Editing List of conjectures (section)

==Open problems==
The following conjectures remain open.  The (incomplete) column "cites" lists the number of results for a [[Google Scholar]] search for the term, in double quotes {{as of|lc=y|September 2022}}.
{| class="wikitable sortable" style="text-align:center; border:none;"
|-
!Conjecture
!Field
!Comments
!Eponym(s)
!Cites
|-
|[[1/3–2/3 conjecture]]||order theory|| ||n/a || 70
|-
|[[abc conjecture]]||number theory||⇔Granville–Langevin conjecture,  [[Vojta's conjecture]] in dimension 1<br>⇒[[Erdős–Woods conjecture]], [[Fermat–Catalan conjecture]]<br>Formulated by [[David Masser]] and [[Joseph Oesterlé]].<ref>{{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2002 |publisher=CRC Press |isbn=9781420035223 |page=13 |url=https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA13 |language=en}}</ref><br>Proof claimed in 2012 by [[Shinichi Mochizuki]]||n/a || 2440
|-
|[[Agoh–Giuga conjecture]]||number theory|| ||Takashi Agoh and Giuseppe Giuga ||8
|-
|[[Agrawal's conjecture]]||number theory|| ||[[Manindra Agrawal]] || 10
|-
|[[Andrews–Curtis conjecture]]||combinatorial group theory|| ||[[James J. Andrews (mathematician)|James J. Andrews]] and [[Morton L. Curtis]] || 358
|-
|[[Andrica's conjecture]]||number theory|| || Dorin Andrica || 45
|-
|[[Artin conjecture (L-functions)]]||number theory|| || [[Emil Artin]] || 650
|-
|[[Artin's conjecture on primitive roots]]||number theory||⇐[[generalized Riemann hypothesis]]<ref>{{cite book |last1=Frei |first1=Günther |last2=Lemmermeyer |first2=Franz |last3=Roquette |first3=Peter J. |title=Emil Artin and Helmut Hasse: The Correspondence 1923-1958 |date=2014 |publisher=Springer Science & Business Media |isbn=9783034807159 |page=215 |url=https://books.google.com/books?id=6rDBBAAAQBAJ&pg=PA215 |language=en}}</ref><br>⇐[[Selberg conjecture B]]<ref>{{cite book |last1=Steuding |first1=Jörn |last2=Morel |first2=J.-M. |last3=Steuding |first3=Jr̲n |title=Value-Distribution of L-Functions |date=2007 |publisher=Springer Science & Business Media |isbn=9783540265269 |page=118 |url=https://books.google.com/books?id=gzUxpU-PXVoC&pg=PA118 |language=en}}</ref>|| [[Emil Artin]] || 325
|-
|[[Bateman–Horn conjecture]]||number theory|| ||[[Paul T. Bateman]] and [[Roger Horn]] || 245
|-
|[[Baum–Connes conjecture]]||operator K-theory||⇒[[Gromov-Lawson-Rosenberg conjecture]]<ref name="Valette">{{cite book |last1=Valette |first1=Alain |title=Introduction to the Baum-Connes Conjecture |date=2002 |publisher=Springer Science & Business Media |isbn=9783764367060 |page=viii |url=https://books.google.com/books?id=fRWjukxro3oC&pg=PR8 |language=en}}</ref><br>⇒[[Kaplansky-Kadison conjecture]]<ref name="Valette"/><br>⇒[[Novikov conjecture]]<ref name="Valette"/>||[[Paul Baum (mathematician)|Paul Baum]] and [[Alain Connes]] || 2670
|-
|[[Beal's conjecture]]||number theory|| ||[[Andrew Beal]] || 142
|-
|[[Beilinson conjecture]]||number theory|| ||[[Alexander Beilinson]] || 461
|-
|[[Quantum chaos#Berry–Tabor conjecture|Berry–Tabor conjecture]]||geodesic flow|| ||[[Michael Berry (physicist)|Michael Berry]] and Michael Tabor || 239
|-
|[[Big-line-big-clique conjecture]]||discrete geometry|| || ||
|-
