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-5051 Virtual Fibrations with Precisely Controlled Finiteness Properties
- Math-5052 Recursive Homological Filling and the Word Problem
- Math-5053 Bounded Conjugation-Invariant Metrics on Higher-Rank Lattices
- Math-5054 Interval Structure of Cohomology-Vanishing Exponents
- Math-5055 Belief-Propagation Uniqueness Boundary for Randomly Colored Ising Models
- Math-5056 Sharp Min-Entropy Power Inequalities
- Math-5057 Boundary Curvature and Stickiness of Nonlocal Minimal Surfaces
- Math-5058 Habiro-Ring Refinements of Three-Manifold Quantum Invariants
- Math-5059 Outer automorphisms of oligomorphic groups in finite languages
- Math-5060 Determinants of prime alternating achiral knots
- Math-5061 Continuity and strict monotonicity of Nyman–Beurling distances
- Math-5062 Irrational strict local maxima of the fractional-part autocorrelation
- Math-5063 Commutative semigroups with cancellative endomorphism semigroups
- Math-5064 Element orders in locally finite products of prime-power subgroups
- Math-5065 Multiplicative groups of braces with finitely generated addition
- Math-5066 Exact vertical tangent defects for canonical genus-four curves
- Math-5067 Proper-point defects and the degree-21 bottleneck
- Math-5068 A topological node-parity reduction for the next-to-minimal Welschinger sign
- Math-5069 Koszul complexes as derived intersections and splitting obstructions
- Math-5070 Rank correction, top-Chern criterion, and an affine-surface counterexample
- Math-5071 Arc-space termination and a Betti budget for standard smooth flips
- Math-5072 Frobenius contraction and a log-canonical non-F-pure stress test for the symbolic cube
- Math-5073 Sharp factoriality threshold and defect-one equality cases
- Math-5074 Q-Cartierness versus pluricanonical base change
- Math-5075 Quotient stacks, inertia obstructions, and polarized point blowups
- Math-5076 Explicit diagonal 1-PS bounds and the current hypersurface GIT classification status
- Math-5077 Nonnested span ranks and corrected jet-span estimates for Hilbert weights
- Math-5078 Normal directions and forced nodes for two explicit stable limits
- Math-5079 A level-cover ramification budget for rational and affine coarse curves in M_g
- Math-5080 Arithmetic surjectivity forces recurrence of locally soluble fibers
- Math-5081 Correcting the threshold and computing the singular locus
- Math-5082 Monotone means and a Poisson moving-target limit for complete-intersection curves
- Math-5083 Additive gaps and an affine-coordinate audit
- Math-5084 Odd-degree Jacobian mean and its arithmetic correction
- Math-5085 A cubefree local model for trigonal discriminants
- Math-5086 Variance coefficients as hook multiplicities
- Math-5087 Polynomial Ramanujan sums and finite von Mangoldt expansions
- Math-5088 Wild ramification strata and an exact characteristic-two point-count law
- Math-5089 Orthogonal low-lying zeros and forced-zero deflation
- Math-5090 Quantitative averages of function-field prime-tuple singular series
- Math-5091 Section retractions obstruct the fibre-product line topoi
- Math-5092 Solved intended local pencil problem and dyadic rank-seven annuli
- Math-5093 Thin-deleted asymptotic and an explicit split-fibre surplus
- Math-5094 Galois-stable cyclotomic interlacing pairs
- Math-5095 An explicit geometric Picard-rank-one quintic over F_2
- Math-5096 Fixed-length sums of 2/(x^2-2)
- Math-5097 The infinity 5-torsion line and Kummer quotient of the pentagonal quintic
- Math-5098 An explicit cubic point and its descent certificate
- Math-5099 A certified orbit-lattice algorithm for M_3(Z)
- Math-5100 A representation-sensitive decidability dichotomy for integer rotation constraints