List of conjectures

This is a list of mathematical conjectures.

Open problems

Conjecture	Field	Comments	Eponym(s)
1/3–2/3 conjecture	order theory		n/a
abc conjecture	number theory	⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé.[1] Proof claimed in 2012 by Shinichi Mochizuki	n/a
Agoh–Giuga conjecture	number theory		Takashi Agoh and Giuseppe Giuga
Agrawal's conjecture	number theory		Manindra Agrawal
Andrews–Curtis conjecture	combinatorial group theory		James J. Andrews and Morton L. Curtis
Andrica's conjecture	number theory		Dorin Andrica
Artin conjecture (L-functions)	number theory		Emil Artin
Artin's conjecture on primitive roots	number theory	⇐generalized Riemann hypothesis[2] ⇐Selberg conjecture B[3]	Emil Artin
Bateman–Horn conjecture	number theory		Paul T. Bateman and Roger Horn
Baum–Connes conjecture	operator K-theory	⇒Gromov-Lawson-Rosenberg conjecture[4] ⇒Kaplansky-Kadison conjecture[4] ⇒Novikov conjecture[4]	Paul Baum and Alain Connes
Beal's conjecture	number theory		Andrew Beal
Beilinson conjecture	number theory		Alexander Beilinson
Berry–Tabor conjecture	geodesic flow		Michael Berry and Michael Tabor
Birch and Swinnerton-Dyer conjecture	number theory		Bryan John Birch and Peter Swinnerton-Dyer
Birch–Tate conjecture	number theory		Bryan John Birch and John Tate
Birkhoff conjecture	integrable systems		George David Birkhoff
Bloch–Beilinson conjectures	number theory		Spencer Bloch and Alexander Beilinson
Bloch–Kato conjecture	algebraic K-theory		Spencer Bloch and Kazuya Kato
Bochner–Riesz conjecture	harmonic analysis	⇒restriction conjecture⇒Kakeya maximal function conjecture⇒Kakeya dimension conjecture[5]	Salomon Bochner and Marcel Riesz
Bombieri–Lang conjecture	diophantine geometry		Enrico Bombieri and Serge Lang
Borel conjecture	geometric topology		Armand Borel
Bost conjecture	geometric topology		Jean-Benoît Bost
Brennan conjecture	complex analysis		James E. Brennan
Brocard's conjecture	number theory		Henri Brocard
Brumer–Stark conjecture	number theory		Armand Brumer and Harold Stark
Bunyakovsky conjecture	number theory		Viktor Bunyakovsky
Carathéodory conjecture	differential geometry		Constantin Carathéodory
Carmichael totient conjecture	number theory		Robert Daniel Carmichael
Casas-Alvero conjecture	polynomials		Eduardo Casas-Alvero
Catalan–Dickson conjecture on aliquot sequences	number theory		Eugène Charles Catalan and Leonard Eugene Dickson
Catalan's Mersenne conjecture	number theory		Eugène Charles Catalan
Cherlin–Zilber conjecture	group theory		Gregory Cherlin and Boris Zilber
Chowla conjecture	Möbius function	⇒Sarnak conjecture[6][7]	Sarvadaman Chowla
Collatz conjecture	number theory		Lothar Collatz
Cramér's conjecture	number theory		Harald Cramér
Conway's thrackle conjecture	graph theory		John Horton Conway
Deligne conjecture	monodromy		Pierre Deligne
Dittert conjecture	combinatorics		Eric Dittert
Eilenberg−Ganea conjecture	algebraic topology		Samuel Eilenberg and Tudor Ganea
Elliott–Halberstam conjecture	number theory		Peter D. T. A. Elliott and Heini Halberstam
Erdős–Faber–Lovász conjecture	graph theory		Paul Erdős, Vance Faber, and László Lovász
Erdős–Gyárfás conjecture	graph theory		Paul Erdős and András Gyárfás
Erdős–Straus conjecture	number theory		Paul Erdős and Ernst G. Straus
Farrell–Jones conjecture	geometric topology		F. Thomas Farrell and Lowell E. Jones
Filling area conjecture	differential geometry		n/a
Firoozbakht's conjecture	number theory		Farideh Firoozbakht
Fortune's conjecture	number theory		Reo Fortune
Four exponentials conjecture	number theory		n/a
Frankl conjecture	combinatorics		Péter Frankl
Gauss circle problem	number theory		Carl Friedrich Gauss
Gilbreath conjecture	number theory		Norman Laurence Gilbreath
Goldbach's conjecture	number theory	⇒The ternary Goldbach conjecture, which was the original formulation.[8]	Christian Goldbach
Gold partition conjecture[9]	order theory		n/a
Goldberg–Seymour conjecture	graph theory		Mark K. Goldberg and Paul Seymour
Goormaghtigh conjecture	number theory		René Goormaghtigh
