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-2351 Exponential Distribution of Normalized Prime Gaps
- Math-2352 Convexity of Injectivity Loci Under MTW
- Math-2353 Wolff Cone-Decomposition and Local-Smoothing Conjectures
- Math-2354 Algebraic Dimension and Reduction of Hyperkähler Manifolds
- Math-2355 Variational Principles for Dilute Spin Systems
- Math-2356 Local $p$-Adic Section Conjecture
- Math-2357 Alperin Weight Conjecture and Perfect Localities
- Math-2358 The Lex-Plus-Powers Betti Number Conjecture
- Math-2359 Parity of 2-Primary Tate–Shafarevich Groups
- Math-2360 Section Conjecture for Hyperbolic Curves Without Boundary Points
- Math-2361 Section Conjecture for Hyperbolic Curves
- Math-2362 Decidability of Rational Points over Number Fields
- Math-2363 Transience Implies Ballisticity for Uniformly Elliptic RWRE
- Math-2364 Weak Zariski Decompositions of Pseudo-Effective Divisors
- Math-2365 Unique Games Approximation-Threshold Conjecture
- Math-2366 Naimark's problem for $C^*$-algebras
- Math-2367 The Toms–Winter regularity conjecture
- Math-2368 Naimark's Problem for Nonseparable $C^*$-Algebras
- Math-2369 Birkhoff Conjecture for Integrable Convex Billiards
- Math-2370 Rigidity and Assembly Conjectures for Discrete Groups
- Math-2371 Surface Subgroups of Word-Hyperbolic Groups
- Math-2372 Strict Cost–$\ell^2$-Betti Inequalities for Free Group Actions
- Math-2373 Multipoint Seshadri Constants and Nagata-Type Conjectures
- Math-2374 Brennan-Type Integrability for Crescent-Domain Conformal Maps
- Math-2375 Forcing Graphs for Quasirandomness
- Math-2376 Forcing Conjecture for Bipartite Cyclic Graphs
- Math-2377 Rational Ellipticity, Entropy, Euler Characteristic, and Formality
- Math-2378 Algebraic K-Theory and Rigidity Conjectures for Discrete Groups
- Math-2379 Uniform Rectifiability from Bounded Riesz Transforms
- Math-2380 Higher-Dimensional Riesz Transforms and Uniform Rectifiability
- Math-2381 Hill Conjecture for Complete Graph Crossing Numbers
- Math-2382 Classification of Class-VII Complex Surfaces
- Math-2383 Inductive Proofs of Alperin Conjectures
- Math-2384 Inductive Blockwise Alperin Weight Condition
- Math-2385 Uniqueness of Tangent Flows in Mean Curvature Flow
- Math-2386 The Zariski Multiplicity Problem
- Math-2387 De Giorgi Conjecture for Allen–Cahn
- Math-2388 Log Abundance for Semi-Log-Canonical Pairs
- Math-2389 Euclidean Ramsey Configurations and Sphericity
- Math-2390 Toms–Winter Regularity Conjecture
- Math-2391 $\mathcal Z$-Stability and Regularity of Nuclear $C^*$-Algebras
- Math-2392 Kadison–Kastler Conjecture for Separable $C^*$-Algebras
- Math-2393 The Kadison–Kastler conjecture for $C^*$-algebras
- Math-2394 Trace-Cone Classification after Razak–Jacelon Stabilization
- Math-2395 Jiang–Su Embeddings in Character-Free Central Sequence Algebras
- Math-2396 Subhomogeneous Character-Free Subalgebras of Infinite Tensor Powers
- Math-2397 Comparison Properties and Jiang–Su Absorption
- Math-2398 Nuclear Dimension after Jiang–Su Stabilization
- Math-2399 Variance Conjecture for Log-Concave Random Vectors
- Math-2400 Dual-Graph Generation of Tautological Relations