Physics
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-3 Yang–Mills Existence and Mass Gap
- Math-74 Prove the Penrose inequality or present a counterexample
- Math-95 Entanglement Area Law for 2D Gapped Quantum Systems
- Math-96 Extended States in the Anderson Model
- Math-97 Conformal Field Theory Limit of the Critical Three-Dimensional Ising Model
- Math-98 Non-Perturbative Construction and Non-Triviality of 4D Euclidean Phi4 Quantum Field Theory
- Math-99 Bose-Einstein Condensation in Continuum Models
- Math-133 Non-Triviality of the Three-Dimensional Ising Model
- Math-144 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains
- Math-145 Quantum Unique Ergodicity on Negatively Curved Manifolds
- Math-148 Prove the BKL locality conjecture in the general inhomogeneous context
- Math-192 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3
- Math-206 Long-Range Order in the Quantum Heisenberg Ferromagnet
- Math-218 Global Dynamics of the Vlasov–Maxwell System
- Math-233 Berry random-wave conjecture: real negative-curvature BS formulation
- Math-267 Equivalence or Strict Containment of QMA and QMA(2)
- Math-277 Exact Unassisted Quantum Capacity of the Qubit Depolarizing Channel
- Math-280 Bound Entanglement with Negative Partial Transpose
- Math-304 Secret key from all entangled states
- Math-329 Néel Order for the Spin-1/2 Square-Lattice Heisenberg Antiferromagnet (Averaged Ground-State Order)
- Math-337 Discontinuity of the q-State Potts Phase Transition on Z^d for d >= 3 and q >= 3
- Math-358 Constant-Parameter Quantum Locally Testable Codes
- Math-439 Mutually Unbiased Bases in Non-Prime-Power Dimensions
- Math-447 Aaronson-Ambainis Conjecture
- Math-2244 Soft Phases in Two-Dimensional O(N) Models
- Math-2245 Long-Range Order for the Quantum Heisenberg Model
- Math-2246 Extended States with Extensive Disorder
- Math-2247 Localization in Two Dimensions
- Math-2248 Bounded Excess Electrons
- Math-2249 Asymptotics of Atomic Ionization Energy
- Math-2250 One-Dimensional Lieb-Thirring Constants
- Math-2251 Mutually Unbiased Bases in Dimension Six
- Math-2309 Non-self-adjoint spectral theory: completeness, reconstruction, and matrix-function bounds
- Math-2414 Strong Cosmic Censorship at Weak Regularity
- Math-2421 Hemisphere Partition Functions and Stability Across GLSM Phases
- Math-2427 Universal Bounds on Atomic Excess Charge
- Math-2447 Mass–Angular-Momentum Inequalities with Trapped and Multiple Horizons
- Math-2463 Maximum Excess Charge of Atoms
- Math-2487 Rigorous Mesoscopic Limits of Many-Particle Systems
- Math-2497 Low-Temperature Order in Quantum Heisenberg Ferromagnets
- Math-2498 AQFT Locality of Unitary Vertex Operator Algebras
- Math-2726 The numerical spacetime enclosing-area inequality in every dimension
- Math-2727 Single-letter classical capacity of generalized amplitude damping
- Math-2728 Unbounded positive point spectrum of relative SU(2) BFSS
- Math-2729 Exactly one threshold bound state in every relative SU(N) BFSS model
- Math-2730 QMA hardness of continuum electronic energy with binary nuclear charges
- Math-2731 The first lattice correction to quantum Bloch magnetization
- Math-2732 Polynomial quantum synthesis of any unitary using a suitable Boolean oracle
- Math-2733 A gap in the open spin-one chain with fixed same-sign boundary fields
- Math-2734 A conditional charged Penrose bound in spatial dimension at least four