Atlas of Conjectures

Doubling the cube (Delian problem)

Greek geometers · Athens, Greece

Angle trisection

Greek geometers · Athens, Greece

Squaring the circle

Anaxagoras, Hippocrates of Chios and others · Athens, Greece

The fifth postulate (parallel postulate)

Euclid · Alexandria, Egypt

Do odd perfect numbers exist?

Euclid / Nicomachus · Alexandria, Egypt

Honeycomb conjecture

Pappus of Alexandria · Alexandria, Egypt

Congruent number problem

Al-Karaji (and Arab mathematicians) · Baghdad, present-day Iraq

Kepler conjecture (sphere packing)

Johannes Kepler · Prague (imperial court of Rudolf II)

Fermat's Last Theorem

Pierre de Fermat · Toulouse, France

Fermat polygonal number theorem

Pierre de Fermat · Toulouse, France

Primality of Fermat numbers

Pierre de Fermat · Toulouse, France

Infinitude of Mersenne primes

Marin Mersenne · Paris, France

Kissing number problem

Isaac Newton and David Gregory · Cambridge, England

Goldbach's conjecture

Christian Goldbach · Moscow, Russia

Weak (ternary) Goldbach conjecture

Christian Goldbach · Moscow, Russia

Euler's sum of powers conjecture

Leonhard Euler · Saint Petersburg, Russia

Waring's problem

Edward Waring · Cambridge, England

Perfect cuboid conjecture (Euler brick)

Leonhard Euler · Saint Petersburg, Russia

Gauss class number problem

Carl Friedrich Gauss · Brunswick, Germany

Prime number theorem

A.-M. Legendre and C. F. Gauss · Paris, France

Legendre's conjecture

Adrien-Marie Legendre · Paris, France

Infinitude of Sophie Germain primes

Sophie Germain · Paris, France

Gauss circle problem

Carl Friedrich Gauss · Göttingen, Germany

Catalan's conjecture

Eugène Catalan · Paris, France

Bertrand's postulate

Joseph Bertrand · Paris, France

Twin prime conjecture (de Polignac's conjecture)

Alphonse de Polignac · Paris, France

Dirichlet divisor problem

Peter Gustav Lejeune Dirichlet · Berlin, Germany

Four color conjecture

Francis Guthrie · London (University College London)

Bunyakovsky conjecture

Viktor Bunyakovsky · Saint Petersburg, Russia

Riemann hypothesis

Bernhard Riemann · Göttingen, Germany

Generalized Riemann hypothesis (GRH)

Bernhard Riemann · Göttingen, Germany

Brocard's problem

Henri Brocard · Algiers, Algeria

Tait conjectures (alternating knots)

Peter Guthrie Tait · Edinburgh, Scotland

Continuum hypothesis

Georg Cantor · Halle, Germany

Oppermann's conjecture

Ludvig Oppermann · Copenhagen, Denmark

Kelvin problem (optimal foam)

William Thomson (Lord Kelvin) · Glasgow, United Kingdom

Catalan–Dickson conjecture (aliquot sequences)

Eugène Catalan · Liège, Belgium

Inverse Galois problem

David Hilbert · Göttingen, Germany

Lemoine's conjecture

Émile Lemoine · Quimper, France

Mertens conjecture

Franz Mertens · Vienna, Austria

Painlevé conjecture

Paul Painlevé · Stockholm, Sweden

Hilbert's tenth problem

David Hilbert · Paris, France

Hilbert's third problem

David Hilbert · Paris, France

Hilbert's sixteenth problem (limit cycles)

David Hilbert · Paris, France

No-three-in-line problem

Henry Dudeney · London, England

General Burnside problem (periodic groups)

William Burnside · Greenwich, London, United Kingdom

Poincaré conjecture

Henri Poincaré · Paris, France

Thomson problem (charges on a sphere)

J. J. Thomson · Cambridge, England

Denjoy conjecture

Arnaud Denjoy · Paris, France

Carmichael's totient function conjecture

Robert Carmichael · Hartselle, Alabama, United States

Lindelöf hypothesis

Ernst Lindelöf · Helsinki, Finland

Hauptvermutung of topology

Ernst Steinitz and Heinrich Tietze · Vienna, Austria

Torsion conjecture (elliptic curves)

Beppo Levi · Turin, Italy

Infinitude of Wieferich primes

Arthur Wieferich · Münster, Germany

Unknotting problem

Max Dehn · Göttingen, Germany

Burnside's conjecture (odd order)

