ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAI
1
NameYear posed
Years ago posed
Year resolvedLength
#open,solved later
#open,unsolved#open
Empirical estimate of survivorship
Exponential regression
Power-law regression
Linear regressionFieldWikipediaSourceSource with date
2
Form of even perfect numbers1000100017507501010#REF!#REF!#REF!
3
Four color theorem18521681976124816240#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Four_color_theorem
Wikipedia list of conjecturesW. W. Rouse Ball (1960) The Four Color Theorem, in Mathematical Recreations and Essays, Macmillan, New York, pp 222-232.
4
Waring's problem17702501909139711180#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Waring%27s_conjecture
Wikipedia list of conjectures Hilbert, D. (1909). "Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)". Mathematische Annalen 67: 281–300. doi:10.1007/bf01450405.
5
Hasse's theorem on elliptic curves19249619339761342100#REF!#REF!#REF!Zeta functions
http://en.wikipedia.org/wiki/Hasse%27s_theorem_on_elliptic_curves
Wikipedia list of conjectures
Artin, Emil (1924), "Quadratische Körper im Gebiete der höheren Kongruenzen. II. Analytischer Teil", Mathematische Zeitschrift 19 (1): 207–246, doi:10.1007/BF01181075, ISSN 0025-5874,MR 1544652, Zbl 51.0144.05
6
Hodge conjecture194080Not Resolved000#DIV/0!#REF!#REF!#REF!Algebraic Topology
http://en.wikipedia.org/wiki/Hodge_conjecture
Wikipedia list of conjecturesHodge, W. V. D. (1950), "The topological invariants of algebraic varieties", Proceedings of the International Congress of Mathematicians (Cambridge, MA) 1: 181–192.
7
Tait's conjecture1884136194662216384#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Tait%27s_conjecture
Wikipedia list of conjecturesTait, P. G. (1884), "Listing's Topologie", Philosophical Magazine (5th ser.) 17: 30–46. Reprinted in Scientific Papers, Vol. II, pp. 85–98.
8
Brauer's theorem on forms1945751950581134215#DIV/0!#REF!#REF!#REF!
http://en.wikipedia.org/wiki/Brauer%27s_theorem_on_forms
Wikipedia list of conjecturesR. Brauer, A note on systems of homogeneous algebraic equations, Bulletin of the American Mathematical Society, 51, pages 749-755 (1945)
9
Hanna Neumann conjecture1954661957383134217#DIV/0!#REF!#REF!#REF!Group theory
http://en.wikipedia.org/wiki/Hanna_Neumann_conjecture
Wikipedia list of conjecturesHanna Neumann. On the intersection of finitely generated free groups. Addendum. Publicationes Mathematicae Debrecen, vol. 5 (1957), p. 128
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Pólya conjecture191910119583938106144#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/P%C3%B3lya_conjecture
Wikipedia list of conjecturesPólya, G. (1919). "Verschiedene Bemerkungen zur Zahlentheorie". Jahresbericht der Deutschen Mathematiker-Vereinigung 28: 31–40. JFM 47.0882.06.
11
Sierpinski number1960601960089134223#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Selfridge%27s_conjecture
Wikipedia list of conjectures Sierpinski number at The Prime Glossary
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Hauptvermutung19081121961532785112#DIV/0!#REF!#REF!#REF!Geometric Topology
http://en.wikipedia.org/wiki/Hauptvermutung
Wikipedia list of conjectures Milnor, John W. (1961). "Two complexes which are homeomorphic but combinatorially distinct". Annals of Mathematics 74 (2): 575–590. doi:10.2307/1970299. JSTOR 1970299. MR 133127.
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Feit–Thompson theorem19111091962512989118#DIV/0!#REF!#REF!#REF!Group theory
http://en.wikipedia.org/wiki/Feit%E2%80%93Thompson_theorem
Wikipedia list of conjecturesFeit, Walter; Thompson, John G. (1962), "A solvability criterion for finite groups and some consequences", Proc. Nat. Acad. Sci. 48 (6): 968–970, doi:10.1073/pnas.48.6.968, JSTOR 71265, MR 0143802
14
Andrews–Curtis conjecture1965551965089134223#DIV/0!#REF!#REF!#REF!
