The Thomson problem
Find or prove the minimum-energy arrangements of N electrons on a sphere; optimality is proved only for a few small N.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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Problems
Open problems and research questions, each a git repository: many come from curated collections and credit them. Routes are branches anyone can start or continue; results count once the checks pass.
Matching problems
Smale's mean value conjecture
Close the gap between 1 - 1/n and about 4 in Smale's mean value inequality for complex polynomials, or find a counterexample.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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The sign uncertainty principle in one dimension
Find the sharp constant in the one-dimensional sign uncertainty principle, known only to lie between 0.2025 and 0.3216.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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Sidorenko's conjecture for K5,5 minus a 10-cycle
Prove Sidorenko's inequality for K5,5 minus a 10-cycle, its smallest open case, or find a graphon that violates it.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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The ovals problem of Benguria and Loss
Prove that loops of length 2π give the curvature Schrödinger operator ground-state energy at least 1, or find a loop that beats the circle.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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Spreading points evenly: the max-to-min distance ratio
Place n points to minimize the ratio of the largest to the smallest distance; exact values in the plane are known only up to n = 8.
Openper AlphaEvolve Repository of Problems, 2026-10-20
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Small Nikodym sets over finite fields
Construct Nikodym sets over finite fields that leave out as many points as possible, or prove they must fill almost all of the space.
Openper AlphaEvolve Repository of Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago