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-401 Whitehead Conjecture
- Math-402 Bartnik's cosmological splitting conjecture
- Math-403 Clemens Conjecture for Rational Curves on a General Quintic Threefold
- Math-404 Gromov-Lawson-Rosenberg Conjecture for Finite Fundamental Groups
- Math-405 Long-Time Existence of the Calabi Flow on Compact Kaehler Manifolds
- Math-406 Pólya's Conjecture for Dirichlet Eigenvalues
- Math-407 Coleman-Oort conjecture: eventual special-subvariety exclusion
- Math-408 Coding Theory and Combinatorics Problem CC-6: Existence of Finite Projective Planes of Non-Prime-Power Orders
- Math-409 Separable Quotient Problem for Banach Spaces
- Math-410 Turan Conjecture on the Turan Density of K_4^{(3)}
- Math-411 Yau's Conjecture on First Eigenvalues
- Math-412 Computability of the Shannon Capacity of Finite Graphs
- Math-413 GNRS Conjecture
- Math-414 Smale's 6th Problem: Finiteness of Central Configurations
- Math-415 Frankl's Union-Closed Sets Conjecture
- Math-416 Fourier Entropy-Influence Conjecture
- Math-417 Irrationality of Catalan’s Constant
- Math-418 Measure-zero singular set of stationary integral varifolds
- 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-421 Brown-Erdos-Sos Conjecture on Sparse Triple Systems
- Math-422 Uniqueness of Tangent Cones for Area-Minimizing Integral Currents in Higher Codimension
- Math-423 Zariski Cancellation Problem (characteristic zero, dimension ≥ 3)
- Math-424 Lebesgue measure of the boundary of the Mandelbrot set
- Math-425 Boundedness of Compact Hyperkahler Manifolds: Finiteness of Deformation Types in Each Dimension
- Math-426 Realizable Limit Shapes in Two-Dimensional First-Passage Percolation
- Math-427 Combinatorial Invariance of Kazhdan–Lusztig Polynomials
- Math-428 Polynomial-Time P-Matrix Linear Complementarity Problem
- Math-429 Lück's Determinant Conjecture for Discrete Groups
- Math-430 Absolute continuity of Bernoulli convolutions outside reciprocal Pisot parameters
- Math-431 Colmezs Conjecture on Faltings Heights of CM Abelian Varieties
- Math-432 Greenberg's Iwasawa-invariants conjecture
- Math-433 Minkowski's conjecture on products of non-homogeneous linear forms
- Math-434 Sums of Three Cubes Representation Conjecture
- Math-435 Chen-Yang Volume Conjecture for Turaev-Viro Invariants
- Math-436 Matroid Secretary Conjecture
- Math-437 Exact value of the site-percolation threshold on the square lattice
- Math-438 Stein's Conjecture on the Hilbert Transform along Lipschitz Vector Fields
- Math-439 Mutually Unbiased Bases in Non-Prime-Power Dimensions
- Math-440 Hamiltonian paths and cycles in vertex transitive graphs
- Math-441 Deterministic Linear-Time Minimum Spanning Tree Problem
- Math-442 Piltz Divisor Problem for k-Fold Divisor Error Terms
- Math-443 Von Neumann's Problem for II_1 Factors
- Math-444 Kaplansky's Direct Finiteness Conjecture
- Math-445 Exponential-Algebraic Closedness
- Math-446 LeBrun-Salamon Conjecture: positive quaternion-Kahler manifolds are symmetric spaces
- Math-447 Aaronson-Ambainis Conjecture
- Math-448 Balanced L4 boundedness of the trilinear Hilbert transform
- Math-449 Shub entropy conjecture
- Math-450 Hilbert's Tenth Problem over C(t) with named t