Combinatorial group theory
http://en.wikipedia.org/wiki/Andrews%E2%80%93Curtis_conjecture
Wikipedia list of conjecturesAndrews, J. J.; Curtis, M. L. (1965), "Free groups and handlebodies", Proceedings of the American Mathematical Society (American Mathematical Society) 16 (2): 192–195, doi:10.2307/2033843, JSTOR 2033843, MR 0173241
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Euler's sum of powers conjecture17692511966197314#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture
Wikipedia list of conjectures-
16
Standard conjectures on algebraic cycles
1960601968877134211#DIV/0!#REF!#REF!#REF!Algebraic Cycles
http://en.wikipedia.org/wiki/Standard_conjectures_on_algebraic_cycles
Wikipedia list of conjecturesGrothendieck, A. (1969), "Standard Conjectures on Algebraic Cycles", Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford University Press, pp. 193–199, MR 0268189.
17
Heawood conjecture1890130196878174360#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Heawood_conjecture
Wikipedia list of conjecturesFranklin, P. (1934). "A six color problem". Journal of Mathematical Physics 13: 363–379.
Heawood, P. J. (1890). "Map colour theorem". Quarterly Journal of Mathematics 24: 332–338.
18
Equitable Coloring1964561970680134214#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Equitable_coloring
List of conjectures by Paul Erdős
19
Happy Ending problem19358519703542112154#DIV/0!#REF!#REF!#REF!Discrete geometry
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres_conjecture
List of conjectures by Paul Erdős
20
Artin L-function1923971970473199130#DIV/0!#REF!#REF!#REF!
Linear Representation
http://en.wikipedia.org/wiki/Artin_conjecture_(L-functions)
Wikipedia list of conjecturesArtin, E. (1923). "Über eine neue Art von L Reihen". Hamb. Math. Abh. 3. Reprinted in his collected works, ISBN 0-387-90686-X. English translation in Artin L-Functions: A Historical Approach by N. Snyder.
21
J-homomorphism19437719712850120170#DIV/0!#REF!#REF!#REF!Homotopy theory
http://en.wikipedia.org/wiki/Adams_conjecture
Wikipedia list of conjecturesWhitehead, George W. (1942), "On the homotopy groups of spheres and rotation groups", Annals of Mathematics. Second Series 43 (4): 634–640, doi:10.2307/1968956, ISSN 0003-486X, JSTOR 1968956, MR 0007107
22
Blattner's conjecture1968521972482134216#DIV/0!#REF!#REF!#REF!
Representation theory of Lie groups
http://en.wikipedia.org/wiki/Blattner%27s_conjecture
Wikipedia list of conjecturesOkamoto, Kiyosato; Ozeki, Hideki (1967), "On square-integrable ∂-cohomology spaces attached to hermitian symmetric spaces", Osaka Journal of Mathematics 4: 95–110, ISSN 0030-6126, MR 0229260
23
Weil conjectures19497119742556126182#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Weil_conjectures
Wikipedia list of conjecturesArtin, Emil (1924), "Quadratische Körper im Gebiete der höheren Kongruenzen. II. Analytischer Teil", Mathematische Zeitschrift 19 (1): 207–246, doi:10.1007/BF01181075, ISSN 0025-5874
24
Haboush's theorem19655519751073134207#DIV/0!#REF!#REF!#REF!
Representation theory
http://en.wikipedia.org/wiki/Haboush%27s_theorem
Wikipedia list of conjecturesD. Mumford, "Geometric invariant theory" , Springer (1965)
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Clifford's theorem on special divisors
1878142197799122133#DIV/0!#REF!#REF!#REF!algebraic geometry
http://en.wikipedia.org/wiki/Green%27s_conjecture
Wikipedia list of conjecturesClifford, W. K. (1878), "On the Classification of Loci", Philosophical Transactions of the Royal Society of London (The Royal Society) 169: 663–681, doi:10.1098/rstl.1878.0020, ISSN 0080-4614, JSTOR 109316
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Quillen–Suslin theorem19556519782359128187#DIV/0!#REF!#REF!#REF!