Green's conjecture	algebraic curves		Mark Lee Green
Grimm's conjecture	number theory		Carl Albert Grimm
Grothendieck–Katz p-curvature conjecture	differential equations		Alexander Grothendieck and Nick Katz
Hadamard conjecture	combinatorics		Jacques Hadamard
Herzog–Schönheim conjecture	group theory		Marcel Herzog and Jochanan Schönheim
Hilbert–Smith conjecture	geometric topology		David Hilbert and Paul Althaus Smith
Hodge conjecture	algebraic geometry		W. V. D. Hodge
Homological conjectures in commutative algebra	commutative algebra		n/a
Hopf conjectures	geometry		Heinz Hopf
Invariant subspace problem	functional analysis		n/a
Jacobian conjecture	polynomials		Carl Gustav Jacob Jacobi (by way of the Jacobian determinant)
Jacobson's conjecture	ring theory		Nathan Jacobson
Kaplansky conjectures	ring theory		Irving Kaplansky
Keating–Snaith conjecture	number theory		Jonathan Keating and Nina Snaith
Köthe conjecture	ring theory		Gottfried Köthe
Kung–Traub conjecture	iterative methods		H. T. Kung and Joseph F. Traub
Legendre's conjecture	number theory		Adrien-Marie Legendre
Lemoine's conjecture	number theory		Émile Lemoine
Lenstra–Pomerance–Wagstaff conjecture	number theory		Hendrik Lenstra, Carl Pomerance, and Samuel S. Wagstaff Jr.
Leopoldt's conjecture	number theory		Heinrich-Wolfgang Leopoldt
List coloring conjecture	graph theory		n/a
Littlewood conjecture	diophantine approximation	⇐Margulis conjecture[10]	John Edensor Littlewood
Lovász conjecture	graph theory		László Lovász
MNOP conjecture	algebraic geometry		n/a
Manin conjecture	diophantine geometry		Yuri Manin
Marshall Hall's conjecture	number theory		Marshall Hall, Jr.
Mazur's conjectures	diophantine geometry		Barry Mazur
Montgomery's pair correlation conjecture	number theory		Hugh Lowell Montgomery
n conjecture	number theory		n/a
New Mersenne conjecture	number theory		Marin Mersenne
Novikov conjecture	algebraic topology		Sergei Novikov
Oppermann's conjecture	number theory		Ludvig Oppermann
Petersen coloring conjecture	graph theory		Julius Petersen
Pierce–Birkhoff conjecture	real algebraic geometry		Richard S. Pierce and Garrett Birkhoff
Pillai's conjecture	number theory		Subbayya Sivasankaranarayana Pillai
De Polignac's conjecture	number theory		Alphonse de Polignac
quantum unique ergodicity conjecture	dynamical systems	2004, Elon Lindenstrauss, for arithmetic hyperbolic surfaces,[11] 2008, Kannan Soundararajan & Roman Holowinsky, for holomorphic forms of increasing weight for Hecke eigenforms on noncompact arithmetic surfaces[12]	n/a
Reconstruction conjecture	graph theory		n/a
Riemann hypothesis	number theory	⇐Generalized Riemann hypothesis⇐Grand Riemann hypothesis ⇔De Bruijn–Newman constant=0 ⇒density hypothesis, Lindelöf hypothesis See Hilbert–Pólya conjecture. For other Riemann hypotheses, see the Weil conjectures (now theorems).	Bernhard Riemann
Ringel–Kotzig conjecture	graph theory		Gerhard Ringel and Anton Kotzig
Rudin's conjecture	additive combinatorics		Walter Rudin
Sarnak conjecture	topological entropy		Peter Sarnak
Sato–Tate conjecture	number theory		Mikio Sato and John Tate
Schanuel's conjecture	number theory		Stephen Schanuel
Schinzel's hypothesis H	number theory		Andrzej Schinzel
Scholz conjecture	addition chains		Arnold Scholz
Second Hardy–Littlewood conjecture	number theory		G. H. Hardy and John Edensor Littlewood
Selfridge's conjecture	number theory		John Selfridge
Sendov's conjecture	complex polynomials		Blagovest Sendov
Serre's multiplicity conjectures	commutative algebra		Jean-Pierre Serre
Singmaster's conjecture	binomial coefficients		David Singmaster
Standard conjectures on algebraic cycles	algebraic geometry		n/a
Tate conjecture	algebraic geometry		John Tate
Toeplitz' conjecture	Jordan curves		Otto Toeplitz
Twin prime conjecture	number theory		n/a
Ulam's packing conjecture	packing		Stanislaw Ulam
Unicity conjecture for Markov numbers	number theory		Andrey Markov (by way of Markov numbers)
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
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

