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-12001 Fractional Coefficient Savings in Algebraic Proof Systems
- Math-12002 Circuit-Size Hierarchy in Bounded Arithmetic
- Math-12003 Online Model Selection for Nonparametric Classes
- Math-12004 Global Convergence of Low-Rank Multi-Penalty Optimization
- Math-12005 Pre-Asymptotic Sampling Numbers of Barron Spaces
- Math-12006 Near-Linear Subgraph Isomorphism for Acyclic Patterns
- Math-12007 Mixing Times from Spectral Independence
- Math-12008 Unconditionally Ruling Out Heuristica
- Math-12009 Semi-Supervised Sparse Gaussian Classification
- Math-12010 Moment-SOS Convergence for PDE-Constrained Variational Problems
- Math-12011 Quasilinear Finite-Field Polynomial Multiplication
- Math-12012 Adjoint-Free Approximation of Nonsymmetric Low-Rank Matrices
- Math-12013 Nash Equilibria over Unbounded Measure Spaces
- Math-12014 Integer Feasibility with Bounded Subdeterminants
- Math-12015 Fixed-Parameter Tractability of Zonotope Containment
- Math-12016 Approximating Fare-Zone Assignment on Trees
- Math-12017 Foundational Assumptions for Obfuscation, FHE, and SNARGs
- Math-12018 Efficient Verification of Distribution Properties
- Math-12019 Information-Theoretic Additive Randomized Encodings
- Math-12020 Degree Automatability of Sum-of-Squares Proofs
- Math-12021 Complexity-Bounded Computation of Maximum Destabilizing Subgroups
- Math-12022 Minimal Convex Difference Decompositions of CPWL Functions
- Math-12023 Freeness of Two-Generator Integral Matrix Groups
- Math-12024 Near-Linear List Decoding of AEL and Ta-Shma Codes
- Math-12025 Zero Submatrices in Sparse Low-Rank Matrices
- Math-12026 Optimal Bounds for Pairs of Commuting Integer Matrices
- Math-12027 Quantum Advantage in Threefold Repetition of Feige’s Game
- Math-12028 Semidefinite Relaxations for Quantum Equilibria
- Math-12029 Universal-Cover Isomorphism Algorithms for Cube Complexes
- Math-12030 Cross-Entropy Dynamics Beyond Hadamard Initialization
- Math-12031 Hidden-Layer Depth Complexity of Piecewise-Linear Functions
- Math-12032 Hilbert's 6th Problem: Axiomatization of Physics
- Math-12033 Biological Quantum Field Theory
- Math-12034 Fundamental Laws of Biology
- Math-12035 Symmetries and Action Principles for Biology
- Math-12036 Geometric Langlands and Quantum Physics
- Math-12037 Meaning and Nonexistence of an Exact Three-Dimensional Ising Formula
- Math-12038 One-Dimensional Fermi Gas with Attractive Interaction
- Math-12039 Entropy Production in Nonequilibrium Statistical Mechanics
- Math-12040 Short-Range Spin Glasses
- Math-12041 Meaning and Impossibility of Exact Helium Energy Levels
- Math-12042 Quantum Diffusion in the Anderson Model
- Math-12043 Absolutely Continuous Spectrum Under a Weighted L2 Condition
- Math-12044 Mathematical Nuclear Shell Model
- Math-12045 First-Principles Molecular Configurations
- Math-12046 Existence of Quantum Crystals
- Math-12047 Continuity of the Integrated Density of States
- Math-12048 Riemann-Hilbert Problem with non-analytic data
- Math-12049 Painlev\'e equations
- Math-12050 Non-self adjoint spectral problems