Editing List of conjectures (section)

==Conjectures now proved (theorems)==
{{further|List of unsolved problems in mathematics#Problems solved since 1995}}
The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names.
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!Priority date<ref>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.</ref>
!Proved by
!Former name
!Field
!Comments
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|1962||[[Walter Feit]] and [[John G. Thompson]]||Burnside conjecture that, apart from [[cyclic group]]s, 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 group]]s
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|1968||[[Gerhard Ringel]] and [[John William Theodore Youngs]]||[[Heawood conjecture]]||graph theory||Ringel-Youngs theorem
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|1971||[[Daniel Quillen]]||[[Adams conjecture]]||algebraic topology||On the J-homomorphism, proposed 1963 by [[Frank Adams]]
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|1973||[[Pierre Deligne]]||[[Weil conjectures]]||algebraic geometry||⇒[[Ramanujan–Petersson conjecture]]<br>Proposed by [[André Weil]]. Deligne's theorems completed around 15 years of work on the general case.
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|1975||Henryk Hecht and [[Wilfried Schmid]]||[[Blattner's conjecture]]||representation theory for semisimple groups||
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|1975||[[William Haboush]]||Mumford conjecture||geometric invariant theory||[[Haboush's theorem]]
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|1976||[[Kenneth Appel]] and [[Wolfgang Haken]]||[[Four color theorem]]||graph colouring||Traditionally called a "theorem", long before the proof.
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|1976||[[Daniel Quillen]]; and independently by [[Andrei Suslin]]||Serre's conjecture on projective modules||polynomial rings||[[Quillen–Suslin theorem]]
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|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 operator]]s<ref>{{cite book |last1=Dudziak |first1=James |title=Vitushkin's Conjecture for Removable Sets |date=2011 |publisher=Springer Science & Business Media |isbn=9781441967091 |page=39 |url=https://books.google.com/books?id=89A3gdCfPFUC&pg=PA39 |language=en}}</ref>
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|1978||[[Roger Heath-Brown]] and [[Samuel James Patterson]]||[[Kummer's conjecture on cubic Gauss sums]]||equidistribution|| 
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|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]].
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|1983 onwards||[[Neil Robertson (mathematician)|Neil Robertson]] and [[Paul Seymour (mathematician)|Paul D. Seymour]]||[[Wagner's conjecture]]||graph theory||Now generally known as the [[graph minor theorem]].
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|1983||[[Michel Raynaud]]||[[Manin–Mumford conjecture]]||diophantine geometry||The [[Tate–Voloch conjecture]] is a quantitative (diophantine approximation) derived conjecture for p-adic varieties.
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|c.1984||Collective work||[[Smith conjecture]]||knot theory||Based on work of [[William Thurston]] on [[hyperbolic 3-manifold|hyperbolic structures]] on 3-manifolds, with results by [[William Hamilton Meeks, III|William Meeks]] and [[Shing-Tung Yau]] on [[minimal surface]]s in 3-manifolds, also with [[Hyman Bass]], [[Cameron Gordon (mathematician)|Cameron Gordon]], [[Peter Shalen]], and Rick Litherland, written up by Bass and [[John Morgan (mathematician)|John Morgan]].
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|1984||[[Louis de Branges de Bourcia]]||[[Bieberbach conjecture]], 1916||complex analysis||⇐[[Robertson conjecture]]⇐[[Milin conjecture]]⇐[[de Branges's theorem]]<ref>{{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2002 |publisher=CRC Press |isbn=9781420035223 |page=218 |url=https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA218 |language=en}}</ref>
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|1984||[[Gunnar Carlsson]]||[[Segal's conjecture]]||homotopy theory||
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|1984||[[Haynes Miller]]||[[Sullivan conjecture]]||classifying spaces||Miller proved the version on mapping BG to a finite complex.
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|1987||[[Grigory Margulis]]||[[Oppenheim conjecture]]||diophantine approximation||Margulis proved the conjecture with [[ergodic theory]] methods.
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|1989||Vladimir 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.
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|1990||[[Ken Ribet]]||[[epsilon conjecture]]||modular forms||
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|1992||[[Richard Borcherds]]||[[Conway–Norton conjecture]]||sporadic groups||Usually called [[monstrous moonshine]]
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|1994||[[David Harbater]] and [[Michel Raynaud]]||[[Abhyankar's conjecture]]||algebraic geometry||
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|1994||[[Andrew Wiles]]||[[Fermat's Last Theorem]]||number theory||⇔The [[modularity theorem]] for semistable elliptic curves.<br>Proof completed with [[Richard Taylor (mathematician)|Richard Taylor]].
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|1994||[[Fred Galvin]]||[[Dinitz conjecture]]||combinatorics||
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|1995||[[Doron Zeilberger]]<ref>{{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2002 |publisher=CRC Press |isbn=9781420035223 |page=65 |url=https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA65 |language=en}}</ref>||[[Alternating sign matrix conjecture]],||enumerative combinatorics||
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|1996||[[Vladimir Voevodsky]]||[[Milnor conjecture (K-theory)|Milnor conjecture]]||algebraic K-theory||Voevodsky's theorem, ⇐[[norm residue isomorphism theorem]]⇔[[Beilinson–Lichtenbaum conjecture]], [[Quillen–Lichtenbaum conjecture]].<br> The ambiguous term "Bloch-Kato conjecture" may refer to what is now the norm residue isomorphism theorem.
