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-4651 Hilbert's 6th Problem: Axiomatization of Physics
- Math-4652 Biological Quantum Field Theory
- Math-4653 Fundamental Laws of Biology
- Math-4654 Symmetries and Action Principles for Biology
- Math-4655 Geometric Langlands and Quantum Physics
- Math-4656 Meaning and Nonexistence of an Exact Three-Dimensional Ising Formula
- Math-4657 One-Dimensional Fermi Gas with Attractive Interaction
- Math-4658 Entropy Production in Nonequilibrium Statistical Mechanics
- Math-4659 Short-Range Spin Glasses
- Math-4660 Meaning and Impossibility of Exact Helium Energy Levels
- Math-4661 Quantum Diffusion in the Anderson Model
- Math-4662 Absolutely Continuous Spectrum Under a Weighted L2 Condition
- Math-4663 Mathematical Nuclear Shell Model
- Math-4664 First-Principles Molecular Configurations
- Math-4665 Existence of Quantum Crystals
- Math-4666 Continuity of the Integrated Density of States
- Math-4667 Riemann-Hilbert Problem with non-analytic data
- Math-4668 Painlev\'e equations
- Math-4669 Non-self adjoint spectral problems
- Math-4670 Long-time behavior with non-generic initial data
- Math-4671 The parking problem
- Math-4672 A Tracy-Widom Central Limit Theorem
- Math-4673 Perturbation theory for infinite dimensional integrable systems
- Math-4674 Perturbation theory for exactly solvable combinatorial problems
- Math-4675 Initial/boundary value problems for integrable systems
- Math-4676 Multi-matrix models and models with an external field
- Math-4677 KdV with almost periodic initial data
- Math-4678 interacting particle systems and KPZ
- Math-4679 numerical computation with random data
- Math-4680 initial boundary value problems for integrable systems (IBVP)
- Math-4681 numerical solution of integrable systems
- Math-4682 additional problems for integrable systems
- Math-4683 Rigorous Diffraction from Two Slits
- Math-4684 When semiclassical spectra follow curves—and when they fill area
- Math-4685 Complex Bohr-Sommerfeld action and a stability obstruction
- Math-4686 Exact zero-Kerr spectrum and high-energy Kerr localization
- Math-4687 Canonical versus abstract hyper-Kähler structures on cotangent bundles
- Math-4688 Exact complex-linear spin propagation and a nonlinear coherence-loss benchmark
- Math-4689 The sharp Laptev-Safronov threshold and a Lorentz-stable tube obstruction
- Math-4690 Axis and low-dimensional cases of Levitin's disk-intersection conjecture
- Math-4691 A non-polynomial complex potential with entirely real spectrum
- Math-4692 A one-coupling J-Schur certificate for projected spectral enclosures
- Math-4693 When holomorphic anomaly equations survive fiber integration
- Math-4694 Differential fingerprints of eta-products
- Math-4695 Holomorphic anomaly, fibrations, and the BPS multiple-cover transform
- Math-4696 Compact-fixed-locus definitions and pole obstructions for noncompact elliptic genera
- Math-4697 A normal-symbol criterion for lower-dimensional modular reduction
- Math-4698 Coefficientwise indices and a level-two Calabi--Yau/CFT test
- Math-4699 Paramodular consistency tests for Calabi-Yau counting series
- Math-4700 Normalization-aware leading quintic amplitudes at the Gepner point