Geometry
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-3 Yang–Mills Existence and Mass Gap
- Math-4 Hodge Conjecture
- Math-70 Cannon's Conjecture
- Math-71 The Jacobian Conjecture
- Math-73 Kannan–Lovász–Simonovits Isoperimetric Conjecture
- Math-117 Positive Scalar Curvature on Aspherical Manifolds
- Math-143 The Kissing Number Problem
- Math-213 Falconer Distance Conjecture
- Math-215 Hopf Conjecture
- Math-222 Sharp Erdos Distinct-Distances Conjecture in the Plane
- Math-247 Universal Optimality of the Hexagonal Lattice in Dimension Two
- Math-251 Hopf conjecture for nonnegative sectional curvature
- Math-278 Cartan-Hadamard isoperimetric conjecture
- Math-279 Michel Boundary Rigidity Conjecture for Simple Manifolds
- Math-294 Erdös-Szekeres conjecture
- Math-306 Mahler Volume Product Conjecture
- Math-313 Marked Length Spectrum Rigidity Conjecture
- Math-322 Smale's 10th Problem: The Pugh Closing Lemma
- Math-335 Arnold Chord Conjecture in Higher Dimensions
- Math-349 Log-Brunn-Minkowski Inequality for Symmetric Convex Bodies
- Math-351 Hopf Conjecture: no metric of positive sectional curvature on S^2 x S^2
- Math-352 Bott Conjecture: nonnegatively curved simply connected manifolds are rationally elliptic
- Math-362 Strong Hyperplane Conjecture for Isotropic Constants
- Math-388 The Filling Area Conjecture
- Math-395 The Thomson problem
- Math-399 Arnold-Givental Lagrangian intersection conjecture
- Math-402 Bartnik's cosmological splitting conjecture
- Math-405 Long-Time Existence of the Calabi Flow on Compact Kaehler Manifolds
- Math-411 Yau's Conjecture on First Eigenvalues
- Math-414 Smale's 6th Problem: Finiteness of Central Configurations
- Math-418 Measure-zero singular set of stationary integral varifolds
- Math-422 Uniqueness of Tangent Cones for Area-Minimizing Integral Currents in Higher Codimension
- Math-433 Minkowski's conjecture on products of non-homogeneous linear forms
- Math-446 LeBrun-Salamon Conjecture: positive quaternion-Kahler manifolds are symmetric spaces
- Math-463 Katok entropy rigidity and an exact time-change obstruction
- Math-476 Auslander Conjecture for Complete Affine Manifolds
- Math-477 The Illumination Conjecture
- Math-481 Does every higher-dimensional tiling by translations of convex polytope tiles have an affine transformation taking it to a Voronoi diagram
- Math-493 Inscribed Square Problem (Toeplitz Conjecture)
- Math-502 Chern's Affine Conjecture
- Math-508 Sphere Packing in Higher Dimensions
- Math-535 No Three in Line in [N]^2
- Math-536 Small Triangles in the Unit Disc
- Math-537 Axis-Parallel Rectangles in Dense Sets
- Math-551 Pyjama Set Covering
- Math-552 Cohn-Elkies Scheme for Circle Packings
- Math-565 The Carathéodory Conjecture
- Math-566 Kalai's $3^d$ Conjecture
- Math-567 The Unit Distance Problem
- Math-569 Ulam's Packing Conjecture