Number theory
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-2 The Riemann Hypothesis
- Math-6 Birch and Swinnerton-Dyer Conjecture
- Math-7 Global Langlands Functoriality Conjecture
- Math-12 Extended Riemann hypothesis for Dedekind zeta functions
- Math-13 Generalized Riemann Hypothesis for Dirichlet L-functions
- Math-14 Schanuel's Conjecture
- Math-15 Vojta's Diophantine Approximation Conjecture
- Math-18 Hilbert's Tenth Problem over the Rationals
- Math-20 Fontaine–Mazur geometric Galois-representation conjecture
- Math-21 Hilbert's 12th Problem: Extension of Kronecker-Weber Theorem
- Math-23 Birch & Swinnerton-Dyer conjecture
- Math-31 Equivariant Tamagawa number conjecture: Burns-Flach Conjecture4 package
- Math-32 Artins Conjecture on the Holomorphy of Non-Abelian Artin L-Functions
- Math-35 ABC Conjecture
- Math-40 Generalized Ramanujan conjecture for automorphic representations
- Math-59 Hardy-Littlewood Prime k-Tuple Conjecture
- Math-60 Bateman-Horn conjecture
- Math-61 Schinzel's Hypothesis H
- Math-62 Collatz 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-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-81 The Mumford-Tate Conjecture for Abelian Varieties over Number Fields
- Math-83 Effective Mordell Bounds for Rational Points
- Math-84 Unbounded Ranks of Elliptic Curves over Q
- Math-87 Cohen-Lenstra class-group distributions for quadratic number fields
- Math-88 Chowla conjecture on correlations of the Liouville function
- Math-90 Keating-Snaith Conjecture on Moments of the Riemann Zeta Function
- Math-103 Grothendieck–Teichmüller Conjecture
- Math-119 Torsion Conjecture for Abelian Varieties of Dimension at Least Two
- Math-120 Uniform Boundedness Conjecture for Rational Points on Curves
- Math-128 Bombieri–Lang conjecture
- Math-130 Dickson's Conjecture
- Math-132 Deligne's Conjecture for Critical Motive Values
- Math-137 Littlewood Conjecture
- Math-139 Selberg's 1/4 conjecture
- Math-140 Bunyakovsky Conjecture
- Math-141 Szpiro's conjecture
- Math-142 Polignac's Conjecture
- Math-146 Erdős Problem #52
- Math-152 Density Hypothesis for Riemann-Zeta Zeros
- Math-154 Erdős Conjecture on Arithmetic Progressions