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[13]	Proved by	Former name	Field	Comments
1962	Walter Feit and John G. 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
1968	Gerhard Ringel and John William Theodore Youngs	Heawood conjecture	graph theory	Ringel-Youngs theorem
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
1975	William Haboush	Mumford conjecture	geometric invariant theory	Haboush's theorem
1976	Kenneth Appel and Wolfgang Haken	Four color theorem	graph colouring	Traditionally called a "theorem", long before the proof.
1976	Daniel Quillen; and independently by Andrei Suslin	Serre's conjecture on projective modules	polynomial rings	Quillen–Suslin theorem
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[14]
1978	Roger Heath-Brown and Samuel James Patterson	Kummer's conjecture on cubic Gauss sums	equidistribution
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 onwards	Neil Robertson and Paul D. Seymour	Wagner's conjecture	graph theory	Now generally known as the graph minor theorem.
1983	Michel Raynaud	Manin–Mumford conjecture	diophantine geometry	The Tate–Voloch conjecture is a quantitative (diophantine approximation) derived conjecture for p-adic varieties.
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 de Bourcia	Bieberbach conjecture, 1916	complex analysis	⇐Robertson conjecture⇐Milin conjecture⇐de Branges's theorem[15]
1984	Gunnar Carlsson	Segal's conjecture	homotopy theory
1984	Haynes Miller	Sullivan conjecture	classifying spaces	Miller proved the version on mapping BG to a finite complex.
1987	Grigory Margulis	Oppenheim conjecture	diophantine approximation	Margulis proved the conjecture with ergodic theory methods.
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.
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[16]	Alternating sign matrix conjecture,	enumerative combinatorics
1996	Vladimir Voevodsky	Milnor conjecture	algebraic K-theory	Voevodsky's theorem, ⇐norm residue isomorphism theorem⇔Beilinson–Lichtenbaum conjecture, Quillen–Lichtenbaum conjecture. The ambiguous term "Bloch-Kato conjecture" may refer to what is now the norm residue isomorphism theorem.
1998	Thomas Callister Hales	Kepler conjecture	sphere packing
1998	Thomas Callister Hales and Sean McLaughlin	dodecahedral conjecture	Voronoi decompositions
2000	Krzysztof Kurdyka, Tadeusz Mostowski, and Adam Parusiński	Gradient conjecture	gradient vector fields	Attributed to René Thom, c.1970.
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".
2001	Mark Haiman	n! conjecture	representation theory
2001	Daniel Frohardt and Kay Magaard[17]	Guralnick–Thompson conjecture	monodromy groups
2002	Preda Mihăilescu	Catalan's conjecture, 1844	exponential diophantine equations	⇐Pillai's conjecture⇐abc conjecture Mihăilescu's theorem
2002	Maria Chudnovsky, Neil Robertson, Paul D. Seymour, and Robin Thomas	strong perfect graph conjecture	perfect graphs	Chudnovsky–Robertson–Seymour–Thomas theorem
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
2003	Nils Dencker	Nirenberg–Treves conjecture	pseudo-differential operators
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.
2004	Adam Marcus and Gábor Tardos	Stanley–Wilf conjecture	permutation classes	Marcus–Tardos theorem
2004	Ualbai U. Umirbaev and Ivan P. Shestakov	Nagata's conjecture on automorphisms	polynomial rings
2004	Ian Agol; and independently by Danny Calegari–David Gabai	tameness conjecture	geometric topology	⇒Ahlfors measure conjecture
2008	Avraham Trahtman	Road coloring conjecture	graph theory
2008	Chandrashekhar Khare and Jean-Pierre Wintenberger	Serre's modularity conjecture	modular forms
2009	Jeremy Kahn and Vladimir Markovic	surface subgroup conjecture	3-manifolds	⇒Ehrenpreis conjecture on quasiconformality
2009	Jeremie Chalopin and Daniel Gonçalves	Scheinerman's conjecture	intersection graphs
2010	Terence Tao and Van H. Vu	circular law	random matrix theory
2011	Joel Friedman; and independently by Igor Mineyev	Hanna Neumann conjecture	group theory
2012	Simon Brendle	Hsiang–Lawson's conjecture	differential geometry
2012	Fernando Codá Marques and André Neves	Willmore conjecture	differential geometry
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.
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.
2015	Jean Bourgain, Ciprian Demeter, and Larry Guth	Main conjecture in Vinogradov's mean-value theorem	analytic number theory	Bourgain–Demeter–Guth theorem, ⇐ decoupling theorem[18]
2018	Karim Adiprasito	g-conjecture	combinatorics
2019	Dimitris Koukoulopoulos and James Maynard	Duffin–Schaeffer conjecture	number theory	Rational approximation of irrational numbers

