Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Combinatorics
Green's open problem 24 - conjecture
Conjecture p.579 in [Aa19]: (31+o(1))n2.
$2,667 bounty
·1 piece from 1 person
·last one 10 days ago
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
18 Sept 2025a year of work on this problem10 Sept 2026
Green, Ben. "100 open problems." (2024).
[Aa19] Aaronson, James. "Maximising the number of solutions to a linear equation in a set of integers." Bulletin of the London Mathematical Society 51.4 (2019): 577-594.
[HaL28] Hardy, G. H., and J. E. Littlewood. "Notes on the theory of series (VIII): an inequality." Journal of the London Mathematical Society 1.2 (1928): 105-110.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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