Commutative algebra
http://en.wikipedia.org/wiki/Quillen%E2%80%93Suslin_theorem
Wikipedia list of conjecturesSerre, Jean-Pierre (March 1955), "Faisceaux algébriques cohérents", Annals of Mathematics. Second Series. 61 (2): 197–278, doi:10.2307/1969915, JSTOR 1969915
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Kummer sum1970501979976134210#DIV/0!#REF!#REF!#REF!Cyclotomic fields
http://en.wikipedia.org/wiki/Kummer%27s_conjecture_on_cubic_Gauss_sums
Wikipedia list of conjecturesHeath-Brown, D.R.; Patterson, S.I. (1979), "The distribution of Kummer sums at prime arguments", J. Reine Angew. Math. 310: 111–130, MR 0546667
28
Ragsdale conjecture1900120197979164359#DIV/0!#REF!#REF!#REF!Algebraic geometry
http://en.wikipedia.org/wiki/Ragsdale_conjecture
Wikipedia list of conjecturesViro, Oleg Ya. (1980). "Кривые степени 7, кривые степени 8 и гипотеза Рэгсдейл" [Curves of degree 7, curves of degree 8 and the hypothesis of Ragsdale]. Doklady Akademii Nauk SSSR 254 (6): 1306–1309. Translated in Soviet Mathematics - Doklady 22: 566–570. 1980. Zbl 0422.14032.
29
Von Neumann conjecture1928921980522886114#DIV/0!#REF!#REF!#REF!
Geometric Group theory
http://en.wikipedia.org/wiki/Von_Neumann_conjecture
Wikipedia list of conjecturesAdian, S. (1982), "Random walks on free periodic groups", Izv. Akad. Nauk SSSR, Ser. Mat. (in Russian) 46 (6): 1139–1149,1343
30
Faltings' theorem192298198361236386#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Mordell_conjecture
Wikipedia list of conjecturesMordell, Louis J. (1922). "On the rational solutions of the indeterminate equation of the third and fourth degrees". Proc. Cambridge Philos. Soc. 21: 179–192.
31
Sullivan conjecture19705019841470133203#DIV/0!#REF!#REF!#REF!Homotopy theory
http://en.wikipedia.org/wiki/Sullivan_conjecture
Wikipedia list of conjectures Haynes Miller, The Sullivan Conjecture on Maps from Classifying Spaces, The Annals of Mathematics, second series, Vol. 120 No. 1, 1984, pp. 39-87. JSTOR: The Annals of Mathematics. Accessed May 9, 2012.
32
de Branges's theorem1916104198569184967#DIV/0!#REF!#REF!#REF!Complex analysis
http://en.wikipedia.org/wiki/Bieberbach_conjecture
Wikipedia list of conjecturesBieberbach, L. (1916), "Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln", Sitzungsber. Preuss. Akad. Wiss. Phys-Math. Kl.: 940–955
33
Mertens conjecture18851351985100112132#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Mertens_conjecture
Wikipedia list of conjecturesF. Mertens (1897), "Über eine zahlentheoretische Funktion", Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse, Abteilung 2a, 106, pp. 761–830.
34
Ribet's theorem1985351986186134220#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Epsilon_conjecture
Wikipedia list of conjecturesFrey, Gerhard (1986), "Links between stable elliptic curves and certain Diophantine equations", Annales Universitatis Saraviensis. Series Mathematicae 1 (1): iv+40, ISSN 0933-8268, MR 853387
35
Weyl-Berry conjecture1979411986779134213#DIV/0!#REF!#REF!#REF!Spectral theory
http://en.wikipedia.org/wiki/Weyl%E2%80%93Berry_conjecture#The_Weyl.E2.80.93Berry_conjecture
Mentioned in wikipedia page on "Hearing the shape of a drum"
https://www.math.dartmouth.edu/~carlp/counterfractal.pdf
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Montgomery's pair correlation conjecture
19734719871470133203#DIV/0!#REF!#REF!#REF!
Analytic number theory
http://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture
Wikipedia list of conjecturesOdlyzko, A. M. (1987), "On the distribution of spacings between zeros of the zeta function", Mathematics of Computation (American Mathematical Society) 48 (177): 273–308, doi:10.2307/2007890, ISSN 0025-5718, JSTOR 2007890, MR 866115
37
Oppenheim conjecture192991198758247296#DIV/0!#REF!#REF!#REF!