William Burnside · London (Royal Naval College, Greenwich)

Inscribed square problem (Toeplitz)

Otto Toeplitz · Göttingen, Germany

Hilbert–Pólya conjecture

David Hilbert and George Pólya · Göttingen, Germany

Lebesgue's universal covering problem

Henri Lebesgue · Paris, France

Bieberbach conjecture

Ludwig Bieberbach · Frankfurt am Main, Germany

Ramanujan conjecture

Srinivasa Ramanujan · Cambridge, United Kingdom

Kakeya conjecture

Sōichi Kakeya · Sendai, Japan

Goormaghtigh conjecture

René Goormaghtigh · Ostend, Belgium

Classification of convex pentagonal tilings

Karl Reinhardt · Frankfurt am Main, Germany

Pólya conjecture

George Pólya · Zurich, Switzerland

Vandiver's conjecture

Harry Vandiver · Ithaca, New York, United States

Suslin's hypothesis

Mikhail Suslin · Moscow, Russia

Carathéodory conjecture

Constantin Carathéodory · Munich, Germany

Mordell conjecture

Louis Mordell · Manchester, England

Hardy–Littlewood conjectures (prime k-tuples)

G. H. Hardy and J. E. Littlewood · Oxford, United Kingdom

Second Hardy–Littlewood conjecture

G. H. Hardy and J. E. Littlewood · Cambridge, England

Artin's conjecture on primitive roots

Emil Artin · Hamburg, Germany

Birkhoff conjecture (billiards)

George David Birkhoff · Overisel, Michigan, United States

Entscheidungsproblem (decision problem)

David Hilbert · Göttingen, Germany

Von Neumann conjecture

John von Neumann · Berlin, Germany

Oppenheim conjecture

Alexander Oppenheim · Salford, England

Keller's conjecture

Ott-Heinrich Keller · Berlin, Germany

Littlewood conjecture

John Edensor Littlewood · Cambridge, England

Hilbert–Smith conjecture

David Hilbert and Paul Althaus Smith · Göttingen, Germany

Köthe conjecture

Gottfried Köthe · Münster, Germany

Hopf invariant one problem

Heinz Hopf · Zurich, Switzerland

Pillai's conjecture

Subbayya Sivasankaranarayana Pillai · Chidambaram, Tamil Nadu, India

Hopf conjecture on positive curvature (S²×S²)

Heinz Hopf · Zurich, Switzerland

Erdős discrepancy problem

Paul Erdős · Budapest, Hungary

Borsuk's conjecture

Karol Borsuk · Warsaw, Poland

Lehmer's totient problem

Derrick Henry Lehmer · Stanford, California, United States

Hopf conjecture (Euler characteristic and positive curvature)

Heinz Hopf · Zurich, Switzerland

Lehmer's Mahler measure problem

Derrick Henry Lehmer · Princeton, United States

Invariant subspace problem

John von Neumann · Princeton, United States

Happy ending problem (Erdős–Szekeres)

Esther Klein, Paul Erdős and George Szekeres · Budapest, Hungary

Cramér's conjecture

Harald Cramér · Stockholm, Sweden

Bochner–Riesz conjecture

Salomon Bochner · Princeton, United States

Erdős conjecture on arithmetic progressions

Paul Erdős · Manchester, England

Collatz conjecture

Lothar Collatz · Berlin, Germany

Scholz conjecture (addition chains)

Arnold Scholz · Berlin, Germany

Waring–Goldbach problem

Ivan Vinogradov and Hua Luogeng · Velikiye Luki, Russia

Smith conjecture

Paul A. Smith · New York, United States

Jacobian conjecture

Ott-Heinrich Keller · Berlin, Germany

Mahler conjecture

Kurt Mahler · Manchester, United Kingdom

Duffin–Schaeffer conjecture

Richard J. Duffin and Albert C. Schaeffer · West Lafayette, Indiana, United States

Reconstruction conjecture

Stanislaw Ulam and Paul Kelly · Madison, United States

Whitehead asphericity conjecture

J. H. C. Whitehead · Oxford, United Kingdom

Erdős–Turán conjecture on additive bases

Paul Erdős and Pál Turán · Budapest, Hungary

Hadwiger conjecture

Hugo Hadwiger · Bern, Switzerland

Erdős–Ulam problem (points at rational distances)

Paul Erdős and Stanisław Ulam · Los Alamos, New Mexico, United States

Erdős unit distance problem

Paul Erdős · Budapest, Hungary

Erdős distinct distances problem

Paul Erdős · Budapest, Hungary

Lehmer's tau conjecture

Derrick Henry Lehmer · Berkeley, California, United States

Growth of diagonal Ramsey numbers

Paul Erdős · Budapest, Hungary

Erdős–Straus conjecture

Paul Erdős · Budapest, Hungary

Weil conjectures

André Weil · Chicago, United States

Hodge conjecture

William Hodge · Cambridge, United Kingdom

Seifert conjecture

Herbert Seifert · Heidelberg, Germany

Hadwiger–Nelson problem

Edward Nelson and Hugo Hadwiger · Chicago, United States

Giuga's conjecture

Giuseppe Giuga · Rome, Italy

Kaplansky's conjectures on group rings

Irving Kaplansky · Chicago, United States

Whitehead problem

J. H. C. Whitehead · Oxford, United Kingdom

Ore conjecture

Øystein Ore · New Haven, Connecticut, United States

Borel conjecture

Armand Borel · Princeton, United States

Erdős–Moser conjecture

Paul Erdős · Budapest, Hungary

Calabi conjecture

Eugenio Calabi · Amsterdam, Netherlands

Tutte's 5-flow conjecture

William Thomas Tutte · Toronto, Canada

Zarankiewicz crossing number conjecture

Kazimierz Zarankiewicz · Warsaw, Poland

Taniyama–Shimura conjecture (modularity)

Yutaka Taniyama · Tokyo, Japan

Brauer's height zero conjecture

Richard Brauer · Cambridge, Massachusetts, United States

Chern conjecture (flat affine manifolds)

Shiing-Shen Chern · Chicago, United States

Kneser–Poulsen conjecture

Martin Kneser and Ernst Poulsen · Berlin, Germany

Jacobson's conjecture

Nathan Jacobson · New Haven, Connecticut, United States

Hirsch conjecture

Warren M. Hirsch · New York, United States

Strengthened Hanna Neumann conjecture

Hanna Neumann · Hull, United Kingdom

Eilenberg–Ganea conjecture

Samuel Eilenberg and Tudor Ganea · New York, United States

Gilbreath's conjecture

Norman Gilbreath · Los Angeles, United States

Schinzel's hypothesis H

Andrzej Schinzel · Warsaw, Poland

Nakayama conjecture (representation theory)

Tadasi Nakayama · Nagoya, Japan

Sendov's conjecture

Blagovest Sendov · Sofia, Bulgaria

Kadison–Singer problem

Richard Kadison and Isadore Singer · New York, United States

Nagata's conjecture

Masayoshi Nagata · Kyoto, Japan

Sato–Tate conjecture

Mikio Sato and John Tate · Tokyo, Japan

Kervaire invariant problem

Michel Kervaire · New York, United States

Schanuel's conjecture

Stephen Schanuel · New York, United States

Sierpiński problem

Wacław Sierpiński · Warsaw, Poland

Lang's conjectures

Serge Lang · New York, United States

Sunflower conjecture

Paul Erdős and Richard Rado · Budapest, Hungary

Wall–Sun–Sun primes (Fibonacci–Wieferich)

Donald Dines Wall · United States

Generalized Poincaré conjecture

Stephen Smale · Berkeley, United States

Strong perfect graph conjecture

Claude Berge · Paris, France

Aperiodic monotile problem (the “hat” / einstein)

David Smith, J. S. Myers, C. S. Kaplan and C. Goodman-Strauss · Bridlington, United Kingdom

Vaught conjecture

Robert Lawson Vaught · Berkeley, United States

Kato square root problem

Tosio Kato · Berkeley, California, United States

Vector fields on spheres problem

Frank Adams · Cambridge, United Kingdom

Slice-ribbon conjecture

Ralph Fox · Princeton, United States

Leopoldt's conjecture

Heinrich-Wolfgang Leopoldt · Erlangen, Germany

Bateman–Horn conjecture

Paul Bateman and Roger Horn · Urbana, Illinois, United States

Gaussian moat problem

Basil Gordon · Los Angeles, United States

Erdős–Sós conjecture

Paul Erdős and Vera Sós · Budapest, Hungary

Feit–Thompson conjecture

Walter Feit and John Thompson · Vienna, Austria

Ringel's conjecture

Gerhard Ringel · Berlin, Germany

Tate conjecture

John Tate · Cambridge, Massachusetts, United States

Zeeman conjecture (collapsibility)

