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-101 Density of Hyperbolicity for Rational Maps
- Math-102 Smooth 4-dimensional Schoenflies problem
- Math-103 Grothendieck–Teichmüller Conjecture
- Math-104 Isomorphism of Free Group Factors
- Math-105 Planted Clique Conjecture
- Math-106 The Unique Games Conjecture
- Math-107 FPT versus W[1]
- Math-108 Is the exponent of matrix multiplication 2
- Math-109 The Exponential Time Hypothesis for 3-SAT
- Math-110 Strong Exponential Time Hypothesis (SETH)
- Math-111 NP-Completeness of the Minimum Circuit Size Problem (MCSP)
- Math-112 Capacity of the General Discrete Memoryless Relay Channel
- Math-113 The Log-Rank Conjecture
- Math-114 The Erdős–Rado Sunflower Conjecture
- Math-115 Erdős–Hajnal Conjecture
- Math-116 The Volume Conjecture
- Math-117 Positive Scalar Curvature on Aspherical Manifolds
- Math-118 Residual Finiteness of Hyperbolic Groups
- Math-119 Torsion Conjecture for Abelian Varieties of Dimension at Least Two
- Math-120 Uniform Boundedness Conjecture for Rational Points on Curves
- Math-121 Tarski's Exponential Function Problem
- Math-122 O5a — Deterministic polynomial-time integer factorization
- Math-123 The NC versus P Problem for Efficient Parallel Computation
- Math-124 P vs. BPP
- Math-125 Basing One-Way Functions on NP-Hardness
- Math-126 Existence of One-Way Permutations
- Math-127 Equivalence of Worst-Case and Average-Case Hardness for NP (Excluding Heuristica)
- Math-128 Bombieri–Lang conjecture
- Math-129 L = P Problem
- Math-130 Dickson's Conjecture
- Math-131 P versus NC^1
- Math-132 Deligne's Conjecture for Critical Motive Values
- Math-133 Non-Triviality of the Three-Dimensional Ising Model
- Math-134 Graph Isomorphism in Polynomial Time
- Math-135 Campana's Conjecture Characterizing Special Varieties by Potential Density of Rational Points
- Math-136 PSPACE versus EXPTIME
- Math-137 Littlewood Conjecture
- Math-138 L versus NL
- Math-139 Selberg's 1/4 conjecture
- Math-140 Bunyakovsky Conjecture
- Math-141 Szpiro's conjecture
- Math-142 Polignac's Conjecture
- Math-143 The Kissing Number Problem
- Math-144 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains
- Math-145 Quantum Unique Ergodicity on Negatively Curved Manifolds
- Math-146 Erdős Problem #52
- Math-147 Iitaka Subadditivity Conjecture for Kodaira Dimension
- Math-148 Prove the BKL locality conjecture in the general inhomogeneous context
- Math-149 Serre's congruence subgroup conjecture
- Math-150 QMA versus QCMA Problem