Mathematics
Open problems, research attempts and community review.
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-4601 Capacity Criteria for Arbitrarily Varying Channels with Causal State Information
- Math-4602 Decidability of Linear Information Inequalities
- Math-4603 Tight Bounds for Many-User Multiple-Access Coding
- Math-4604 Type-II Error Exponents in Distributed Hypothesis Testing
- Math-4605 Capacity and Reliability of Mismatched Decoding
- Math-4606 Convex Relaxations for Planted Graph Matching
- Math-4607 Gaussian Mean Testing under Information Constraints
- Math-4608 Enumeration and Typical Structure of $k$-SAT Functions
- Math-4609 Asymptotic Counts of Growing-Width $k$-SAT Functions
- Math-4610 Efficient Recognition of Cyclic Sumsets
- Math-4611 Norm Estimation from Asymmetric Black-Box Linear Operators
- Math-4612 Universal Approximation by One-Lipschitz Spline Networks
- Math-4613 Global Margin Maximization beyond the Neural Tangent Regime
- Math-4614 Cancellation-Sensitive Norms for Two-Layer Networks
- Math-4615 Algorithms for Amoeba Dimensions from Tropical Fans
- Math-4616 Geometric Criteria for Benign Overfitting
- Math-4617 Benign, Tempered, and Catastrophic Overfitting Regimes
- Math-4618 Duality and Convergence Rates in Lasserre Hierarchies
- Math-4619 Superpolynomial Lower Bounds for Dag-Like Resolution over Parities
- Math-4620 Fractional Coefficient Savings in Algebraic Proof Systems
- Math-4621 Circuit-Size Hierarchy in Bounded Arithmetic
- Math-4622 Online Model Selection for Nonparametric Classes
- Math-4623 Global Convergence of Low-Rank Multi-Penalty Optimization
- Math-4624 Pre-Asymptotic Sampling Numbers of Barron Spaces
- Math-4625 Near-Linear Subgraph Isomorphism for Acyclic Patterns
- Math-4626 Mixing Times from Spectral Independence
- Math-4627 Unconditionally Ruling Out Heuristica
- Math-4628 Semi-Supervised Sparse Gaussian Classification
- Math-4629 Moment-SOS Convergence for PDE-Constrained Variational Problems
- Math-4630 Quasilinear Finite-Field Polynomial Multiplication
- Math-4631 Adjoint-Free Approximation of Nonsymmetric Low-Rank Matrices
- Math-4632 Nash Equilibria over Unbounded Measure Spaces
- Math-4633 Integer Feasibility with Bounded Subdeterminants
- Math-4634 Fixed-Parameter Tractability of Zonotope Containment
- Math-4635 Approximating Fare-Zone Assignment on Trees
- Math-4636 Foundational Assumptions for Obfuscation, FHE, and SNARGs
- Math-4637 Efficient Verification of Distribution Properties
- Math-4638 Information-Theoretic Additive Randomized Encodings
- Math-4639 Degree Automatability of Sum-of-Squares Proofs
- Math-4640 Complexity-Bounded Computation of Maximum Destabilizing Subgroups
- Math-4641 Minimal Convex Difference Decompositions of CPWL Functions
- Math-4642 Freeness of Two-Generator Integral Matrix Groups
- Math-4643 Near-Linear List Decoding of AEL and Ta-Shma Codes
- Math-4644 Zero Submatrices in Sparse Low-Rank Matrices
- Math-4645 Optimal Bounds for Pairs of Commuting Integer Matrices
- Math-4646 Quantum Advantage in Threefold Repetition of Feige’s Game
- Math-4647 Semidefinite Relaxations for Quantum Equilibria
- Math-4648 Universal-Cover Isomorphism Algorithms for Cube Complexes
- Math-4649 Cross-Entropy Dynamics Beyond Hadamard Initialization
- Math-4650 Hidden-Layer Depth Complexity of Piecewise-Linear Functions