|[[Birch and Swinnerton-Dyer conjecture]]||number theory|| ||[[Bryan John Birch]] and [[Peter Swinnerton-Dyer]] || 2830
|-
|[[Birch–Tate conjecture]]||number theory|| ||[[Bryan John Birch]] and [[John Tate (mathematician)|John Tate]] || 149
|-
|[[Birkhoff conjecture]]||integrable systems|| || [[George David Birkhoff]] || 345
|-
|[[Bloch–Beilinson conjectures]]||number theory|| ||[[Spencer Bloch]] and [[Alexander Beilinson]] || 152
|-
|[[Bloch–Kato conjecture]]||algebraic K-theory|| ||[[Spencer Bloch]] and [[Kazuya Kato]] || 1620
|-
|[[Bochner–Riesz conjecture]]||harmonic analysis|| ⇒restriction conjecture⇒[[Kakeya maximal function conjecture]]⇒[[Kakeya dimension conjecture]]<ref>{{cite book |last1=Simon |first1=Barry |title=Harmonic Analysis |date=2015 |publisher=American Mathematical Soc. |isbn=9781470411022 |page=685 |url=https://books.google.com/books?id=YkUACwAAQBAJ&pg=PA685 |language=en}}</ref>||[[Salomon Bochner]] and [[Marcel Riesz]] || 236
|-
|[[Bombieri–Lang conjecture]]||diophantine geometry|| ||[[Enrico Bombieri]] and [[Serge Lang]] || 181
|-
|[[Borel conjecture]]||geometric topology|| ||[[Armand Borel]] || 981
|-
|[[Farrell-Jones conjecture#Bost conjecture|Bost conjecture]]||geometric topology|| || [[Jean-Benoît Bost]] || 65
|-
|[[Brennan conjecture]]||complex analysis|| || James E. Brennan || 110
|-
|[[Brocard's conjecture]]||number theory|| || [[Henri Brocard]] || 16
|-
|[[Brumer–Stark conjecture]]||number theory|| || Armand Brumer and [[Harold Stark]] || 208
|-
|[[Bunyakovsky conjecture]]||number theory|| || [[Viktor Bunyakovsky]] || 43
|-
|[[Carathéodory conjecture]]||differential geometry|| || [[Constantin Carathéodory]] || 173
|-
|[[Carmichael totient conjecture]]||number theory|| || [[Robert Daniel Carmichael]] ||
|-
|[[Casas-Alvero conjecture]]||polynomials|| || Eduardo Casas-Alvero || 56
|-
|[[Aliquot sequence|Catalan–Dickson conjecture on aliquot sequences]]||number theory|| || [[Eugène Charles Catalan]] and [[Leonard Eugene Dickson]] || 46
|-
|[[Catalan's Mersenne conjecture]]||number theory|| || [[Eugène Charles Catalan]]|| 
|-
|[[Cherlin–Zilber conjecture]]||group theory|| || Gregory Cherlin and [[Boris Zilber]] || 86
|-
|[[Chowla conjecture]]||Möbius function||⇒[[Sarnak conjecture]]<ref>{{cite web |last1=Tao |first1=Terence |title=The Chowla conjecture and the Sarnak conjecture |url=https://terrytao.wordpress.com/2012/10/14/the-chowla-conjecture-and-the-sarnak-conjecture/ |website=What's new |language=en |date=15 October 2012}}</ref><ref>{{cite book |last1=Ferenczi |first1=Sébastien |last2=Kułaga-Przymus |first2=Joanna |last3=Lemańczyk |first3=Mariusz |title=Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016 |date=2018 |publisher=Springer |isbn=9783319749082 |page=185 |url=https://books.google.com/books?id=wSpgDwAAQBAJ&pg=PA185 |language=en}}</ref> ||[[Sarvadaman Chowla]] ||
|-
|[[Collatz conjecture]]||number theory|| ||[[Lothar Collatz]] || 1440
|-
|[[Cramér's conjecture]]||number theory|| ||[[Harald Cramér]] || 32
|-
|[[Conway's thrackle conjecture]]||graph theory|| ||[[John Horton Conway]] || 150
|-
|[[Deligne conjecture]]||monodromy|| ||[[Pierre Deligne]] || 788
|-
|[[Dittert conjecture]]||combinatorics|| || Eric Dittert || 11
