf conjecture
- Hodge conjecture
- Homological conjectures in commutative algebra
- Invariant subspace problem
- Jacobian conjecture
- Jacobson's conjecture
- Kakeya conjectures
- Kakeya needle problem
- Kaplansky conjecture
- Keating–Snaith conjecture
- Köthe conjecture
- Lawson's conjecture
- Lemoine's conjecture
- Lenstra–Pomerance–Wagstaff conjecture
- Leopoldt's conjecture
- Lichtenbaum conjecture
- List coloring conjecture
- Littlewood conjecture
- Lovász conjecture
- MNOP conjecture
- Manin conjecture
- Marshall Hall's conjecture
- Mazur's conjectures
- Deligne conjecture in monodromy
- Montgomery's pair correlation conjecture
- Nagata's conjecture on automorphisms
- New Mersenne conjecture
- Nirenberg–Treves conjecture
- Novikov conjecture
- Oppermann's conjecture
- Petersen coloring conjecture
- Pierce–Birkhoff conjecture
- Pillai's conjecture
- De Polignac's conjecture
- quantum unique ergodicity conjecture, (2004, Elon Lindenstrauss, for arithmetic hyperbolic surfaces,[2] 2008, Kannan Soundararajan & Roman Holowinsky, for holomorphic forms of increasing weight for Hecke eigenforms on noncompact arithmetic surfaces [3])
- Quillen–Lichtenbaum conjecture
- Reconstruction conjecture
- Riemann Hypotheses: see also Weil conjectures under Theorems
- Riemann hypothesis
- Density hypothesis
- Lindelöf hypothesis
- Hilbert–Pólya conjecture on the Riemann hypothesis
- Ringel-Kotzig conjecture
- Sato–Tate conjecture
- Schanuel's conjecture
- Schinzel's hypothesis H
- Scholz conjecture
- Second Hardy–Littlewood conjecture
- Selfridge's conjecture
- Sendov's conjecture
- Serre's multiplicity conjectures
- Singmaster's conjecture
- Standard conjectures on algebraic cycles
- Tate conjecture
- Toeplitz' conjecture
- Twin prime conjecture
- Ulam's packing conjecture
- Unicity conjecture for Markov numbers
- Uniformity conjecture
- Vandiver's conjecture
- Vizing's conjecture
- Waring's conjecture
- Weight-monodromy conjecture
- Weinstein conjecture
- Whitehead conjecture
- Zauner's conjecture
- Zhou conjecture
Proved (now theorems)
The theorems may not be their official names.
- Adams conjecture (J-homomorphism)
- Andrews–Curtis conjecture
- Angel problem (several proofs, 2007)
- Bieberbach conjecture, 1916 (De Branges' theorem, 1984)
- Blattner's conjecture (Blattner formula)
- Bounded gap conjecture (Zhang Yitang, 2013)
- Burnside conjecture (Feit–Thompson theorem)
- Cameron–Erdős conjecture
- Catalan's conjecture, 1844 (Mihăilescu's theorem, 2002)
- Circular law (proved in 2010)
- Conway–Norton conjecture (monstrous moonshine)
- Dinitz conjecture (Galvin's theorem)
- Deligne's conjecture on 1-motives
- Denjoy's conjecture
- Dodecahedral conjecture (Hales–McLaughlin theorem)
- Ehrenpreis conjecture (proved in 2011)
- Epsilon conjecture (Ribet's theorem)
- Fermat's Last Theorem (Andrew Wiles' proof in 1994)
- Four color theorem (Appel and Haken, 1976)
- Frobenius conjecture (Iiyori and Yamaki)
- Gradient conjecture (Kurdyka–Mostowski–Parusinski theorem)
- Hanna Neumann conjecture (proved in 2011)
- Heawood conjecture (Ringel–Youngs' theorem)
- Kepler conjecture (proved in 1998)
- 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)
- n! conjecture (proved in 2001)
- Poincaré conjecture, 1904 (theorem about the characterization of the three-dimensional sphere)
- Oppenheim conjecture (Margulis' theorem)
- Ramanujan–Petersson conjecture (consequence of the proof of the Weil conjectures)
- Road coloring conjecture, 1970 (2008)
- Scheinerman's conjecture (proved 2009)
- Segal's Burnside ring conjecture (Carlsson theorem)
- Serre's conjecture (Quillen–Suslin theorem)
- Serre's modularity conjecture (proved 2008)
- 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
- Surface subgroup conjecture (proved in 2009)
- Tameness conjecture (Agol or Calegari–Gabai theorem)
- Taniyama–Shimura conjecture (Modularity theorem)
- Thurston's geometrization conjecture (3-manifolds of the uniformization theorem for surfaces)
- Wagner's conjecture (Robertson–Seymour theorem)
- Weil conjectures (Deligne's theorems)
- Willmore conjecture (proved in 2012)
Disproved (no longer conjectures)
- Atiyah conjecture (not a conjecture to start with)
- Borsuk's conjecture
- Chinese hypothesis (not a conjecture to start with)
- Euler's sum of powers conjecture
- Ganea conjecture
- Generalized Smith conjecture
- Hauptvermutung
- Hirsch conjecture (disproved in 2010)
- Intersection graph conjecture
- Kouchnirenko's conjecture
- Mertens conjecture
- Pólya conjecture, 1919 (1958)
- Ragsdale conjecture
- Tait's conjecture
- Von Neumann conjecture
- Weyl–Berry conjecture
See also
- Erdős conjectures
- Millennium Prize Problems
- Unsolved problems in mathematics
- List of unsolved problems
- List of lemmas
- List of theorems
- List of statements undecidable in ZFC