Diophantine approximation
http://en.wikipedia.org/wiki/Oppenheim_conjecture
Wikipedia list of conjecturesOppenheim, A. The minima of indefinite quaternary quadratic forms. Proc. Nat. Acad. Sci. U.S.A., 15:724-727, 1929. Online PDF
38
Negami's conjecture1986341988284134218#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Negami%27s_conjecture#Negami.27s_conjecture
List of unsolved problems in mathematics
39
Mersenne conjectures1989311989089134223#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/New_Mersenne_conjecture
Wikipedia list of conjecturesDickson, L. E. (1919). History of the Theory of Numbers. Carnegie Institute of Washington. p. 31. OL 6616242M. Reprinted by Chelsea Publishing, New York, 1971, ISBN 0-8284-0086-5.
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Monstrous moonshine19794119921371133204#DIV/0!#REF!#REF!#REF!Ring theory
http://en.wikipedia.org/wiki/Conway%E2%80%93Norton_conjecture
Wikipedia list of conjecturesJohn Horton Conway and Simon P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11, 308–339, 1979. doi: 10.1112/blms/11.3.308
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Hearing the shape of a drum19665419922654123177#DIV/0!#REF!#REF!#REF!Spectral theory
http://en.wikipedia.org/wiki/Weyl%E2%80%93Berry_conjecture#The_Weyl.E2.80.93Berry_conjecture
Wikipedia list of conjecturesLapidus, Michel L.; Pomerance, Carl (1996), "Counterexamples to the modified Weyl–Berry conjecture on fractal drums", Math. Proc. Cambridge Philos. Soc. 119 (1): 167–178, Bibcode:1996MPCPS.119..167L, doi:10.1017/S0305004100074053
42
Borsuk's conjecture193288199361236386#DIV/0!#REF!#REF!#REF!Discrete geometry
http://en.wikipedia.org/wiki/Borsuk%27s_conjecture
Wikipedia list of conjecturesDrei Sätze über die n-dimensionale euklidische Sphäre (German 'Three statements of n-dimensional Euclidean sphere') – original Borsuk's article in Fundamenta Mathematicae, made available by Polish Virtual Library of Science
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Sylvester's sequence1880140199311391726#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Sylvester%27s_sequence
List of conjectures by Paul Erdős
44
Dinitz conjecture19794119941568132200#DIV/0!#REF!#REF!#REF!Combinatorics
http://en.wikipedia.org/wiki/Dinitz_conjecture
Wikipedia list of conjecturesF. Galvin (1995). "The list chromatic index of a bipartite multigraph". Journal of Combinatorial Theory. Series B 63 (1): 153–158. doi:10.1006/jctb.1995.1011.
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Fermat's Last Theorem16373831994357202#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem
Wikipedia list of conjecturesFrénicle de Bessy, Traité des Triangles Rectangles en Nombres, vol. I, 1676, Paris. Reprinted in Mém. Acad. Roy. Sci., 5, 1666–1699 (1729).
46
Whitehead conjecture194179199756257499#DIV/0!#REF!#REF!#REF!Algebraic Topology
http://en.wikipedia.org/wiki/Whitehead_conjecture
Wikipedia list of conjecturesWhitehead, On adding relations to homotopy groups, Annals of Mathematics, 2nd Ser., 42 (1941), no. 2, 409 –428.
47
Ganea conjecture19714919982753123176#DIV/0!#REF!#REF!#REF!Algebraic Topology
http://en.wikipedia.org/wiki/Ganea_conjecture
Wikipedia list of conjecturesGanea, Tudor (1971). "Some problems on numerical homotopy invariants". Lecture Notes in Mathematics (Berlin: Springer-Verlag) 249: 13–22. doi:10.1007/BFb0060892. MR 0339147.
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Dodecahedral conjecture1943771998552678104#DIV/0!#REF!#REF!#REF!Geometry
http://en.wikipedia.org/wiki/Dodecahedral_conjecture
Wikipedia list of conjectures Fejes Tóth, L. (1943). "Über die dichteste Kugellagerung". Mathematische Zeitschrift 48 (1): 676–684. doi:10.1007/BF01180035..
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Circle packing in an equilateral triangle
1993272000779134213#DIV/0!#REF!#REF!#REF!Discrete geometry
http://en.wikipedia.org/wiki/Circle_packing_in_an_equilateral_triangle
List of conjectures by Paul Erdős
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Gradient conjecture19893120001172134206#DIV/0!#REF!#REF!#REF!