|-
|[[Eilenberg−Ganea conjecture]]||algebraic topology|| || [[Samuel Eilenberg]] and [[Tudor Ganea]] || 96
|-
|[[Elliott–Halberstam conjecture]]||number theory|| ||[[Peter D. T. A. Elliott]] and [[Heini Halberstam]] || 300
|-
|[[Erdős–Faber–Lovász conjecture]]||graph theory|| || [[Paul Erdős]], [[Vance Faber]], and [[László Lovász]] || 172
|-
|[[Erdős–Gyárfás conjecture]]||graph theory|| || [[Paul Erdős]] and [[András Gyárfás]] || 37
|-
|[[Erdős–Straus conjecture]]||number theory|| || [[Paul Erdős]] and [[Ernst G. Straus]] || 103
|-
|[[Farrell–Jones conjecture]]||geometric topology|| || [[F. Thomas Farrell]] and [[Lowell E. Jones]] || 545
|-
|[[Filling area conjecture]]||differential geometry|| ||n/a || 60
|-
|[[Firoozbakht's conjecture]]||number theory|| || [[Farideh Firoozbakht]] || 33
|-
|[[Fortune's conjecture]]||number theory|| || [[Reo Fortune]] || 16
|-
|[[Four exponentials conjecture]]||number theory|| ||n/a || 110
|-
|[[Frankl conjecture]]||combinatorics|| || [[Péter Frankl]] || 83
|-
|[[Gauss circle problem]]||number theory|| || [[Carl Friedrich Gauss]] || 553
|-
|[[Gilbert–Pollack conjecture on the Steiner ratio of the Euclidean plane]]||metric geometry|| || [[Edgar Gilbert]] and [[Henry O. Pollak]] || 
|-
|[[Gilbreath conjecture]]||number theory|| || [[Norman Laurence Gilbreath]] || 34
|-
|[[Goldbach's conjecture]]||number theory||⇒The [[ternary Goldbach conjecture]], which was the original formulation.<ref>{{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2002 |publisher=CRC Press |isbn=9781420035223 |page=1203 |url=https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA1203 |language=en}}</ref> ||[[Christian Goldbach]] || 5880
|-
|[[1/3–2/3 conjecture#Generalizations and related results|Gold partition conjecture]]<ref>M. Peczarski, The gold partition conjecture, it Order 23(2006): 89–95.</ref>||order theory|| ||n/a || 25
|-
|[[Goldberg–Seymour conjecture]]||graph theory|| || Mark K. Goldberg and [[Paul Seymour (mathematician)|Paul Seymour]] || 57
|-
|[[Goormaghtigh conjecture]]||number theory|| || [[René Goormaghtigh]] || 14
|-
|[[Green's conjecture]]||algebraic curves|| || [[Mark Lee Green]] || 150
|-
|[[Grimm's conjecture]]||number theory|| || Carl Albert Grimm || 46
|-
|[[Grothendieck–Katz p-curvature conjecture]]||differential equations|| ||[[Alexander Grothendieck]] and [[Nick Katz]] || 98
|-
|[[Hadamard conjecture]]||combinatorics|| || [[Jacques Hadamard]] || 858
|-
|[[Herzog–Schönheim conjecture]]||group theory|| || Marcel Herzog and Jochanan Schönheim || 44
|-
|[[Hilbert–Smith conjecture]]||geometric topology|| || [[David Hilbert]] and [[Paul Althaus Smith]] || 219
|-
|[[Hodge conjecture]]||algebraic geometry|| || [[W. V. D. Hodge]] || 2490
|-
|[[Homological conjectures in commutative algebra]]||commutative algebra|| ||n/a ||
|-
|[[Hopf conjecture]]s||geometry|| ||[[Heinz Hopf]] || 476
|- 
| [[Ibragimov–Iosifescu conjecture for φ-mixing sequences]]||probability theory|| ||[[Ildar Ibragimov]], [[:ro:Marius Iosifescu]] ||
|-
|[[Invariant subspace problem]]||functional analysis|| ||n/a || 2120
|-
|[[Jacobian conjecture]]||polynomials|| || [[Carl Gustav Jacob Jacobi]] (by way of the [[Jacobian matrix and determinant|Jacobian determinant]]) || 2860
