Top 100 unsolved math problems by their estimated public recognition. The rankings differ quite a bit from the importance rankings! 1. Riemann Hypothesis ↑ 1 2. P versus NP ↓ 1 3. Collatz conjecture ↑ 158 4. Goldbach conjecture ↑ 18 5. Twin Prime Conjecture ↑ 15 6. Navier–Stokes existence and smoothness (Fefferman A) ↓ 2 7. Polynomial-time classical integer factorization ↑ 9 8. Yang–Mills existence and mass gap ↓ 5 9. abc conjecture ↑ 3 10. Birch and Swinnerton-Dyer conjecture ↓ 4 11. Existence of an odd perfect number ↑ 228 12. Normality of π ↑ 289 13. Hodge conjecture ↓ 8 14. Infinitude of Mersenne primes ↑ 231 15. Sums of three cubes representation conjecture ↑ 390 16. Beal’s conjecture ↑ 332 17. Minimal superpermutation length ↑* 18. Magic square of squares ↑* 19. Multiplicative persistence bound of 11 ↑* 20. Generalized Riemann Hypothesis for Dirichlet L-functions ↓ 11 21. Square peg problem ↑ 461 22. BQP versus NP: complete language-class relation ↓ 5 23. Chromatic number of the plane ↑ 215 24. Exact Ramsey number R(5,5) ↑* 25. Algebraic independence of e and π ↑ 132 26. Irrationality of Euler’s constant ↑ 252 27. Kelvin problem: least-area partitions into unit-volume cells ↑* 28. Graph isomorphism in polynomial time ↑ 52 29. Perfect cuboid problem ↑* 30. Existence of one-way functions ↓ 22 31. Matrix-multiplication exponent equals two ↓ 5 32. Unconditional separation of BQP from BPP ↓ 13 33. Lonely runner conjecture ↑* 34. Exact kissing numbers in dimensions greater than four ↑ 315 35. Graham–Rothschild hypercube Ramsey problem: exact planar K₄ threshold ↑* 36. Infinitude of Fermat primes ↑ 458 37. Legendre’s conjecture ↑ 270 38. No-three-in-line problem ↑* 39. Infinitude of amicable pairs ↑* 40. Landau’s fourth problem: primes of the form n² + 1 ↑ 140 41. Erdős–Straus conjecture ↑* 42. Infinitude of Sophie Germain primes ↑ 269 43. Polignac’s conjecture ↑ 59 44. Higher-dimensional Euclidean Kakeya conjecture ↓ 6 45. Frankl’s union-closed sets conjecture ↑ 358 46. Unique Games Conjecture ↓ 12 47. Infinitude of Fibonacci primes ↑* 48. Brocard’s problem ↑* 49. Thomson problem ↑ 319 50. Gauss circle problem ↑ 192 51. Erdős–Szekeres convex polygon problem ↑ 294 52. Montgomery’s pair correlation conjecture ↑ 23 53. Congruent number problem ↑ 79 54. NP versus coNP ↓ 41 55. Local connectivity of the Mandelbrot set ↑ 66 56. Smooth four-dimensional Poincaré conjecture ↓ 35 57. Edge-unfolding of convex polyhedra ↑* 58. Schanuel’s conjecture ↓ 30 59. Catalan–Dickson conjecture on boundedness of aliquot sequences ↑* 60. Erdős’s conjecture on divergent reciprocal sums and long arithmetic progressions ↑ 70 61. Hardy–Littlewood prime k-tuple conjecture ↓ 43 62. Existence of a periodic trajectory in every triangular billiard ↑* 63. Elliott–Halberstam conjecture ↑ 24 64. Hadwiger’s conjecture ↑ 15 65. Irrationality of ζ(5) ↑ 268 66. P versus PSPACE ↓ 52 67. P versus BPP ↓ 40 68. Selfridge’s conjecture on the smallest Sierpiński number ↑* 69. Erdős–Rado sunflower conjecture ↑ 77 70. Kolakoski sequence half-density conjecture ↑* 71. Polynomial-time unknot recognition ↑ 268 72. Inverse Galois problem over the rationals ↓ 23 73. Conway’s thrackle conjecture ↑* 74. Gilbreath’s conjecture ↑* 75. Infinitude of cousin primes ↑* 76. Conway’s 99-graph problem ↑* 77. Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions ↓ 34 78. Resolvent degree of the general degree-seven polynomial ↑ 183 79. Hilbert’s sixteenth problem, second part ↓ 40 80. Graph reconstruction conjecture ↑ 242 81. Singmaster’s conjecture on Pascal’s triangle ↑* 82. Exponential Time Hypothesis for 3-SAT ↓ 40 83. Irrationality of Catalan’s constant ↑ 339 84. Borel’s normal number conjecture for irrational algebraic numbers ↑ 54 85. Finite projective planes of non-prime-power orders ↑ 308 86. Fermat–Catalan conjecture ↑ 172 87. Convergence of the Flint Hills series ↑* 88. Existence of an odd weird number ↑* 89. Maximum packing density of regular tetrahedra ↑* 90. Exact exponential growth constant of cap sets in F₃ⁿ ↑* 91. Invariant subspace problem for Hilbert-space operators ↑ 14 92. Fejes Tóth’s sausage conjecture ↑* 93. Cramér’s conjecture on the limsup of normalized prime gaps ↑ 61 94. Kobon triangle problem ↑* 95. Four-distance problem for the unit square ↑* 96. Artin’s primitive root conjecture ↑ 96 97. Tammes problem: optimal spherical packing for general N ↑* 98. Extended Riemann Hypothesis for Dedekind zeta functions ↓ 88 99. Ringel–Kotzig graceful tree conjecture ↑* 100. Global Langlands functoriality conjecture ↓ 93 Fable 5.1 and GPT-6 Astra judged 3,791 distinct pairs using shared evidence, including reviewed public sources and Wikipedia page-view data. Includes theoretical computer science and mathematical physics. ↑/↓ indicate how many places higher or lower a problem ranks by public recognition than in the overall Top 500. ↑* indicates a problem outside the overall Top 500. They will be added to