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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-17 Smooth 4-Dimensional Poincaré Conjecture
- Math-37 Baum-Connes Conjecture
- Math-38 Novikov Homotopy Invariance Conjecture
- Math-41 The Borel Conjecture on Topological Rigidity of Aspherical Manifolds
- Math-102 Smooth 4-dimensional Schoenflies problem
- Math-116 The Volume Conjecture
- Math-183 Arnold Conjecture on Hamiltonian Fixed Points
- Math-186 L-space Conjecture
- Math-209 Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)
- Math-211 Hilbert-Smith Conjecture
- Math-237 Kirby Problem 4.15
- Math-248 Witten's Asymptotic Expansion Conjecture for SU(2) WRT Invariants
- Math-260 All groups are good: the four-dimensional disc-embedding conjecture
- Math-263 The Singer Conjecture on Vanishing of L2-Cohomology of Aspherical Manifolds
- Math-274 Nearby Lagrangian conjecture
- Math-292 Vassiliev Separation by Abelian-Valued Finite-Type Invariants
- Math-305 Slice-ribbon problem
- Math-321 Unknotting Problem
- Math-338 Atiyah Conjecture on $L^2$-Betti Numbers
- Math-343 Jones Unknot Conjecture
- Math-350 Mazur's finite-components conjecture for rational points
- Math-401 Whitehead Conjecture
- Math-404 Gromov-Lawson-Rosenberg Conjecture for Finite Fundamental Groups
- Math-435 Chen-Yang Volume Conjecture for Turaev-Viro Invariants
- Math-486 Major problems 2 — The generating hypothesis, which asserts that the stable homotopy functor is faithful on the category…
- Math-633 Zeeman Conjecture
- Math-1177 The Inscribed Square Problem
- Math-1178 Smooth 4-dimensional Poincare conjecture
- Math-1179 Realisation problem for the space of knots in the 3-sphere
- Math-1180 Which homology 3-spheres bound homology 4-balls?
- Math-1181 Fundamental group torsion for subsets of Euclidean 3-space
- Math-1182 Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?
- Math-1183 What is the homotopy type of the group of diffeomorphisms of the 4-sphere?
- Math-1184 Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?
- Math-1185 Unsolvability of word problem for 2-knot complements
- Math-1186 Closing Lemma for Diffeomorphism (Dynamical Systems)
- Math-1288 Kirby Problem 1.1
- Math-1289 Kirby Problem 1.2
- Math-1290 Kirby Problem 1.3
- Math-1291 Kirby Problem 1.5
- Math-1292 Kirby Problem 1.6
- Math-1293 Kirby Problem 1.8
- Math-1294 Kirby Problem 1.9
- Math-1295 Kirby Problem 1.10
- Math-1296 Kirby Problem 1.11
- Math-1297 Kirby Problem 1.13
- Math-1298 Kirby Problem 1.14
- Math-1299 Kirby Problem 1.16
- Math-1300 Kirby Problem 1.17
- Math-1301 Kirby Problem 1.19