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-4951 Fermionic Character of Low-Lying Excitations
- Math-4952 From Dislocation Mechanics to Continuum Plasticity
- Math-4953 Nonperiodic and Nonquadratic FFT Schemes for Materials
- Math-4954 Dissipation and Interface Misorientation in Phase-Field Plasticity
- Math-4955 Ericksen Universal Deformations of Incompressible Solids
- Math-4956 Multiphysics Frameworks for Computational Homogenization
- Math-4957 Finite-Shear Hashin–Shtrikman Bounds and Rod–Hinge Deformations
- Math-4958 Lower Bounds for Hamiltonian Mass
- Math-4959 Vacuum Failure of the Third Law of Black-Hole Thermodynamics
- Math-4960 Rigorous Construction of Conformal Field Theories
- Math-4961 Open Structures in Compactified Imaginary Liouville Theory
- Math-4962 Robustness of Climate Models at Unresolved Scales
- Math-4963 Mechanisms and Scales of Tropical-Cyclone Edge Intensification
- Math-4964 Entrainment-Mediated Tropical-Cyclone Intensification
- Math-4965 Cloud-Organization Limit Cycles
- Math-4966 Dynamics Near Generic Spacetime Singularities
- Math-4967 Uniqueness of Spherical Schwarzschild–Anti-de Sitter Spacetimes
- Math-4968 Teukolsky Energy Decay on Extremal Kerr Spacetimes
- Math-4969 Stability of Extremal Critical Collapse
- Math-4970 Global Stability and Asymptotics of Cosmological Spacetimes
- Math-4971 Tensorial Mode Stability of Kerr–de Sitter Spacetimes
- Math-4972 Query Complexity and Achievable Functions in Multivariable Quantum Signal Processing
- Math-4973 Lieb–Robinson Bounds for Nonrelativistic Fermions
- Math-4974 Strong Continuity Without Ultraviolet Regularization
- Math-4975 Counterexamples to Strongly Continuous Many-Fermion Dynamics
- Math-4976 Irreducible Components of Landau Varieties
- Math-4977 Feasible High-Performance Plasma Flows for Stellarators
- Math-4978 Unique Ground-State Representability under Linear Constraints
- Math-4979 Multitask Hamiltonian Learning across Levels of Theory
- Math-4980 Reflection-Positive Two-Dimensional Quantum Field Theories with Boundary
- Math-4981 Superselection Sectors of Braided Fusion Spin Systems
- Math-4982 SU(3) Braided Fusion Spin Systems and Haah Nets
- Math-4983 Vertex Operator Algebras with Haagerup Symmetry
- Math-4984 New Quantum LDPC Codes with Good Parameters
- Math-4985 Quasi-Bosonic Ground States and Excitation Spectra
- Math-4986 The Gell–Mann–Brueckner Formula in the Thermodynamic Limit
- Math-4987 Open Problems on Spectral-Parameter Yang–Baxter Solutions
- Math-4988 Classification and Applications of Yang–Baxter Operators
- Math-4989 Orthogonal Symmetry Conjecture for Rigid Higher Categories
- Math-4990 Higher-Categorical Models of Continuous and Spacetime Symmetries
- Math-4991 Two-Categorical Interpretation of a Quantum Lattice Model
- Math-4992 Liouville Theory from the Virasoro Conformal Net
- Math-4993 Extending Trisection Invariants to Four-Dimensional TQFTs
- Math-4994 Finite-Depth Channel Classification of Mixed-State Topological Order
- Math-4995 Higher-Dimensional Quantum Cellular Automata beyond Translations
- Math-4996 Quantum Cellular Automata Realizing the Full Witt Group
- Math-4997 Smale's 4th Problem: Integer Zeros of Polynomials
- Math-4998 Beyond Convex Optimization
- Math-4999 Mathematics of Quantum Computing
- Math-5000 Game Theory at Scale