Christopher Zeeman · Coventry, United Kingdom

Edge reconstruction conjecture

Frank Harary · Ann Arbor, Michigan, United States

Novikov conjecture

Sergei Novikov · Moscow, Russia

Birch and Swinnerton-Dyer conjecture

Bryan Birch and Peter Swinnerton-Dyer · Cambridge, England

Chowla conjecture

Sarvadaman Chowla · University Park, Pennsylvania, United States

Willmore conjecture

Thomas Willmore · Durham, United Kingdom

Andrews–Curtis conjecture

James Andrews and Morton Curtis · Houston, United States

Arnold conjecture (symplectic topology)

Vladimir Arnold · Moscow, Russia

Total coloring conjecture

Mehdi Behzad and Vadim G. Vizing · East Lansing, Michigan, United States

Wall's D2 problem

C. T. C. Wall · Cambridge, United Kingdom

Zariski–Lipman conjecture

Oscar Zariski and Joseph Lipman · Cambridge, Massachusetts, United States

Hedetniemi's conjecture

Stephen Hedetniemi · Ann Arbor, United States

Moving sofa problem

Leo Moser · Edmonton, Canada

Birch–Tate conjecture

Bryan Birch and John Tate · Oxford, England

Moser's worm problem

Leo Moser · Edmonton, Canada

Lonely runner conjecture

Jörg Wills · Berlin, Germany

Langlands program

Robert Langlands · Princeton, United States

Ryser's conjecture

Herbert Ryser · Pasadena, United States

Graceful tree conjecture (Kotzig–Ringel–Rosa)

Gerhard Ringel and Anton Kotzig · Bratislava, Czechoslovakia

Stein's restriction conjecture

Elias M. Stein · Princeton, United States

Ryser–Brualdi–Stein conjecture

Herbert Ryser, Richard Brualdi and Sherman Stein · Pasadena, United States

Oberwolfach problem

Gerhard Ringel · Oberwolfach, Germany

Elliott–Halberstam conjecture

Peter D. T. A. Elliott and Heini Halberstam · Nottingham, England

Standard conjectures on algebraic cycles

Alexander Grothendieck · Bures-sur-Yvette, France

Dixmier conjecture

Jacques Dixmier · Paris, France

Virtually Haken conjecture

Friedhelm Waldhausen · Bielefeld, Germany

Surface subgroup conjecture

Friedhelm Waldhausen · Bielefeld, Germany

Vizing's conjecture (domination)

Vadim G. Vizing · Novosibirsk, Russia

Grimm's conjecture

Carl Albert Grimm · Rapid City, South Dakota, United States

Main conjecture of Iwasawa theory

Kenkichi Iwasawa · Princeton, United States

Lovász conjecture

László Lovász · Budapest, Hungary

Barnette's conjecture

David Barnette · Davis, United States

Cosmic censorship hypothesis

Roger Penrose · London, United Kingdom

Milnor conjecture

John Milnor · Princeton, United States

Optimal sphere packing in dimensions 8 and 24

Classical problem (optimality of E8 and Leech) · Berlin, Germany

Singular cardinals hypothesis (SCH)

Set theory · Berkeley, United States

Rota's conjecture on matroids

Gian-Carlo Rota · Cambridge, Massachusetts, United States

Ehrenpreis conjecture

Leon Ehrenpreis · New York, United States

Is the Conway knot slice?

John Horton Conway · Cambridge, United Kingdom

Erdős sumset conjecture

Paul Erdős · Budapest, Hungary

P versus NP

Stephen Cook · Toronto, Canada

Hall's conjecture

Marshall Hall Jr. · Pasadena, California, United States

Singmaster's conjecture

David Singmaster · London, United Kingdom

Berge–Fulkerson conjecture

Delbert Ray Fulkerson · Ithaca, United States

McKay conjecture

John McKay · Montreal, Canada

Stark conjectures

Harold Stark · Cambridge, Massachusetts, United States

Erdős–Faber–Lovász conjecture

Paul Erdős · Budapest, Hungary

Property P for knots

Classical problem (popularized by R. H. Bing) · Madison, United States

Gaussian correlation inequality

Olive Jean Dunn · Los Angeles, United States

Chvátal's conjecture on intersecting families

Václav Chvátal · Columbus, Ohio, United States

Tutte's 3-flow conjecture

William Tutte · Waterloo, Canada

Classification of finite simple groups

Daniel Gorenstein, Richard Brauer, Michael Aschbacher and others · New Brunswick, New Jersey, United States

Cycle double cover conjecture

Paul Seymour and George Szekeres · Sydney, Australia

Montgomery's pair correlation conjecture

Hugh Montgomery · Ann Arbor, Michigan, United States

Chvátal's toughness conjecture

Václav Chvátal · Montreal, Canada

Burr–Erdős conjecture

Stefan Burr and Paul Erdős · Budapest, Hungary

Bombieri–Lang conjecture

Enrico Bombieri and Serge Lang · Pisa, Italy

Fuglede's conjecture (spectral sets)

Bent Fuglede · Copenhagen, Denmark

Tameness conjecture

Albert Marden · Minneapolis, United States

Herzog–Schönheim conjecture

Marcel Herzog and Jochanan Schönheim · Tel Aviv, Israel

List edge-coloring conjecture

Vadim G. Vizing and others · Odesa, Ukraine

Auslander–Reiten conjecture

Maurice Auslander and Idun Reiten · Waltham, Massachusetts, United States

Dürer's conjecture (unfolding polyhedra)

Albrecht Dürer and Geoffrey C. Shephard · Norwich, England

Atiyah conjecture (L² Betti numbers)

Michael Atiyah · Oxford, United Kingdom

Connes embedding problem

Alain Connes · Paris, France

Bass–Quillen conjecture

Hyman Bass and Daniel Quillen · Cambridge, Massachusetts, United States

Greenberg's conjecture

Ralph Greenberg · Philadelphia, Pennsylvania, United States

Kelmans–Seymour conjecture

Paul Seymour (and, independently, Alexander Kelmans) · Oxford, United Kingdom

Erdős–Hajnal conjecture

Paul Erdős and András Hajnal · Budapest, Hungary

Inscribed rectangle problem (rectangular peg)

Herbert Vaughan · Urbana, United States

Berry–Tabor conjecture

Michael Berry and Michael Tabor · Bristol, England

Caccetta–Häggkvist conjecture

Louis Caccetta and Roland Häggkvist · Perth, Australia

Weinstein conjecture

Alan Weinstein · Berkeley, United States

Dinitz problem

Jeff Dinitz · Columbus, United States

Kobon triangle problem

Kobon Fujimura · Tokyo, Japan

Shelah's PCF conjecture

Saharon Shelah · Jerusalem, Israel

Union-closed sets conjecture (Frankl)

Péter Frankl · Paris, France

Goldfeld's conjecture (rank of elliptic curves)

Dorian Goldfeld · Cambridge, Massachusetts, United States

Deligne's conjecture on special values of L-functions

Pierre Deligne · Bures-sur-Yvette, France

Kazhdan–Lusztig conjectures

David Kazhdan and George Lusztig · Cambridge, Massachusetts, United States

Cherlin–Zilber conjecture

Gregory Cherlin and Boris Zilber · New Brunswick, New Jersey, United States

Monstrous moonshine

John Conway and Simon Norton · Cambridge, England

Fundamental lemma (Langlands program)

Robert Langlands and Diana Shelstad · Princeton, United States

Fortune's conjecture (fortunate numbers)

Reo Fortune · Cambridge, England

Boolean Pythagorean triples problem

Ronald Graham · Murray Hill, New Jersey, United States

Szpiro's conjecture

Lucien Szpiro · Paris, France

Gyárfás–Sumner conjecture

András Gyárfás and David Sumner · Budapest, Hungary

Smale's mean value conjecture

Stephen Smale · Berkeley, United States

Alspach's conjecture (cycle decompositions)

Brian Alspach · Burnaby, Canada

Tuza's conjecture

Zsolt Tuza · Budapest, Hungary

Geometrization conjecture

William Thurston · Princeton, United States

Firoozbakht's conjecture

Farideh Firoozbakht · Isfahan, Iran

Baum–Connes conjecture

Paul Baum and Alain Connes · Bures-sur-Yvette, France

Yau's conjecture on minimal surfaces

Shing-Tung Yau · Princeton, United States

Ending lamination theorem

William Thurston · Princeton, New Jersey, United States

Local connectivity of the Mandelbrot set (MLC)

Adrien Douady and John Hubbard · Orsay, France

Section conjecture (anabelian geometry)