|-
|[[Jacobson's conjecture]]||ring theory|| ||[[Nathan Jacobson]] || 127
|-
|[[Kaplansky conjecture]]s||ring theory|| ||[[Irving Kaplansky]] || 466
|-
|[[Keating–Snaith conjecture]]||number theory|| || [[Jonathan Keating]] and [[Nina Snaith]] || 48
|-
|[[Köthe conjecture]]||ring theory|| || [[Gottfried Köthe]] || 167
|-
|[[Kung–Traub conjecture]]||iterative methods|| || [[H. T. Kung]] and [[Joseph F. Traub]] || 332
|-
|[[Legendre's conjecture]]||number theory|| || [[Adrien-Marie Legendre]] || 110
|-
|[[Lemoine's conjecture]]||number theory|| || [[Émile Lemoine]] || 13
|-
|[[Lenstra–Pomerance–Wagstaff conjecture]]||number theory|| || [[Hendrik Lenstra]], [[Carl Pomerance]], and [[Samuel S. Wagstaff Jr.]] || 32
|-
|[[Leopoldt's conjecture]]||number theory|| || [[Heinrich-Wolfgang Leopoldt]] || 773 <!-- match without 's -->
|-
|[[List coloring conjecture]]||graph theory|| ||n/a || 300 <!-- including colour -->
|-
|[[Littlewood conjecture]]||diophantine approximation||⇐[[Margulis conjecture]]<ref>{{cite book |last1=Burger |first1=Marc |last2=Iozzi |first2=Alessandra|author2-link=Alessandra Iozzi |title=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 |date=2013 |publisher=Springer Science & Business Media |isbn=9783662047439 |page=408 |url=https://books.google.com/books?id=hJ7zCAAAQBAJ&pg=PA408 |language=en}}</ref> ||[[John Edensor Littlewood]] || 1230
|-
|[[Lovász conjecture]]||graph theory|| || [[László Lovász]] || 560
|-
|[[MNOP conjecture]]||algebraic geometry|| ||n/a || 63
|-
|[[Manin conjecture]]||diophantine geometry|| ||[[Yuri Manin]] || 338
|-
|[[Marshall Hall's conjecture]]||number theory|| ||[[Marshall Hall, Jr.]] || 44 <!-- results ("Hall's conjecture" cube) -->
|-
|[[Mazur's conjectures]]||diophantine geometry|| || [[Barry Mazur]] || 97
|-
|[[Montgomery's pair correlation conjecture]]||number theory|| ||[[Hugh Lowell Montgomery]] || 77
|-
|[[n conjecture]]||number theory|| ||n/a || 126 <!-- results for ("n conjecture" coprime) -->
|-
|[[New Mersenne conjecture]]||number theory|| || [[Marin Mersenne]] || 47
|-
|[[Novikov conjecture]]||algebraic topology|| ||[[Sergei Novikov (mathematician)|Sergei Novikov]] || 3090
|-
|[[Oppermann's conjecture]]||number theory|| || [[Ludvig Oppermann]] || 12
|-
|[[Petersen graph#Petersen coloring conjecture|Petersen coloring conjecture]]||graph theory|| || [[Julius Petersen]] || 52
|-
|[[Pierce–Birkhoff conjecture]]||real algebraic geometry|| || Richard S. Pierce and [[Garrett Birkhoff]] || 96
|-
|[[Pillai's conjecture]]||number theory|| || [[Subbayya Sivasankaranarayana Pillai]] || 33
|-
|[[De Polignac's conjecture]]||number theory|| || [[Alphonse de Polignac]] || 46
|-
|[[Quantum PCP conjecture]]||quantum information theory|| || ||
|-
|[[quantum unique ergodicity conjecture]]||dynamical systems|| 2004, [[Elon Lindenstrauss]], for arithmetic [[hyperbolic surface]]s,<ref>{{cite web|url=http://www.math.kth.se/4ecm/prizes.ecm.html|title=EMS Prizes|website=www.math.kth.se}}</ref> 2008, [[Kannan Soundararajan]] & [[Roman Holowinsky]], for [[holomorphic form]]s of increasing weight for [[Hecke eigenform]]s on noncompact [[arithmetic surface]]s<ref>{{cite web |url=http://matematikkforeningen.no/INFOMAT/08/0810.pdf |title=Archived copy |accessdate=2008-12-12 |url-status=dead |archiveurl=https://web.archive.org/web/20110724181506/http://matematikkforeningen.no/INFOMAT/08/0810.pdf |archivedate=2011-07-24 }}</ref>||n/a || 281
