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-5001 Aubin–Talenti Optimizers for Critical Dirac Potentials
- Math-5002 Lee–Huang–Yang Upper Bound for Hard-Sphere Bosons
- Math-5003 Modular Generators for Massive Double Cones
- Math-5004 Local Density Approximation for the Canonical Functional
- Math-5005 Higher-Dimensional Semiclassical Kinetic-Energy Corrections
- Math-5006 Fermionic Character of Low-Lying Excitations
- Math-5007 From Dislocation Mechanics to Continuum Plasticity
- Math-5008 Nonperiodic and Nonquadratic FFT Schemes for Materials
- Math-5009 Dissipation and Interface Misorientation in Phase-Field Plasticity
- Math-5010 Ericksen Universal Deformations of Incompressible Solids
- Math-5011 Multiphysics Frameworks for Computational Homogenization
- Math-5012 Finite-Shear Hashin–Shtrikman Bounds and Rod–Hinge Deformations
- Math-5013 Lower Bounds for Hamiltonian Mass
- Math-5014 Vacuum Failure of the Third Law of Black-Hole Thermodynamics
- Math-5015 Rigorous Construction of Conformal Field Theories
- Math-5016 Open Structures in Compactified Imaginary Liouville Theory
- Math-5017 Robustness of Climate Models at Unresolved Scales
- Math-5018 Mechanisms and Scales of Tropical-Cyclone Edge Intensification
- Math-5019 Entrainment-Mediated Tropical-Cyclone Intensification
- Math-5020 Cloud-Organization Limit Cycles
- Math-5021 Dynamics Near Generic Spacetime Singularities
- Math-5022 Uniqueness of Spherical Schwarzschild–Anti-de Sitter Spacetimes
- Math-5023 Teukolsky Energy Decay on Extremal Kerr Spacetimes
- Math-5024 Stability of Extremal Critical Collapse
- Math-5025 Global Stability and Asymptotics of Cosmological Spacetimes
- Math-5026 Tensorial Mode Stability of Kerr–de Sitter Spacetimes
- Math-5027 Query Complexity and Achievable Functions in Multivariable Quantum Signal Processing
- Math-5028 Lieb–Robinson Bounds for Nonrelativistic Fermions
- Math-5029 Strong Continuity Without Ultraviolet Regularization
- Math-5030 Counterexamples to Strongly Continuous Many-Fermion Dynamics
- Math-5031 Irreducible Components of Landau Varieties
- Math-5032 Feasible High-Performance Plasma Flows for Stellarators
- Math-5033 Unique Ground-State Representability under Linear Constraints
- Math-5034 Multitask Hamiltonian Learning across Levels of Theory
- Math-5035 Reflection-Positive Two-Dimensional Quantum Field Theories with Boundary
- Math-5036 Superselection Sectors of Braided Fusion Spin Systems
- Math-5037 SU(3) Braided Fusion Spin Systems and Haah Nets
- Math-5038 Vertex Operator Algebras with Haagerup Symmetry
- Math-5039 New Quantum LDPC Codes with Good Parameters
- Math-5040 Quasi-Bosonic Ground States and Excitation Spectra
- Math-5041 The Gell–Mann–Brueckner Formula in the Thermodynamic Limit
- Math-5042 Open Problems on Spectral-Parameter Yang–Baxter Solutions
- Math-5043 Classification and Applications of Yang–Baxter Operators
- Math-5044 Orthogonal Symmetry Conjecture for Rigid Higher Categories
- Math-5045 Higher-Categorical Models of Continuous and Spacetime Symmetries
- Math-5046 Two-Categorical Interpretation of a Quantum Lattice Model
- Math-5047 Liouville Theory from the Virasoro Conformal Net
- Math-5048 Extending Trisection Invariants to Four-Dimensional TQFTs
- Math-5049 Finite-Depth Channel Classification of Mixed-State Topological Order
- Math-5050 Higher-Dimensional Quantum Cellular Automata beyond Translations