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-2601 Circulant Hadamard conjecture
- Math-2602 Logarithmic correspondence-coloring bound for fixed forbidden cliques
- Math-2603 Colin de Verdière chromatic-number conjecture
- Math-2604 Deterministic nonbipartite Ramanujan graphs in every fixed degree
- Math-2605 Fractional chromatic number versus ordinary Hadwiger number
- Math-2606 Gopalan–Servedio square-root-degree Fourier bound
- Math-2607 Shareshian–Wachs elementary positivity for chromatic quasisymmetric functions
- Math-2608 Graph decomposition at the integral expectation threshold
- Math-2609 Log-squared sharp threshold for monotone graph properties
- Math-2610 Power improvement for planar halving lines
- Math-2611 Power improvement over exponent two in Heilbronn triangle constructions
- Math-2612 Optimal-order distinct distances in every dimension at least three
- Math-2613 Uniform variance-influence bound for hypergraph properties
- Math-2614 Integral and fractional expectation thresholds within a constant factor
- Math-2615 Degree-uniform power saving for intersective polynomial differences
- Math-2616 Polynomial induced removal for ordered binary matrices
- Math-2617 Periodic tilings by bounded measurable sets in three dimensions
- Math-2618 Periodic translational tiling in dimension three
- Math-2619 Five-colorability of the unit-distance plane
- Math-2620 Power saving for prime-intersective polynomial differences
- Math-2621 Quasipolynomial density decay for progression-free sets
- Math-2622 Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers
- Math-2623 Maker winning strategy for Snaky on the infinite square lattice
- Math-2624 Talagrand discrete convexity conjecture
- Math-2625 Sharp terminal edge count in random triangle removal
- Math-2626 Power improvement over the planar unit-distance exponent four thirds
- Math-2627 Weak pinned planar distance assertion
- Math-2628 Triangular-cylinder approximation of aligned radial sweeps
- Math-2629 Half-minimum-area bound for cylinder covers
- Math-2630 Linear coefficient of minimum spherical logarithmic energy
- Math-2631 Binary edit distance has exponential-scale L1 distortion
- Math-2632 Uniform L1 distortion for bounded treewidth
- Math-2633 Simplex maximum for projection-body volume
- Math-2634 Directionwise normalized cylinder-covering bound
- Math-2635 Sharp exponential scale of edit-distance distortion
- Math-2636 One signing for all Euclidean prefixes
- Math-2637 Euclidean Steinitz–Bergström bound
- Math-2638 Gaussian propeller partition bound
- Math-2639 Logarithmic Sobolev inequality from subgaussian marginals
- Math-2640 Sharp entropy lower bound for log-concave densities
- Math-2641 Subpolynomial nonlinear dimension reduction in Lp
- Math-2642 Liftability without spectrahedrality for a hyperbolicity cone
- Math-2643 Uniform L1 distortion of planar graph metrics
- Math-2644 Projected Lax conjecture
- Math-2645 Finite cylinder approximation of ruled sets
- Math-2646 Single-lattice covering density of order n log n
- Math-2647 Gromov width of symmetric polar products
- Math-2648 Worst-case symmetric translative covering density
- Math-2649 Triangular minimum of planar Coulomb renormalized energy
- Math-2650 Affine Bernstein assertion for entire graphs in dimension ten