Alexander Grothendieck · Montpellier, France

Zimmer's conjecture

Robert Zimmer · Chicago, United States

Telescope conjecture

Douglas Ravenel · Seattle, Washington, United States

abc conjecture

David Masser and Joseph Oesterlé · Paris, France

Falconer's conjecture

Kenneth Falconer · Bristol, United Kingdom

Fujita conjecture

Takao Fujita · Tokyo, Japan

Beilinson conjectures (special values of L-functions)

Alexander Beilinson · Moscow, Russia

Bunkbed conjecture

Pieter Kasteleyn · Leiden, Netherlands

1-factorization conjecture

Amanda Chetwynd and Anthony Hilton · Reading, United Kingdom

Andrica's conjecture

Dorin Andrica · Cluj-Napoca, Romania

Alperin's weight conjecture

Jonathan Alperin · Chicago, United States

Sidorenko's conjecture

Alexander Sidorenko · Moscow, Russia

Nearby Lagrangian conjecture

Vladimir Arnold · Moscow, Russia

Serre's modularity conjecture

Jean-Pierre Serre · Paris, France

Vojta's conjecture

Paul Vojta · New Haven, United States

Log-rank conjecture

László Lovász and Michael Saks · Budapest, Hungary

New Mersenne conjecture (Bateman–Selfridge–Wagstaff)

Paul T. Bateman, John Selfridge and Samuel Wagstaff · Urbana, Illinois, United States

Rota's basis conjecture

Gian-Carlo Rota · Cambridge, Massachusetts, United States

Bloch–Kato conjecture (Tamagawa numbers)

Spencer Bloch and Kazuya Kato · Chicago, United States

Second neighborhood conjecture

Paul Seymour · Princeton, New Jersey, United States

Berge conjecture (knots and Dehn surgery)

John Berge · United States

Superpermutations (minimal length)

Classical combinatorics problem · United States

Double bubble conjecture

Classical problem (3D statement by J. Foisy) · Williamstown, United States

Sensitivity conjecture

Noam Nisan and Mario Szegedy · Jerusalem, Israel

Beal conjecture

Andrew Beal · Dallas, United States

Farrell–Jones conjecture

F. Thomas Farrell and Lowell E. Jones · Binghamton, United States

Cannon's conjecture

James W. Cannon · Provo, United States

Fermat–Catalan conjecture

Henri Darmon and Andrew Granville · Athens, Georgia, United States

André–Oort conjecture

Yves André and Frans Oort · Paris, France

Erdős–Gyárfás conjecture

Paul Erdős and András Gyárfás · Budapest, Hungary

Fontaine–Mazur conjecture

Jean-Marc Fontaine and Barry Mazur · Paris, France

Cobordism hypothesis

John C. Baez and James Dolan · Riverside, California, United States

HRT conjecture (linear independence of time-frequency translates)

Christopher Heil, Jayakumar Ramanathan and Pankaj Topiwala · Atlanta, United States

Angel problem

John Horton Conway · Liverpool, England

Volume conjecture (knots)

Rinat Kashaev and Hitoshi Murakami · Tokyo, Japan

Zauner's conjecture (SIC-POVMs)

Gerhard Zauner · Vienna, Austria

Navier–Stokes existence and smoothness

Clay Mathematics Institute · Cambridge, Massachusetts, United States

Yang–Mills existence and mass gap

Clay Mathematics Institute · Cambridge, Massachusetts, United States

Casas-Alvero conjecture

Eduardo Casas-Alvero · Barcelona, Spain

Exponential time hypothesis (ETH)

Russell Impagliazzo and Ramamohan Paturi · San Diego, United States

Strong exponential time hypothesis (SETH)

Russell Impagliazzo, Ramamohan Paturi and Chris Calabro · San Diego, California, United States

Unique games conjecture

Subhash Khot · Princeton, United States

Crouzeix's conjecture

Michel Crouzeix · Rennes, France

1-2-3 conjecture

Maciej Karoński, Tomasz Łuczak and Andrew Thomason · Poznań, Poland

Zilber–Pink conjecture

Boris Zilber and Richard Pink · Oxford, United Kingdom

Kahn–Kalai conjecture

Jeff Kahn and Gil Kalai · Jerusalem, Israel

Sarnak's conjecture

Peter Sarnak · Princeton, United States

Quadrisecant approximation conjecture

Gyo Taek Jin and Hyoung Seop Kim · Daejeon, South Korea

Bounded gaps between primes

Yitang Zhang · Durham, New Hampshire, United States