Algebra
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-24 Inverse Galois Problem
- Math-36 Farrell-Jones Conjecture
- Math-45 Hilbert's Sixteenth Problem
- Math-71 The Jacobian Conjecture
- Math-72 Two-Dimensional Jacobian Conjecture in Characteristic Zero
- Math-85 Grothendieck–Katz p-curvature conjecture
- Math-86 Regular Inverse Galois Problem over Q
- Math-121 Tarski's Exponential Function Problem
- Math-196 Grothendieck–Serre Conjecture for Regular Local Rings
- Math-208 Kaplansky's Zero-Divisor Conjecture for Torsion-Free Groups
- Math-230 Serre's Conjecture II on Galois Cohomology of Simply Connected Semisimple Groups
- Math-235 Zauner's Conjecture (SIC-POVM)
- Math-246 Vaught Conjecture
- Math-261 Moonshine Uniqueness Conjecture (Strongly Rational Holomorphic VOA Form)
- Math-287 Resolvent Degree of the General Degree-Seven Polynomial (Algebraic Form of Hilbert's Thirteenth Problem)
- Math-289 Kaplansky's Idempotent Conjecture
- Math-323 Finiteness of Finitely Presented Periodic Groups
- Math-340 Dixmier Conjecture
- Math-342 Hadamard Matrix Conjecture
- Math-346 Alperins Weight Conjecture for Modular Representations of Finite Groups
- Math-356 Brauer's k(B) Conjecture
- Math-363 The Word Problem for One-Relation Monoids
- Math-380 The Dixmier Unitarisability Problem
- Math-393 Serre's Positivity Conjecture
- Math-427 Combinatorial Invariance of Kazhdan–Lusztig Polynomials
- Math-444 Kaplansky's Direct Finiteness Conjecture
- Math-452 Deligne–Drinfeld Freeness Conjecture for grt_1
- Math-453 Small Cohen-Macaulay Conjecture
- Math-460 Andrews-Curtis Conjecture
- Math-468 Lusztig's P1-P15 Conjectures for Bounded Weighted Coxeter Groups
- Math-471 The Köthe Conjecture
- Math-499 The McKay-Navarro Conjecture for Finite Groups
- Math-516 Product-Free Sets in Finite Groups
- Math-547 Large Subsets of Approximate Groups
- Math-557 Existence of Perfect Cuboids
- Math-562 Herzog-Schönheim Conjecture
- Math-563 The Isomorphism Problem for Coxeter Groups
- Math-564 Infinitude of Leinster Groups
- Math-568 The Generalized Star Height Problem
- Math-627 Eilenberg-Ganea Conjecture
- Math-628 Finite Lattice Representation Problem
- Math-629 Rota's Basis Conjecture
- Math-630 Stable Field Conjecture
- Math-631 O-Minimal Theory with Trans-Exponential Growth
- Math-632 Infinite Minimal Field Algebraic Closure
- Math-1008 Graphs of exact colorings
- Math-1009 Waring rank of determinant
- Math-1168 Perfect Cuboid
- Math-1837 Problems Around Polynomials — Problem 1
- Math-1838 Problems Around Polynomials — Problem 2