Theorems in analysis
http://en.wikipedia.org/wiki/Gradient_conjecture
Wikipedia list of conjecturesA published statement of the conjecture: R. Thom, Problèmes rencontrés dans mon parcours mathématique: un bilan, Publ. Math. IHES 70 (1989), 200-214. (This gradient conjecture due to René Thom was in fact well-known among specialists by the early 70's, having been often discussed during that period by Thom during his weekly seminar on singularities at the IHES.)
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Stanley–Wilf conjecture19804020002064130194#DIV/0!#REF!#REF!#REF!Combinatorics
http://en.wikipedia.org/wiki/Stanley%E2%80%93Wilf_conjecture
Wikipedia list of conjecturesArratia, Richard (1999), "On the Stanley–Wilf conjecture for the number of permutations avoiding a given pattern", Electronic Journal of Combinatorics 6: N1, MR 1710623.
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Erdős–Graham problem19804020002064130194#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Graham_conjecture
List of conjectures by Paul Erdős
53
Vizing's conjecture19685220003245115160#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Vizing%27s_conjecture
Wikipedia list of conjecturesBarcalkin, A. M.; German, L. F. (1979), "The external stability number of the Cartesian product of graphs", Bul. Akad. Stiince RSS Moldoven (in Russian) 1: 5–8, MR 0544028.
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Modularity theorem19566420014533101134#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Taniyama%E2%80%93Shimura_conjecture
Wikipedia list of conjecturesWeil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR 0207658
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Star height problem19635720023938106144#DIV/0!#REF!#REF!#REF!Automata theory
http://en.wikipedia.org/wiki/Star_height_problem
Wikipedia list of conjecturesEggan, Lawrence C. (1963). "Transition graphs and the star-height of regular events". Michigan Mathematical Journal 10 (4): 385–397. doi:10.1307/mmj/1028998975. Zbl 0173.01504.
56
Strong perfect graph theorem19615920024135105140#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Strong_perfect_graph_conjecture
Wikipedia list of conjecturesBerge, Claude (1961), "Färbung von Graphen, deren sämtliche bzw. deren ungerade Kreise starr sind", Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10: 114.
57
Catalan's conjecture184417620021586814#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Catalan%27s_conjecture
Wikipedia list of conjecturesCatalan, Eugene. (1844): Note extraite d’une lettre adressée à l’éditeur. J. Reine Angew. Math., 27:192.
58
Cameron–Erdős conjecture19883220031568132200#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Cameron%E2%80%93Erd%C5%91s_conjecture
Wikipedia list of conjecturesCameron, P. J.; Erdős, P. (1990), "On the number of sets of integers with various properties", Number theory: proceedings of the First Conference of the Canadian Number Theory Association, held at the Banff Center, Banff, Alberta, April 17-27, 1988, Berlin: de Gruyter, pp. 61–79, MR 1106651.
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Cameron–Erdős conjecture19883220031568132200#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Cameron%E2%80%93Erd%C5%91s_conjecture
List of conjectures by Paul Erdős
60
Geometrization conjecture19823820032162130192#DIV/0!#REF!#REF!#REF!Geometric Topology
http://en.wikipedia.org/wiki/Thurston%27s_geometrization_conjecture
Wikipedia list of conjecturesThurston, William P. (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry". American Mathematical Society. Bulletin. New Series 6 (3): 357–381. doi:10.1090/S0273-0979-1982-15003-0. ISSN 0002-9904. MR 648524 This gives the original statement of the conjecture.
61
Poincaré conjecture19586220034533101134#DIV/0!#REF!#REF!#REF!Geometric Topology
http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture
Wikipedia list of conjecturesBing, RH (1958). "Necessary and sufficient conditions that a 3-manifold be S3". Annals of Mathematics. Second Series 68 (1): 17–37. doi:10.2307/1970041. JSTOR 1970041.
62
Robertson–Seymour theorem19833720042162130192#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Wagner%27s_conjecture
Wikipedia list of conjecturesBienstock, Daniel; Langston, Michael A. (1995), "Algorithmic implications of the graph minor theorem", Network Models, Handbooks in Operations Research and Management Science 7, pp. 481–502, doi:10.1016/S0927-0507(05)80125-2.
63
Tameness theorem19744620043048119167#DIV/0!#REF!#REF!#REF!