|-
|[[Reconstruction conjecture]]||graph theory|| ||n/a || 1040
|-
|[[Riemann hypothesis]]||number theory||⇐[[Generalized Riemann hypothesis]]⇐[[Grand Riemann hypothesis]]<br>⇔[[De Bruijn–Newman constant]]=0<br>⇒[[density hypothesis]], [[Lindelöf hypothesis]]<br>See [[Hilbert–Pólya conjecture]]. For other ''Riemann hypotheses'', see the [[Weil conjectures]] (now theorems).||[[Bernhard Riemann]]||24900
|-
|[[Ringel–Kotzig conjecture]]||graph theory|| || [[Gerhard Ringel]] and [[Anton Kotzig]] || 187
|-
|[[Rudin's conjecture]]||additive combinatorics|| ||[[Walter Rudin]] || 16
|-
|[[Sarnak conjecture]]||topological entropy|| ||[[Peter Sarnak]] || 295
|-
|[[Sato–Tate conjecture]]||number theory|| || [[Mikio Sato]] and [[John Tate (mathematician)|John Tate]] || 1080
|-
|[[Schanuel's conjecture]]||number theory|| || [[Stephen Schanuel]] || 329
|-
|[[Schinzel's hypothesis H]]||number theory|| ||[[Andrzej Schinzel]] || 49
|-
|[[Scholz conjecture]]||addition chains|| || [[Arnold Scholz]] || 41
|-
|[[Second Hardy–Littlewood conjecture]]||number theory|| ||[[G. H. Hardy]] and [[John Edensor Littlewood]] || 30
|-
|[[Selfridge's conjecture]]||number theory|| || [[John Selfridge]] || 6
|-
|[[Sendov's conjecture]]||complex polynomials|| || [[Blagovest Sendov]] || 77
|-
|[[Serre's multiplicity conjectures]]||commutative algebra|| ||[[Jean-Pierre Serre]] || 221 <!-- results for ("Serre's conjecture" multiplicity) -->
|-
|[[Singmaster's conjecture]]||binomial coefficients|| ||[[David Singmaster]] || 8
|-
|[[Standard conjectures on algebraic cycles]]||algebraic geometry|| ||n/a || 234 <!-- most citations of a book of that name -->
|-
|[[Tate conjecture]]||algebraic geometry|| || [[John Tate (mathematician)|John Tate]] ||
|-
|[[Toeplitz' conjecture]]||Jordan curves|| || [[Otto Toeplitz]] ||
|-
|[[Tuza's conjecture]]||graph theory|| ||Zsolt Tuza||
|-
|[[Twin prime]] conjecture||number theory|| ||n/a ||1700
|-
|[[Ulam's packing conjecture]]||packing|| || [[Stanislaw Ulam]] ||
|-
|Unicity conjecture for [[Markov number]]s||number theory|| || [[Andrey Markov]] (by way of [[Markov number]]s) ||
|-
|[[Uniformity conjecture]]||diophantine geometry|| ||n/a ||
|-
|[[Unique games conjecture]]||number theory|| ||n/a ||
|-
|[[Vandiver's conjecture]]||number theory|| || [[Ernst Kummer]] and [[Harry Vandiver]] ||
|-
|[[Virasoro conjecture]]||algebraic geometry|| || [[Miguel Ángel Virasoro (physicist)|Miguel Ángel Virasoro]] ||
|-
|[[Vizing's conjecture]]||graph theory|| || [[Vadim G. Vizing]] ||
|-
|[[Vojta's conjecture]]||number theory||⇒[[abc conjecture]] ||[[Paul Vojta]] ||
|-
|[[Waring's conjecture]]||number theory|| || [[Edward Waring]] ||
|-
|[[Weight monodromy conjecture]]||algebraic geometry|| ||n/a ||
|-
|[[Weinstein conjecture]]||periodic orbits|| || [[Alan Weinstein]] ||
|-
|[[Whitehead conjecture]]||algebraic topology|| || [[J. H. C. Whitehead]] ||
|-
|[[Zauner's conjecture]]||operator theory|| || Gerhard Zauner ||
|}