Mathematics catalogue
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 Sampling Complexity of Hyperbolic-Cross Approximation
- Math-4602 Resolution Lower Bounds for Clique Certification
- Math-4603 Practical Sum-of-Squares Tensor Completion
- Math-4604 Information–Computation Gaps in Sparse Linear Regression
- Math-4605 Global Optimization of Overparameterized Shallow Networks
- Math-4606 Extrapolating Clusterings from Semidefinite Subsamples
- Math-4607 Local Approximation of Random-Graph Semidefinite Programs
- Math-4608 Uniqueness of Equilibria in Rank-One Bimatrix Games
- Math-4609 Proximity and Sparsity of Optimal Integer Solutions
- Math-4610 Convergence Rates for Convex-Body Bounds
- Math-4611 Fast Low-Rank Maximum-Weight Assignment
- Math-4612 Integrality Gaps for Directed Linear k-Cut
- Math-4613 Hardness of Root-Dependent Spanning-Tree Optimization
- Math-4614 Hardness of Path-Cost Arborescence Optimization
- Math-4615 Polynomial-Time Comparison of Sparse Algebraic Power Sums
- Math-4616 Degree-Utility Optimization in Graphs
- Math-4617 Real Tau Conjecture for Depth-Four Circuits
- Math-4618 Karchmer–Raz–Wigderson Composition Conjecture
- Math-4619 Subquadratic Approximation for Longest Common Subsequences
- Math-4620 Geometric Explanations and Polynomial Pivot Rules for Simplex
- Math-4621 Sharp Smoothed Complexity of Simplex Pivot Rules
- Math-4622 Theta Invariants and New Families of MRD Codes
- Math-4623 Explicit RIP Matrices Beyond Square-Root Sparsity
- Math-4624 Square-Root Sparsity for Explicit RIP Matrices
- Math-4625 Sample Complexity of Vertex-Distribution-Free Graph Testing
- Math-4626 Complexity of Approximate Counting in Spin Systems
- Math-4627 Exact Higher-Order Matrix Decomposability
- Math-4628 Semidefinite Hierarchies for Equiangular Line Bounds
- Math-4629 Computational Recognition of Polytope Face Vectors and Cones
- Math-4630 Recognition of Virtually Special Hyperbolic Three-Manifolds
- Math-4631 Minimum Crossing Realizations of Spatial Polygon Angle Sequences
- Math-4632 Submultiplicativity Gaps for Stabilizer Extent
- Math-4633 Complexity of Submodular $k$-Partition
- Math-4634 Integer Programming with Bounded Subdeterminants
- Math-4635 Extension Complexity of Inscribed Fixed-Dimensional Polytopes
- Math-4636 Arborescences Induced by Linear-Programming Pivot Rules
- Math-4637 Near-Optimal Algorithms for Mixed-Integer Convex Optimization
- Math-4638 Linear Bounds for Minimally Integer-Infeasible Systems
- Math-4639 Approximating Maximum Nonsymmetric Principal Subdeterminants
- Math-4640 Better-Than-Two Approximation for Multiplicative Connectivity Augmentation
- Math-4641 Balanced Signings in the Subtour Polytope
- Math-4642 Compact Representations of Four-Thirds Near-Mincuts
- Math-4643 Better Approximations for Unrelated Graph Balancing
- Math-4644 Deterministic Optimization of Top-$k$ Perfect-Matching Edges
- Math-4645 Property Testing for Noncommutative Quantum Functions
- Math-4646 Algebraic and Graph-Property Tests for Quantum Functions
- Math-4647 Canonical Paths Versus Spectral Independence
- Math-4648 Good Locally Testable Quantum Codes and Linear-Rate PCPs
- Math-4649 Convergence and Effective Rates of Unwinding Series
- Math-4650 Phase Retrieval from Gabor and Wavelet Magnitudes