Hyperbolic geometry
http://en.wikipedia.org/wiki/Tameness_conjecture
Wikipedia list of conjecturesMarden, Albert (1974), "The geometry of finitely generated kleinian groups", Annals of Mathematics, Second Series 99: 383–462, ISSN 0003-486X, JSTOR 1971059, MR 0349992, Zbl 0282.30014
64
Nagata's conjecture19724820043245115160#DIV/0!#REF!#REF!#REF!Field theory
http://en.wikipedia.org/wiki/Nagata%27s_conjecture_on_automorphisms
Wikipedia list of conjecturesNagata, Masayoshi (1972), On automorphism group of k[x,y], Tokyo: Kinokuniya Book-Store Co. Ltd., MR 0337962
65
Manin–Mumford conjecture19833720052260128188#DIV/0!#REF!#REF!#REF!
Diophantine geometry
http://en.wikipedia.org/wiki/Manin%E2%80%93Mumford_conjecture#Manin.E2.80.93Mumford_conjecture
Wikipedia list of conjecturesRaynaud, Michel (1983). "Sous-variétés d'une variété abélienne et points de torsion". In Artin, Michael; Tate, John. Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday. Vol. I: Arithmetic. Progress in Mathematics (in French) 35. Birkhauser-Boston. pp. 327–352. Zbl 0581.14031.
66
Milnor conjecture19705020053542112154#DIV/0!#REF!#REF!#REF!K- theory
http://en.wikipedia.org/wiki/Milnor_conjecture
Wikipedia list of conjecturesMilnor, John Willard (1970), "Algebraic K-theory and quadratic forms", Inventiones Mathematicae 9 (4): 318–344, doi:10.1007/BF01425486, ISSN 0020-9910, MR 0260844
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Bloch–Kato conjecture19903020061665132197#DIV/0!#REF!#REF!#REF!Algebraic K-theory
http://en.wikipedia.org/wiki/Bloch%E2%80%93Kato_conjecture
Wikipedia list of conjecturesBloch & Kato, Tamagawa Numbers of Motives in The Gorthendieck festschrift, vol. 1,
Progress in Math 89, Birkhauser, 1990
68
Angel problem19823820062458126184#DIV/0!#REF!#REF!#REF!Game theory
http://en.wikipedia.org/wiki/Angel_problem
Wikipedia list of conjectures John H. Conway, The angel problem, in: Richard Nowakowski (editor) Games of No Chance, volume 29 of MSRI Publications, pages 3–12, 1996.
69
Segal conjecture19794120062753123176#DIV/0!#REF!#REF!#REF!Homotopy theory
http://en.wikipedia.org/wiki/Segal%27s_Burnside_ring_conjecture
Wikipedia list of conjecturesJ.F. Adams (1979). "Graeme Segal's Burnside ring conjecture". Proc. Topology Symp. Siegen.
70
Quillen–Lichtenbaum conjecture19754520063146119165#DIV/0!#REF!#REF!#REF!Algebraic K-theory
http://en.wikipedia.org/wiki/Quillen%E2%80%93Lichtenbaum_conjecture
Wikipedia list of conjecturesQuillen, Daniel (1975), "Higher algebraic K-theory", Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Canad. Math. Congress, Montreal, Que., pp. 171–176, MR 0422392
71
Erdős–Turán conjecture on additive bases
194179200665195473#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Tur%C3%A1n_conjecture_on_additive_bases
List of conjectures by Paul Erdős
72
Poincaré conjecture19041162006102102030#DIV/0!#REF!#REF!#REF!Geometric Topology
http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture
Millenium Prize Problems
73
Kobon triangle problem1998222007976134210#DIV/0!#REF!#REF!#REF!
Combinatorial geometry
http://en.wikipedia.org/wiki/Kobon_triangle_problem
List of unsolved problems in mathematics
74
Weinstein conjecture19784220072949119168#DIV/0!#REF!#REF!#REF!Homology
http://en.wikipedia.org/wiki/Weinstein_conjecture
Wikipedia list of conjecturesWeinstein, A. (1979). "On the hypotheses of Rabinowitz' periodic orbit theorems". Journal of Differential Equations 33 (3): 353–358. doi:10.1016/0022-0396(79)90070-6.
