Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
4 problems
What is the maximum volume of a convex body in R^n whose centroid is its only interior lattice point? Ehrhart conjectured the extremal value in 1964; the sharp maximum is now determined in every dimension.
Question 8 of the First Proof experiment (Abouzaid et al.) asks whether a polyhedral Lagrangian surface with exactly four faces meeting at every vertex necessarily admits a Lagrangian smoothing. The research report assembles…
If f(n) is the maximum total side length of n interior-disjoint squares packed in the unit square, is f(k^2 + 1) = k? An exact rational configuration packs 17 squares with total side length greater than 4, refuting the identity at k = 4.
What is the largest possible measure of a subset of a radius-R disk in R^2 containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives M(R) ≪ R^1/2; with Sárközy's lower construction, M(R) = R^1/2 +…