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|1998||[[Thomas Callister Hales]]||[[Kepler conjecture]]||sphere packing||
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|1998||[[Thomas Callister Hales]] and Sean McLaughlin||[[dodecahedral conjecture]]||Voronoi decompositions||
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|2000||Krzysztof Kurdyka, Tadeusz Mostowski, and Adam Parusiński ||[[Gradient conjecture]]||gradient vector fields||Attributed to [[René Thom]], c.1970.
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|2001||[[Christophe Breuil]], [[Brian Conrad]], [[Fred Diamond]] and [[Richard Taylor (mathematician)|Richard Taylor]]||[[Taniyama–Shimura conjecture]]||elliptic curves||Now the [[modularity theorem]] for elliptic curves. Once known as the "Weil conjecture".
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|2001||[[Mark Haiman]]||[[n! conjecture]]||representation theory||
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|2001||Daniel Frohardt and Kay Magaard<ref>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}}</ref>||[[Guralnick–Thompson conjecture]]||monodromy groups||
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|2002||[[Preda Mihăilescu]]||[[Catalan's conjecture]], 1844||exponential diophantine equations||⇐[[Pillai's conjecture]]⇐[[abc conjecture]]<br>Mihăilescu's theorem
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|2002||[[Maria Chudnovsky]], [[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul D. Seymour]], and [[Robin Thomas (mathematician)|Robin Thomas]]||[[strong perfect graph conjecture]]||[[perfect graph]]s||Chudnovsky–Robertson–Seymour–Thomas theorem
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|2002||[[Grigori Perelman]]||[[Poincaré conjecture]], 1904||3-manifolds||
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|2003||[[Grigori Perelman]]||[[geometrization conjecture]] of Thurston||3-manifolds||⇒[[spherical space form conjecture]]
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|2003||[[Ben Green (mathematician)|Ben Green]]; and independently by Alexander Sapozhenko||[[Cameron–Erdős conjecture]]||sum-free sets||
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|2003||[[Nils Dencker]]||[[Nirenberg–Treves conjecture]]||pseudo-differential operators||
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|2004 (see comment)||Nobuo Iiyori and Hiroshi Yamaki||[[Frobenius conjecture]]||group theory||A consequence of the [[classification of finite simple groups]], completed in 2004 by the usual standards of pure mathematics.
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|2004||[[Adam Marcus (mathematician)|Adam Marcus]] and [[Gábor Tardos]]||[[Stanley–Wilf conjecture]]||[[permutation class]]es|||Marcus–Tardos theorem
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|2004||Ualbai U. Umirbaev and Ivan P. Shestakov||[[Nagata's conjecture on automorphisms]]||polynomial rings||
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|2004||[[Ian Agol]]; and independently by [[Danny Calegari]]–[[David Gabai]]||tameness conjecture||geometric topology||⇒[[Ahlfors measure conjecture]]
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|2008||[[Avraham Trahtman]]||[[Road coloring conjecture]]||graph theory||
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|2008||[[Chandrashekhar Khare]] and [[Jean-Pierre Wintenberger]]||[[Serre's modularity conjecture]]||modular forms||
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|2009||[[Jeremy Kahn]] and [[Vladimir Markovic]]||[[surface subgroup conjecture]]||3-manifolds||⇒[[Ehrenpreis conjecture]] on quasiconformality
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|2009||Jeremie Chalopin and Daniel Gonçalves||[[Scheinerman's conjecture]]||intersection graphs||
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|2010||[[Terence Tao]] and [[Van H. Vu]]||[[circular law]]||random matrix theory||
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|2011||Joel Friedman; and independently by Igor Mineyev||[[Hanna Neumann conjecture]]||group theory||
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|2012||[[Simon Brendle]]||[[Hsiang–Lawson's conjecture]]||differential geometry||
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|2012||[[Fernando Codá Marques]] and [[André Neves]]||[[Willmore conjecture]]||differential geometry||
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|2013||[[Yitang Zhang]]||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.
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|2013||[[Adam Marcus (mathematician)|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.
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|2015||[[Jean Bourgain]], Ciprian Demeter, and [[Larry Guth]]||[[Vinogradov's mean-value theorem#The conjectured form|Main conjecture in Vinogradov's mean-value theorem]]||analytic number theory||Bourgain–Demeter–Guth theorem, ⇐ decoupling theorem<ref>{{cite web |title=Decoupling and the Bourgain-Demeter-Guth proof of the Vinogradov main conjecture |url=https://terrytao.wordpress.com/2015/12/10/decoupling-and-the-bourgain-demeter-guth-proof-of-the-vinogradov-main-conjecture/ |website=What's new |language=en |date=10 December 2015}}</ref>
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|2018||[[Karim Adiprasito]]||[[g-conjecture]]||combinatorics||
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|2019||[[Dimitris Koukoulopoulos]] and [[James Maynard (mathematician)|James Maynard]]||[[Duffin–Schaeffer conjecture]]||number theory||Rational approximation of irrational numbers
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* [[Deligne's conjecture on 1-motives]]<ref>{{cite book |last1=Holden |first1=Helge |last2=Piene |first2=Ragni |title=The Abel Prize 2013-2017 |date=2018 |publisher=Springer |isbn=9783319990286 |page=51 |url=https://books.google.com/books?id=1NKJDwAAQBAJ&pg=PA51 |language=en}}</ref>
* [[Goldbach's weak conjecture]] (proved in 2013)
* [[Sensitivity conjecture]] (proved in 2019)