75
Ax–Kochen theorem19784220083048119167#DIV/0!#REF!#REF!#REF!Model theory
http://en.wikipedia.org/wiki/Ax%E2%80%93Kochen_theorem
Wikipedia list of conjecturesBrown, Scott Shorey (1978), "Bounds on transfer principles for algebraically closed and complete discretely valued fields", Memoirs of the American Mathematical Society 15 (204), ISBN 978-0-8218-2204-3, ISSN 0065-9266, MR 494980
76
Serre's modularity conjecture19754520083343114157#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Serre%27s_modularity_conjecture
Wikipedia list of conjecturesSerre, Jean-Pierre (1975), Valeurs propres des opérateurs de Hecke modulo l, "Journées Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, 1974)", Astérisque (Paris: Société Mathématique de France), 24–25: 109–117, ISSN 0303-1179, MR 0382173
77
Beilinson conjecture19853520092458126184#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Beilinson_conjecture
Wikipedia list of conjecturesA. A. Beilinson, Higher regulators and values of L-functions, Journal of Soviet Mathematics 30 (1985), 2036–2070
78
Scheinerman's conjecture19843620092556126182#DIV/0!#REF!#REF!#REF!Planar graphs
http://en.wikipedia.org/wiki/Scheinerman%27s_conjecture
Wikipedia list of conjecturesScheinerman, E. R. (1984), Intersection Classes and Multiple Intersection Parameters of Graphs, Ph.D. thesis, Princeton University.
79
Erdős–Menger conjecture19744620093542112154#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Menger_conjecture#Infinite_graphs
List of conjectures by Paul Erdős
80
Road coloring problem19705020093938106144#DIV/0!#REF!#REF!#REF!Graph theory
http://en.wikipedia.org/wiki/Road_coloring_conjecture
Wikipedia list of conjecturesAdler, R.L.; Weiss, B. (1970), Similarity of automorphisms of the torus, Memoires of the American Mathematical Society 98.
81
Ramanujan–Petersson conjecture193090200979164359#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Ramanujan%E2%80%93Petersson_conjecture
Wikipedia list of conjecturesPetersson, H. (1930), "Theorie der automorphen Formen beliebiger reeller Dimension und ihre Darstellung durch eine neue Art Poincaréscher Reihen.", Mathematische Annalen (in German) 103 (1): 369–436, doi:10.1007/BF01455702, ISSN 0025-5831
82
Carathéodory conjecture192496200985143246#DIV/0!#REF!#REF!#REF!
Differential Geometry
http://en.wikipedia.org/wiki/Carath%C3%A9odory_conjecture
Wikipedia list of conjecturesSitzungsberichte der Berliner Mathematischen Gesellschaft, 210. Sitzung am 26. März 1924, Dieterichsche Universitätsbuchdruckerei, Göttingen 1924
83
Erdős distinct distances problem194674201064205676#DIV/0!#REF!#REF!#REF!Discrete geometry
http://en.wikipedia.org/wiki/Erd%C5%91s_distinct_distances_problem
List of conjectures by Paul Erdős
84
Atiyah conjecture19764420113542112154#DIV/0!#REF!#REF!#REF!
Differential geometry
http://en.wikipedia.org/wiki/Atiyah_conjecture
Wikipedia list of conjecturesAtiyah, M. F (1976). "Elliptic operators, discrete groups and von Neumann algebras". Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974). Paris: Soc. Math. France. pp. 43–72. Astérisque, No. 32–33.
85
abc conjecture19853520122753123176#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Abc_conjecture
Wikipedia list of conjecturesMasser, D. W. (1985). "Open problems". In Chen, W. W. L. Proceedings of the Symposium on Analytic Number Theory. London: Imperial College
86
Hsiang–Lawson's conjecture19705020124234103137#DIV/0!#REF!#REF!#REF!
Differential geometry
http://en.wikipedia.org/wiki/Lawson%27s_conjecture
Wikipedia list of conjectures Lawson, H. Blaine, Jr. (1970). "The unknottedness of minimal embeddings". Invent. Math. 11 (3): 183–187. doi:10.1007/BF01404649.
87
Elliott–Halberstam conjecture1965552013483096126#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Elliott%E2%80%93Halberstam_conjecture
Wikipedia list of conjecturesBombieri, E. (1965). "On the large sieve". Mathematika 12: 201–225. doi:10.1112/s0025579300005313.
