Conjectures and Refutations

Conjecture, Kaplansky's conjectures, List of conjectures, Ravenel's conjectures, Stark conjectures, Greenberg's conjectures, Pollock's conjectures, Tate conjecture, Tait conjectures, Arthur's conjectures, Mersenne conjectures, Standard conjectures on algebraic cycles, Hardy–Littlewood zeta function conjectures, Serre's multiplicity conjectures, Vojta's conjecture, Sendov's conjecture, Homological conjectures in commutative algebra, Thurston elliptization conjecture, Goldbach's conjecture, Macdonald conjecture, André–Oort conjecture, Ramanujan–Petersson conjecture, Hirsch conjecture, Dyson conjecture, Kalai's 3^d conjecture, Four exponentials conjecture, Szpiro's conjecture, List of conjectures by Paul Erdős, Local Langlands conjectures, Abc conjecture, Erdős–Gyárfás conjecture, Markus–Yamabe conjecture, Arnold conjecture, Hodge conjecture, Poincaré conjecture, Kummer–Vandiver conjecture, SYZ conjecture, Gan–Gross–Prasad conjecture, Serre's conjecture, Geometrization conjecture, Schanuel's conjecture

Firoozbakht's conjecture, Hedetniemi's conjecture, Dickson's conjecture, Serre's modularity conjecture, Zilber–Pink conjecture, Mertens conjecture, Artin conjecture, Fermat–Catalan conjecture, Special values of L-functions, Quillen–Lichtenbaum conjecture, Farrell–Jones conjecture, Morita conjectures, Main conjecture of Iwasawa theory, Beal conjecture, Sullivan conjecture, Euler's conjecture, N! conjecture, Pólya conjecture, Bunyakovsky conjecture, NLTS conjecture, Eilenberg–Ganea conjecture, Andrica's conjecture, Weil conjectures, Birch and Swinnerton-Dyer conjecture, Second Hardy–Littlewood conjecture, Langlands program, Erdős–Faber–Lovász conjecture, Brumer–Stark conjecture, Reconstruction conjecture, Burr–Erdős conjecture, Kummer's conjecture, Fontaine–Mazur conjecture, Polignac's conjecture, Toida's conjecture, Bateman–Horn conjecture, Mumford conjecture, Catalan's conjecture, Sato–Tate conjecture, Goldbach's weak conjecture, Keller's conjecture, Nakai conjecture, Carathéodory conjecture, Ross's conjecture, Lander, Parkin, and Selfridge conjecture, Hadwiger conjecture, Ibragimov–Iosifescu conjecture for φ-mixing sequences, Zimmer's conjecture, Agrawal's conjecture, Montgomery's pair correlation conjecture, Weil conjecture

Conjecture, Kaplansky's conjectures, List of conjectures, Ravenel's conjectures, Stark conjectures, Greenberg's conjectures, Pollock's conjectures, Tate conjecture, Tait conjectures, Arthur's conjectures, Mersenne conjectures, Standard conjectures on algebraic cycles, Hardy–Littlewood zeta function conjectures, Serre's multiplicity conjectures, Vojta's conjecture, Sendov's conjecture, Homological conjectures in commutative algebra, Thurston elliptization conjecture, Goldbach's conjecture, Macdonald conjecture, André–Oort conjecture, Ramanujan–Petersson conjecture, Hirsch conjecture, Dyson conjecture, Kalai's 3^d conjecture, Four exponentials conjecture, Szpiro's conjecture, List of conjectures by Paul Erdős, Local Langlands conjectures, Abc conjecture, Erdős–Gyárfás conjecture, Markus–Yamabe conjecture, Arnold conjecture, Hodge conjecture, Poincaré conjecture, Kummer–Vandiver conjecture, SYZ conjecture, Gan–Gross–Prasad conjecture, Serre's conjecture, Geometrization conjecture, Schanuel's conjecture, Firoozbakht's conjecture, Hedetniemi's conjecture, Dickson's conjecture, Serre's modularity conjecture, Zilber–Pink conjecture, Mertens conjecture, Artin conjecture, Fermat–Catalan conjecture, Special values of L-functions, Quillen–Lichtenbaum conjecture, Farrell–Jones conjecture, Morita conjectures, Main conjecture of Iwasawa theory, Beal conjecture, Sullivan conjecture, Euler's conjecture, N! conjecture, Pólya conjecture, Bunyakovsky conjecture, NLTS conjecture, Eilenberg–Ganea conjecture, Andrica's conjecture, Weil conjectures, Birch and Swinnerton-Dyer conjecture, Second Hardy–Littlewood conjecture, Langlands program, Erdős–Faber–Lovász conjecture, Brumer–Stark conjecture, Reconstruction conjecture, Burr–Erdős conjecture, Kummer's conjecture, Fontaine–Mazur conjecture, Polignac's conjecture, Toida's conjecture, Bateman–Horn conjecture, Mumford conjecture, Catalan's conjecture, Sato–Tate conjecture, Goldbach's weak conjecture, Keller's conjecture, Nakai conjecture, Carathéodory conjecture, Ross's conjecture, Lander, Parkin, and Selfridge conjecture, Hadwiger conjecture, Ibragimov–Iosifescu conjecture for φ-mixing sequences, Zimmer's conjecture, Agrawal's conjecture, Montgomery's pair correlation conjecture, Weil conjecture, Cramér's conjecture, Brocard's conjecture, Willmore conjecture, Erdős–Straus conjecture, Hall's conjecture, Bing–Borsuk conjecture, Grimm's conjecture, Lovász conjecture, Feit–Thompson conjecture, Generalized Poincaré conjecture, Thomas–Yau conjecture, Vaught conjecture, First Hardy–Littlewood conjecture, Baum–Connes conjecture, Lemoine's conjecture, Gray's conjecture, Legendre's conjecture, Hilbert–Pólya conjecture, Fröberg conjecture, Torsion conjecture, Borel conjecture, Nakayama's conjecture, Agoh–Giuga conjecture, Selberg's 1/4 conjecture, Köthe conjecture, Erdős–Hajnal conjecture, Birch–Tate conjecture, Kepler conjecture, Carmichael's totient function conjecture, Scholz conjecture, Nagata's conjecture, Euler's sum of powers conjecture, Hsiang–Lawson's conjecture, Kalman's conjecture, Gilbreath's conjecture, Norm residue isomorphism theorem, Uniform boundedness conjecture for rational points, Aanderaa–Karp–Rosenberg conjecture, Read's conjecture, Vizing's conjecture, Alternating knot, Pierce–Birkhoff conjecture, Ehrenpreis conjecture, Schoen–Yau conjecture, Dittert conjecture, Cameron–Erdős conjecture, Dwork conjecture, Nagata's conjecture on curves, Egan conjecture, Monomial conjecture, Collatz conjecture, Kahn–Kalai conjecture, Union-closed sets conjecture, Weil's conjecture on Tamagawa numbers, Gilbert–Pollak conjecture, Spherical space form conjecture, Segal's conjecture, Coclass, Littlewood conjecture, Oppenheim conjecture