Mathematics catalogue
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-51 P versus NP ∩ coNP
- Math-52 BQP versus QMA
- Math-53 NEXP versus P/poly
- Math-54 Permanent versus Determinant over C
- Math-55 Permanent–Determinant Separation Through Geometric Complexity Theory
- Math-56 Derandomization of Polynomial Identity Testing
- Math-57 Superpolynomial Lower Bounds for Frege Propositional Proof Systems
- Math-58 Superlinear Circuit Lower Bounds for Explicit Boolean Functions
- Math-59 Hardy-Littlewood Prime k-Tuple Conjecture
- Math-60 Bateman-Horn conjecture
- Math-61 Schinzel's Hypothesis H
- Math-62 Collatz Conjecture
- Math-63 Hadwiger Conjecture
- Math-64 Twin Prime Conjecture
- Math-65 Goldbach's Conjecture
- Math-66 Lindelöf Hypothesis
- Math-67 Montgomery's Pair Correlation Conjecture
- Math-68 Elliott-Halberstam Conjecture
- Math-69 Leopoldt's Conjecture
- Math-70 Cannon's Conjecture
- Math-71 The Jacobian Conjecture
- Math-72 Two-Dimensional Jacobian Conjecture in Characteristic Zero
- Math-73 Kannan–Lovász–Simonovits Isoperimetric Conjecture
- Math-74 Prove the Penrose inequality or present a counterexample
- Math-75 Modularity of Elliptic Curves over Number Fields (End_K(E)=Z)
- Math-76 Modularity of Elliptic Curves over Totally Real Fields
- Math-77 Siegel Zeros
- Math-78 Finiteness of the Tate-Shafarevich Group for Elliptic Curves
- Math-79 Zilber-Pink Conjecture on Unlikely Intersections
- Math-80 Weight–Monodromy Conjecture
- Math-81 The Mumford-Tate Conjecture for Abelian Varieties over Number Fields
- Math-82 Green-Griffiths-Lang Conjecture on entire curves in varieties of general type
- Math-83 Effective Mordell Bounds for Rational Points
- Math-84 Unbounded Ranks of Elliptic Curves over Q
- Math-85 Grothendieck–Katz p-curvature conjecture
- Math-86 Regular Inverse Galois Problem over Q
- Math-87 Cohen-Lenstra class-group distributions for quadratic number fields
- Math-88 Chowla conjecture on correlations of the Liouville function
- Math-89 Sarnak's Möbius Disjointness Conjecture
- Math-90 Keating-Snaith Conjecture on Moments of the Riemann Zeta Function
- Math-91 Global Regularity of Solutions to the Inviscid Surface Quasi-Geostrophic Equation
- Math-92 Global Regularity of the 3D Incompressible Magnetohydrodynamic Equations
- Math-93 No-Slip Vanishing-Viscosity Limit in the Energy Norm
- Math-94 Soliton Resolution for the Focusing Energy-Critical Wave Equation without Radial Symmetry
- Math-95 Entanglement Area Law for 2D Gapped Quantum Systems
- Math-96 Extended States in the Anderson Model
- Math-97 Conformal Field Theory Limit of the Critical Three-Dimensional Ising Model
- Math-98 Non-Perturbative Construction and Non-Triviality of 4D Euclidean Phi4 Quantum Field Theory
- Math-99 Bose-Einstein Condensation in Continuum Models
- Math-100 Local connectivity of the Mandelbrot set