88
Goldbach's weak conjecture192397201390132740#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture
Wikipedia list of conjecturesWeisstein, Eric W., "Goldbach Conjecture", MathWorld.
89
Polignac's conjecture184917120131645611#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/De_Polignac%27s_conjecture
Wikipedia list of conjecturesAlphonse de Polignac, Recherches nouvelles sur les nombres premiers. Comptes Rendus des Séances de l'Académie des Sciences (1849)
90
Twin Prime184917120141654610#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Twin_prime
Wikipedia list of conjecturesMcKee, Maggie (14 May 2013). "First proof that infinitely many prime numbers come in pairs". Nature. ISSN 0028-0836.
91
Goldbach's conjecture1742278Not Resolved000#DIV/0!#REF!#REF!#REF!
Analytic number theory
http://en.wikipedia.org/wiki/Goldbach%27s_conjecture
Wikipedia list of conjecturesDeshouillers, J.-M.; Effinger, G.; te Riele, H. & Zinoviev, D. (1997). "A complete Vinogradov 3-primes theorem under the Riemann hypothesis". Electronic Research Announcements of the American Mathematical Society 3 (15): 99–104. doi:10.1090/S1079-6762-97-00031-0
92
Pillai's conjecture1844176Not Resolved000#DIV/0!#REF!#REF!#REF!
Diophantine equations
http://en.wikipedia.org/wiki/Pillai%27s_conjecture#Pillai.27s_conjecture
Wikipedia list of conjecturesCatalan, Eugene. (1844): Note extraite d’une lettre adressée à l’éditeur. J. Reine Angew. Math., 27:192
93
Kummer–Vandiver conjecture1849171Not Resolved000#DIV/0!#REF!#REF!#REF!Algebraic K-theory
http://en.wikipedia.org/wiki/Vandiver%27s_conjecture
Wikipedia list of conjecturesBuhler, Joe; Crandall, Richard; Ernvall, Reijo; Metsänkylä, Tauno; Shokrollahi, M. Amin (2001), Irregular primes and cyclotomic invariants to 12 million, in Bosma, Wieb, "Computational algebra and number theory. Proceedings of the 2nd International Magma Conference held at Marquette University, Milwaukee, WI, May 12–16, 1996.", Journal of Symbolic Computation 31 (1): 89–96, doi:10.1006/jsco.1999.1011, ISSN 0747-7171, MR 1806208
94
Pollock octahedral numbers conjecture
1850170Not Resolved000#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Pollock_octahedral_numbers_conjecture
List of unsolved problems in mathematics
95
Bunyakovsky conjecture1857163Not Resolved000#DIV/0!#REF!#REF!#REF!Polynomial
http://en.wikipedia.org/wiki/Bunyakovsky_conjecture
Wikipedia list of conjecturesBouniakowsky, V. (1857). "Nouveaux théorèmes relatifs à la distinction des nombres premiers et à la décomposition des entiers en facteurs". Mém. Acad. Sc. St. Pétersbourg 6: 305–32
96
Riemann hypothesis1859161Not Resolved000#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Riemann_hypothesis
Millenium Prize Problems
97
Brocard's problem1876144Not Resolved000#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Brocard%27s_problem
List of unsolved problems in mathematics
98
Catalan–Mersenne number conjecture
1876144Not Resolved000#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Catalan%27s_Mersenne_conjecture#The_Catalan.E2.80.93Mersenne_number_conjecture
List of unsolved problems in mathematics
99
Unicity conjecture for Markov numbers
1879141Not Resolved000#DIV/0!#REF!#REF!#REF!
Diophantine geometry
http://en.wikipedia.org/wiki/Markov_number
Wikipedia list of conjecturesMarkoff, A. "Sur les formes quadratiques binaires indéfinies". Mathematische Annalen (Springer Berlin / Heidelberg). ISSN 0025-5831.
100
Oppermann's conjecture1882138Not Resolved000#DIV/0!#REF!#REF!#REF!Number theory
http://en.wikipedia.org/wiki/Oppermann%27s_conjecture
Wikipedia list of conjecturesOppermann, L. (1882), "Om vor Kundskab om Primtallenes Mængde mellem givne Grændser", Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger og dets Medlemmers Arbejder: 169–179