Deligne's conjecture on 1-motives[19]
Goldbach's weak conjecture (proved in 2013)
Sensitivity conjecture (proved in 2019)

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
Hauptvermutung
Hedetniemi's conjecture, counterexample announced 2019[20]
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)[21]
Tait's conjecture
Von Neumann conjecture
Weyl–Berry conjecture
Williamson conjecture

References

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.
Simon, Barry (2015). Harmonic Analysis. American Mathematical Soc. p. 685. ISBN 9781470411022.
Tao, Terence (15 October 2012). "The Chowla conjecture and the Sarnak conjecture". What's new.
Ferenczi, Sébastien; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz (2018). Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016. Springer. p. 185. ISBN 9783319749082.
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.{{cite web}}: 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.
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
"Decoupling and the Bourgain-Demeter-Guth proof of the Vinogradov main conjecture". What's new. 10 December 2015.
Holden, Helge; Piene, Ragni (2018). The Abel Prize 2013-2017. Springer. p. 51. ISBN 9783319990286.
Kalai, Gil (10 May 2019). "A sensation in the morning news – Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture". Combinatorics and more.
"Schoenflies conjecture", Encyclopedia of Mathematics, EMS Press, 2001 [1994]

External links

Open Problem Garden

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[1] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 13. ISBN 9781420035223.

[2] 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.

[3] Steuding, Jörn; Morel, J.-M.; Steuding, Jr̲n (2007). Value-Distribution of L-Functions. Springer Science & Business Media. p. 118. ISBN 9783540265269.

[Valette-4] Valette, Alain (2002). Introduction to the Baum-Connes Conjecture. Springer Science & Business Media. p. viii. ISBN 9783764367060.

[5] Simon, Barry (2015). Harmonic Analysis. American Mathematical Soc. p. 685. ISBN 9781470411022.

[6] Tao, Terence (15 October 2012). "The Chowla conjecture and the Sarnak conjecture". What's new.

[7] Ferenczi, Sébastien; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz (2018). Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016. Springer. p. 185. ISBN 9783319749082.

[8] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 1203. ISBN 9781420035223.

[9] M. Peczarski, The gold partition conjecture, it Order 23(2006): 89–95.

[10] 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.

[11] "EMS Prizes". www.math.kth.se.

[12] "Archived copy" (PDF). Archived from the original (PDF) on 2011-07-24. Retrieved 2008-12-12.{{cite web}}: CS1 maint: archived copy as title (link)

[13] 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.

[14] Dudziak, James (2011). Vitushkin's Conjecture for Removable Sets. Springer Science & Business Media. p. 39. ISBN 9781441967091.

[15] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 218. ISBN 9781420035223.

[16] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 65. ISBN 9781420035223.

[17] 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

[18] "Decoupling and the Bourgain-Demeter-Guth proof of the Vinogradov main conjecture". What's new. 10 December 2015.

[19] Holden, Helge; Piene, Ragni (2018). The Abel Prize 2013-2017. Springer. p. 51. ISBN 9783319990286.

[20] Kalai, Gil (10 May 2019). "A sensation in the morning news – Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture". Combinatorics and more.

[21] "Schoenflies conjecture", Encyclopedia of Mathematics, EMS Press, 2001 [1994]