Top Open Problems
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-4151 Exponential Degree Growth in Composita of Fibers
- Math-4152 Square-Root Box Discrepancy for Multidimensional Permutations
- Math-4153 Shortest Nontrivial Laws for Symmetric Groups
- Math-4154 Three-Event Correlation Inequalities in Product Spaces
- Math-4155 Maximum Girth-to-Diameter Ratio
- Math-4156 Asymptotic Enumeration of Arithmetic-Progression-Free Sets
- Math-4157 Finite-Time Blowup for Three-Dimensional Zakharov–Kuznetsov
- Math-4158 Long-Time Asymptotics of Homogeneous Ricci Flows
- Math-4159 Hodge Spectral Gaps Under Ricci Bounded Convergence
- Math-4160 Higher-Codimension Weyl Laws and Equidistributed Min–Max Surfaces
- Math-4161 Higher-Dimensional Smale Conjecture for 2-Convex Spheres
- Math-4162 Arithmetic Finiteness of Gushel–Mukai Threefolds
- Math-4163 Deformation Invariance of Rationality
- Math-4164 Generic Regularity of Two-by-Two Conservation Laws
- Math-4165 Integral Reduced Norms in Division-Algebra K-Theory
- Math-4166 Zariski–Nisnevich Comparison for Relative Milnor K-Theory
- Math-4167 Motives and Higher Chow Groups with Modulus
- Math-4168 Descent of Intermediate Jacobians
- Math-4169 Regular Representatives of Homotopy Classes Between Spheres
- Math-4170 Gradient-Tentacle Certificates for Polynomial Nonnegativity
- Math-4171 Mod-p Formality of Little-Disks Cochains
- Math-4172 Decidability of Subgroup Membership in SL3 of the Integers
- Math-4173 Algorithms and Exponent Bounds for Dimension Subgroups
- Math-4174 Adelic Harmonic Metrizations over Global Fields
- Math-4175 Dense Frobenius Eigenvectors in Completed Enveloping Algebras
- Math-4176 Density and Closure of Mixed Hodge Loci
- Math-4177 Type-I Rigidity of Boundary-Transitive Tree Groups
- Math-4178 Scope of the Generalized Tracial-Rank-One Class
- Math-4179 Clopen Strict Comparison for Amenable Cantor Actions
- Math-4180 Thom’s Conjecture for the Hyperfinite Factor’s Unitary Group
- Math-4181 AF Full Group $C^*$-Algebras and Local Finiteness
- Math-4182 Equality of Rokhlin and Sofic Entropies
- Math-4183 Sublinear Generator Growth of Higher-Rank Lattices
- Math-4184 Return Probabilities of Amenable Groups with Exponential Growth
- Math-4185 Measurable Local Lemma for Arbitrary Group Actions
- Math-4186 Symplectic Reduction of Visible Polar Representations
- Math-4187 Categorical Functors from Soergel Bimodules to Flag Hilbert Schemes
- Math-4188 Generators and Support Loci of Bernstein–Sato Ideals
- Math-4189 Stringy Euler Numbers under Mori Flips
- Math-4190 Stringy Euler Numbers under Divisorial Contractions
- Math-4191 Intrinsic Diophantine Exponents of Submanifolds
- Math-4192 Removing Logarithmic Losses in Multiplicative Approximation
- Math-4193 Decidability of Analytic Solutions to Algebraic Equations
- Math-4194 Northcott Property for Bounded-Degree Composita
- Math-4195 Northcott Property for Totally Real Integer Rings
- Math-4196 Sharp Transcendence Bounds for the Modular J-Function
- Math-4197 HTP-Complete Polynomials over Rational Subrings
- Math-4198 Extremality Criteria for Positive-Characteristic Valued Fields
- Math-4199 Composite of Unrelated Field-Theory Questions
- Math-4200 Degree Definability and Existential Theory of Rational Function Fields