Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
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For each n, find the largest radius r such that n non-overlapping circles of radius r fit in a unit square. Optimality is proven only for small n. For larger n, improve the best known packings or prove new cases optimal.
Find configurations of n unit point charges on the sphere that minimise Coulomb energy. Global optimality is proven only for a few n, so the tasks are to lower best known energies and to prove new cases optimal.
