List of conjectures
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This is a list of mathematical conjectures.
Conjectures now proved (theorems)
The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names.
|Priority date||Proved by||Former name||Field||Comments|
|1962||Walter Feit, John Thompson||Burnside conjecture that, apart from cyclic groups, finite simple groups have even order||finite simple groups||Feit–Thompson theorem⇔trivially the "odd order theorem" that finite groups of odd order are solvable groups|
|1971||Daniel Quillen||Adams conjecture||algebraic topology||On the J-homomorphism, proposed 1963 by Frank Adams|
|1973||Pierre Deligne||Weil conjectures||algebraic geometry||⇒Ramanujan–Petersson conjecture|
Proposed by André Weil. Deligne's theorems completed around 15 years of work on the general case.
|1975||Henryk Hecht and Wilfried Schmid||Blattner's conjecture||representation theory for semisimple groups|
|1976||Kenneth Appel and Wolfgang Haken||Four color theorem||graph colouring||Traditionally called a "theorem", long before the proof.|
|1977||Alberto Calderón||Denjoy's conjecture||rectifiable curves||A result claimed in 1909 by Arnaud Denjoy, proved by Calderón as a by-product of work on Cauchy singular operators|
|1983||Gerd Faltings||Mordell conjecture||number theory||⇐Faltings's theorem, the Shafarevich conjecture on finiteness of isomorphism classes of abelian varieties. The reduction step was by Alexey Parshin.|
|1983||Michel Raynaud||Manin–Mumford conjecture||diophantine geometry|
|c.1984||Collective work||Smith conjecture||knot theory||Based on work of William Thurston on hyperbolic structures on 3-manifolds, with results by William Meeks and Shing-Tung Yau on minimal surfaces in 3-manifolds, also with Hyman Bass, Cameron Gordon, Peter Shalen, and Rick Litherland, written up by Bass and John Morgan.|
|1984||Louis de Branges||Bieberbach conjecture, 1916||complex analysis||⇐Robertson conjecture⇐Milin conjecture⇐de Branges's theorem|
|1984||Gunnar Carlsson||Segal's conjecture||homotopy theory|
|1987||Grigory Margulis||Oppenheim conjecture||diophantine approximation||Margulis proved the conjecture with ergodic theory methods.|
|1989||V. I. Chernousov||Weil's conjecture on Tamagawa numbers||algebraic groups||The problem, based on Siegel's theory for quadratic forms, submitted to a long series of case analysis steps.|
|1990||Ken Ribet||epsilon conjecture||modular forms|
|1992||Richard Borcherds||Conway–Norton conjecture||sporadic groups||Usually called monstrous moonshine|
|1994||David Harbater and Michel Raynaud||Abhyankar's conjecture||algebraic geometry|
|1994||Andrew Wiles||Fermat's Last Theorem||number theory||⇔The modularity theorem for semistable elliptic curves.|
Proof completed with Richard Taylor.
|1994||Fred Galvin||Dinitz conjecture||combinatorics|
|1995||Doron Zeilberger||Alternating sign matrix conjecture,||enumerative combinatorics|
|1998||Thomas Callister Hales||Kepler conjecture||sphere packing|
|1998||Thomas Callister Hales and Sean McLaughlin||dodecahedral conjecture||Voronoi decompositions|
|2001||Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor||Taniyama–Shimura conjecture||elliptic curves||Now the modularity theorem for elliptic curves. Once known as the "Weil conjecture".|
|2002||Preda Mihăilescu||Catalan's conjecture, 1844||exponential diophantine equations||⇐Pillai's conjecture⇐abc conjecture|
|2002||Grigori Perelman||Poincaré conjecture, 1904||3-manifolds|
|2003||Grigori Perelman||geometrization conjecture of Thurston||3-manifolds||⇒spherical space form conjecture|
|2003||Ben Green; and independently by Alexander Sapozhenko||Cameron–Erdős conjecture||sum-free sets|
|2009||Jeremy Kahn, Vladimir Markovic||surface subgroup conjecture||3-manifolds||⇒Ehrenpreis conjecture on quasiconformality|
|2010||Terence Tao and Van H. Vu||circular law||random matrix theory|
|2012||Simon Brendle||Hsiang–Lawson's conjecture||differential geometry|
|2013||Zhang Yitang||bounded gap conjecture||number theory||The sequence of gaps between consecutive prime numbers has a finite lim inf. See Polymath Project#Polymath8 for quantitative results.|
|2013||Adam Marcus, Daniel Spielman and Nikhil Srivastava||Kadison–Singer problem||functional analysis||The original problem posed by Kadison and Singer was not a conjecture: its authors believed it false. As reformulated, it became the "paving conjecture" for Euclidean spaces, and then a question on random polynomials, in which latter form it was solved affirmatively.|
- Deligne's conjecture on 1-motives
- Erdős–Burr conjecture
- Frobenius conjecture (Iiyori and Yamaki)
- Goldbach's weak conjecture (proved in 2013)
- Gradient conjecture (Kurdyka–Mostowski–Parusinski theorem)
- Guralnick–Thompson conjecture on Riemann surfaces, proved 2001.
