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-4701 Quantum Advantage in Threefold Repetition of Feige’s Game
- Math-4702 Semidefinite Relaxations for Quantum Equilibria
- Math-4703 Universal-Cover Isomorphism Algorithms for Cube Complexes
- Math-4704 Cross-Entropy Dynamics Beyond Hadamard Initialization
- Math-4705 Hidden-Layer Depth Complexity of Piecewise-Linear Functions
- Math-4706 Hilbert's 6th Problem: Axiomatization of Physics
- Math-4707 Biological Quantum Field Theory
- Math-4708 Fundamental Laws of Biology
- Math-4709 Symmetries and Action Principles for Biology
- Math-4710 Geometric Langlands and Quantum Physics
- Math-4711 Meaning and Nonexistence of an Exact Three-Dimensional Ising Formula
- Math-4712 One-Dimensional Fermi Gas with Attractive Interaction
- Math-4713 Entropy Production in Nonequilibrium Statistical Mechanics
- Math-4714 Short-Range Spin Glasses
- Math-4715 Meaning and Impossibility of Exact Helium Energy Levels
- Math-4716 Quantum Diffusion in the Anderson Model
- Math-4717 Absolutely Continuous Spectrum Under a Weighted L2 Condition
- Math-4718 Mathematical Nuclear Shell Model
- Math-4719 First-Principles Molecular Configurations
- Math-4720 Existence of Quantum Crystals
- Math-4721 Continuity of the Integrated Density of States
- Math-4722 Riemann-Hilbert Problem with non-analytic data
- Math-4723 Painlev\'e equations
- Math-4724 Non-self adjoint spectral problems
- Math-4725 Long-time behavior with non-generic initial data
- Math-4726 The parking problem
- Math-4727 A Tracy-Widom Central Limit Theorem
- Math-4728 Perturbation theory for infinite dimensional integrable systems
- Math-4729 Perturbation theory for exactly solvable combinatorial problems
- Math-4730 Initial/boundary value problems for integrable systems
- Math-4731 Multi-matrix models and models with an external field
- Math-4732 KdV with almost periodic initial data
- Math-4733 interacting particle systems and KPZ
- Math-4734 numerical computation with random data
- Math-4735 initial boundary value problems for integrable systems (IBVP)
- Math-4736 numerical solution of integrable systems
- Math-4737 additional problems for integrable systems
- Math-4738 Rigorous Diffraction from Two Slits
- Math-4739 When semiclassical spectra follow curves—and when they fill area
- Math-4740 Complex Bohr-Sommerfeld action and a stability obstruction
- Math-4741 Exact zero-Kerr spectrum and high-energy Kerr localization
- Math-4742 Canonical versus abstract hyper-Kähler structures on cotangent bundles
- Math-4743 Exact complex-linear spin propagation and a nonlinear coherence-loss benchmark
- Math-4744 The sharp Laptev-Safronov threshold and a Lorentz-stable tube obstruction
- Math-4745 Axis and low-dimensional cases of Levitin's disk-intersection conjecture
- Math-4746 A non-polynomial complex potential with entirely real spectrum
- Math-4747 A one-coupling J-Schur certificate for projected spectral enclosures
- Math-4748 When holomorphic anomaly equations survive fiber integration
- Math-4749 Differential fingerprints of eta-products
- Math-4750 Holomorphic anomaly, fibrations, and the BPS multiple-cover transform