Logic
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-57 Superpolynomial Lower Bounds for Frege Propositional Proof Systems
- Math-121 Tarski's Exponential Function Problem
- Math-228 Sharp integer-root bound for binomial-product programs and a tau-convention audit
- Math-276 Finite Spectrum Problem
- Math-300 Positivity Problem for Linear Recurrence Sequences
- Math-345 Shelah's Conjecture on NIP Fields
- Math-374 Shelah's Categoricity Conjecture for L_omega1,omega
- Math-386 Bad Groups of Finite Morley Rank
- Math-419 Martin's Conjecture for Definable Turing-Invariant Functions
- Math-420 Exact variable accounting for fixed-variable Hilbert's Tenth Problem over the integers
- Math-445 Exponential-Algebraic Closedness
- Math-479 Zilber’s Quasiminimality Conjecture for Complex Exponentiation
- Math-1148 MSO alternation hierarchy over pictures
- Math-1149 Vertex Cover Integrality Gap
- Math-2241 Automorphism Problem for the Turing Degrees
- Math-2242 Shelah's categoricity conjecture for $L_{\omega_1,\omega}$
- Math-2243 Shelah's eventual categoricity conjecture
- Math-2303 One-equation reductions for the rational Hamilton quaternions and Lipschitz order
- Math-2304 Finite-fiber normalization for elliptic Diophantine encodings
- Math-2721 Downward categoricity transfer to the Hanf threshold under CH
- Math-2722 Capturing polynomial time with choiceless computation and counting
- Math-2723 Unique natural-number witnesses for every enumerable set
- Math-2724 Global weak normalization implies strong normalization in pure type systems
- Math-2725 Strict expressive gain from witnessed symmetric choice
- Math-3368 Termination of the sixth Goodstein Sequence
- Math-3369 Fixed-point logic with counting
- Math-3370 Order-invariant queries
- Math-3371 Blatter-Specker Theorem for ternary relations
- Math-3372 Finite entailment of Positive Horn logic
- Math-4066 Increasing Polarized Ramsey Theorem
- Math-4067 Reverse-Mathematical Strength of Hindman's Theorem
- Math-4068 Strength of the Dual Ramsey Theorem
- Math-4069 Strength of the Carlson–Simpson Lemma
- Math-4070 Cancellation and Schröder–Bernstein for Torsion Abelian Groups
- Math-4071 Metrization of Proper MF Spaces
- Math-4072 Lebesgue Differentiation and Weak Weak König's Lemma
- Math-4073 Strength of the Auslander–Ellis Theorem
- Math-4074 Well-Ordered Linearizations
- Math-4075 Reverse Mathematics of Fraïssé's Conjecture
- Math-4076 Lengths of Bounded-Rank Linear-Order WQOs
- Math-4077 Strengths of Laver and Nash–Williams BQO Theorems
- Math-4078 Three-Element Better-Quasi-Order
- Math-4079 Weak Infinitary Comprehension versus Weak Choice
- Math-4080 Open Mapping Theorem for Separable Banach Spaces
- Math-4081 Strength of the Krein–Šmulian Theorem
- Math-4082 Strength of Szemerédi's Theorem
- Math-4083 Strength of Kříž's Labeled-Tree Theorem
- Math-4084 Ramsey's Theorem for Triples over a Weak Base
- Math-4085 Does every simple first-order theory have stable forking
- Math-4086 The universality problem for C-free graphs