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-4501 Alcuin Numbers and Recognition of Small Boat Graphs
- Math-4502 Linear Optimization over Mixed-Integer Bipartite Systems
- Math-4503 Achievable External Behaviors Under Controller Interconnection
- Math-4504 Circular Assume–Guarantee Reasoning for General Systems
- Math-4505 Optimal Feasible Sets from Quantized Trajectory Observations
- Math-4506 Global Observability from Negative Gramian Curvature
- Math-4507 Independence and Density Thresholds for Cuckoo Hashing
- Math-4508 Sensitivity Growth Under Boolean Conjunctions
- Math-4509 Orbit-Closure Obstructions for Permanent–Determinant Separation
- Math-4510 Decidability of Universal Factor Languages
- Math-4511 Symmetry-Preserving Evaluation of Orbitwise Generating Functions
- Math-4512 Integer Carathéodory Property for Intersecting Matroid Base Polytopes
- Math-4513 Integer Carathéodory Property for Arborescence Polytopes
- Math-4514 Greedy Decomposition of the Spanning-Tree Polytope
- Math-4515 Density and Geometry Recovery from Nearest-Neighbor Graphs
- Math-4516 Polynomial-Time Algorithms for High-Dimensional Private Queries
- Math-4517 Multicolored Sunflower Conjecture over Ternary Vector Spaces
- Math-4518 Worst-Case Inputs for Smoothed Caching Complexity
- Math-4519 Polynomial Tractability of Permutation-Invariant Integration
- Math-4520 Decidability and Finiteness of Rational Joint Spectral Radii
- Math-4521 Efficient Moment Relaxations for Polynomial Optimization
- Math-4522 Witness Pseudorandom Functions from Witness Encryption
- Math-4523 Reusable Garbled RAM under Weaker Assumptions
- Math-4524 Polynomial-Time Minimization of K-Submodular Functions
- Math-4525 Complexity of Maximizing Initial Odd Ears
- Math-4526 Additive Integrality Gap for Ring Loading
- Math-4527 Exact Integrality Gap for Capacitated Facility Location
- Math-4528 Compact Constant-Gap Relaxations for Capacitated Facility Location
- Math-4529 Constructive Selection for Bessel Sequences
- Math-4530 Complexity of Embedding Two-Complexes in Three-Manifolds
- Math-4531 Complexity and Rank of Completely Positive Matrices
- Math-4532 Volume of the Boolean Quadric Polytope
- Math-4533 Core Points of Transitive Permutation Groups
- Math-4534 Consequences of Indistinguishability Obfuscation
- Math-4535 Accurate Answers to Adaptively Chosen Statistical Queries
- Math-4536 Randomized Communication Complexity of Distributed Triangle Detection
- Math-4537 Overlap Gaps and Algorithmic Hardness of Submatrix Detection
- Math-4538 Simultaneously Adaptive Universal Source Coding
- Math-4539 Complexity of Bray’s Involution-Centralizer Algorithm
- Math-4540 Sublinear Membership Testing in Two-Generator Matrix Groups
- Math-4541 Computing Hecke Operators for Arithmetic-Group Cohomology
- Math-4542 Security of Interactive Lattice-Based Group Key Exchange
- Math-4543 Assumptions and Function Classes for Function Secret Sharing
- Math-4544 Round Complexity of Non-Malleable Commitments
- Math-4545 Average-Case Hardness of Quasi-Cyclic Code Problems
- Math-4546 Sampling Complexity of Hyperbolic-Cross Approximation
- Math-4547 Resolution Lower Bounds for Clique Certification
- Math-4548 Practical Sum-of-Squares Tensor Completion
- Math-4549 Information–Computation Gaps in Sparse Linear Regression
- Math-4550 Global Optimization of Overparameterized Shallow Networks