- Hanna Neumann conjecture (proved in 2011)
- Heawood conjecture (Ringel–Youngs theorem)
- Kummer's conjecture on cubic Gauss sums (Kummer sum)
- Main conjecture in Vinogradov's mean-value theorem (Bourgain–Demeter–Guth theorem)
- Milnor conjecture (Voevodsky's theorem)
- Mumford conjecture (Haboush's theorem)
- n! conjecture (proved in 2001)
- Nagata's conjecture on automorphisms
- Nirenberg–Treves conjecture
- Quillen–Lichtenbaum conjecture
- Road coloring conjecture, 1970 (2008)
- Scheinerman's conjecture (proved 2009)
- Serre's conjecture (Quillen–Suslin theorem)
- Serre's modularity conjecture (proved 2008)
- Seymour's conjecture
- 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)
- Wagner's conjecture (Robertson–Seymour theorem)
- 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)
- Doomsday conjecture
- Euler's sum of powers conjecture
- Ganea conjecture
- Generalized Smith conjecture
- Hirsch conjecture (disproved in 2010)
- Intersection graph conjecture
- Kelvin's conjecture
- Kouchnirenko's conjecture
- Mertens conjecture
- Pólya conjecture, 1919 (1958)
- Ragsdale conjecture
- Schoenflies conjecture (disproved 1910)
- Tait's conjecture
- Von Neumann conjecture
- Weyl–Berry conjecture
- Erdős conjectures
- Millennium Prize Problems
- List of unsolved problems in mathematics
- List of disproved mathematical ideas
- List of unsolved problems
- List of lemmas
- List of theorems
- List of statements undecidable in ZFC
- Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 13. ISBN 9781420035223.
- Frei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (2014). Emil Artin and Helmut Hasse: The Correspondence 1923-1958. Springer Science & Business Media. p. 215. ISBN 9783034807159.
- Steuding, Jörn; Morel, J.-M.; Steuding, Jr̲n (2007). Value-Distribution of L-Functions. Springer Science & Business Media. p. 118. ISBN 9783540265269.
- Valette, Alain (2002). Introduction to the Baum-Connes Conjecture. Springer Science & Business Media. p. viii. ISBN 9783764367060.
- Tao, Terence (15 October 2012). "The Chowla conjecture and the Sarnak conjecture". What's new.
- Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 1203. ISBN 9781420035223.
- M. Peczarski, The gold partition conjecture, it Order 23(2006): 89–95.
- Burger, Marc; Iozzi, Alessandra (2013). Rigidity in Dynamics and Geometry: Contributions from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences Cambridge, United Kingdom, 5 January – 7 July 2000. Springer Science & Business Media. p. 408. ISBN 9783662047439.
- "EMS Prizes". www.math.kth.se.
- "Archived copy" (PDF). Archived from the original (PDF) on 2011-07-24. Retrieved 2008-12-12.CS1 maint: Archived copy as title (link)
- In the terms normally used for scientific priority, priority claims are typically understood to be settled by publication date. That approach is certainly flawed in contemporary mathematics, because lead times for publication in mathematical journals can run to several years. The understanding in intellectual property is that the priority claim is established by a filing date. Practice in mathematics adheres more closely to that idea, with an early manuscript submission to a journal, or circulation of a preprint, establishing a "filing date" that would be generally accepted.
- Dudziak, James (2011). Vitushkin’s Conjecture for Removable Sets. Springer Science & Business Media. p. 39. ISBN 9781441967091.
- Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 218. ISBN 9781420035223.
- Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 65. ISBN 9781420035223.
- Holden, Helge; Piene, Ragni (2018). The Abel Prize 2013-2017. Springer. p. 51. ISBN 9783319990286.
- Daniel Frohardt and Kay Magaard, Composition Factors of Monodromy Groups, Annals of Mathematics Second Series, Vol. 154, No. 2 (Sep., 2001), pp. 327–345. Published by: Mathematics Department, Princeton University DOI: 10.2307/3062099 JSTOR 3062099
- Hazewinkel, Michiel, ed. (2001) , "Schoenflies conjecture", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4