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-4051 Valid Orderings of Subsets of Finite Groups
- Math-4052 Graham’s Rearrangement Conjecture over Prime Fields
- Math-4053 Cayley-Sum Constructions for Triangle Ramsey Numbers
- Math-4054 Nonfattening and Intersection Principles for Level-Set Flows
- Math-4055 Boundary Branching of Area-Minimizing Currents
- Math-4056 Coexistence of Einstein Metrics with Different Constants
- Math-4057 Stability of Noncollapsing Manifold Submetries
- Math-4058 Contractible Ricci-Nonnegative Four-Manifolds with Euclidean Growth
- Math-4059 Tensor-Factorization Uniqueness for SAW$^*$-Algebras
- Math-4060 Selflessness and Strict Comparison for Reduced Group $C^*$-Algebras
- Math-4061 Single Generation and Free-Group $C^*$-Superrigidity
- Math-4062 Gorenstein Hilbert Series for Reduced Subalgebra Zeta Functions
- Math-4063 Higher-Depth Mock Modular Forms and Polyharmonic Maass Forms
- Math-4064 Uniform Bounds for Transcendental Rational Points
- Math-4065 Generic Linear Projections and Dimensionality Type
- Math-4066 Crepant Resolutions and Smoothings of Toroidal Fano Varieties
- Math-4067 Motivic Igusa Series of Plane Curves
- Math-4068 Small Resolutions Detected by Symplectic Cohomology
- Math-4069 Moments of Quadratic L-Functions over Function Fields
- Math-4070 Reported Uniform Stability Bound for Twisted Braid-Group Homology
- Math-4071 Primitive-Root Orders of Elliptic-Curve Frobenius Traces
- Math-4072 Finiteness of R-Equivalence Classes in Nonabelian Cohomology
- Math-4073 Curves with Unbounded Rational-Point-to-Genus Ratio
- Math-4074 Drinfeld-Twist Classification of Set-Theoretic Solutions
- Math-4075 Root Systems and Classification of Generalized Nichols Algebras
- Math-4076 Virtual Abelianity of Unitary Yang–Baxter Braid Images
- Math-4077 Lattice Packing Conjecture for Origin-Symmetric Convex Bodies
- Math-4078 Banach–Mazur Diameter of Nonsymmetric Convex Bodies
- Math-4079 Large-Genus Hyperbolic Surfaces Above the One-Quarter Spectral Threshold
- Math-4080 Finite Length of Permutation Modules over Arbitrary Fields
- Math-4081 Structural Characterization of Exceptional Borel Graphs
- Math-4082 Automatic Action Reconstruction for Countably Categorical Structures
- Math-4083 Smooth Classification and Outer Automorphisms of Oligomorphic Groups
- Math-4084 Finiteness and Tail Decay of Infinite-Noodle Components
- Math-4085 Cycle Limits for Words in Random Permutations
- Math-4086 Radon Numbers for Unions of Convex Sets
- Math-4087 Maximum-Cut Surplus in Clique-Free Graphs
- Math-4088 Product-Free Sets in Symmetric and Alternating Groups
- Math-4089 Independent Sets in Steiner Triple Systems
- Math-4090 Comparing Monotone and Ordinary Crossing Numbers
- Math-4091 Hamiltonicity of Highly Connected Induced-Star-Free Graphs
- Math-4092 Equilateral Sets in Finite-$p$ Metric Tori
- Math-4093 Independence-Number Degeneracy in Induced-Subdivision-Free Graphs
- Math-4094 Independent Sets in Pseudorandom Regular Graphs
- Math-4095 $L^p$ Approximation for Higher-Rank Group Factors
- Math-4096 Foundations for Quantum Measurable Spaces
- Math-4097 Model Companions and Geometry of Globally Valued Fields
- Math-4098 Effective G-Function Bounds for Unlikely Intersections
- Math-4099 Elementary Equivalences for Ordered Exponential Fields
- Math-4100 Lie Structure of Formal $q$-Zeta Algebras