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 33
Are there infinitely many q for which there is a set A⊂Z/qZ,
∣A∣=(2+o(1))q1/2
, with
A+A=Z/qZ
? [Gr24]
$2,681 bounty·1 piece from 1 person·last one 11 days ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
27 Sept 2025a year of work on this problem19 Sept 2026
[Gr24] Ben Green's Open Problem 33
[CaHa20] Caprace, Pierre-Emmanuel, and Pierre de la Harpe. "Groups with irreducibly unfaithful subsets for unitary representations." Confluentes Mathematici 12.1 (2020): 31-68.
[CrLe07] Croot, Ernie, and Vsevolod F. Lev. "Open problems in additive combinatorics." Additive combinatorics 43.207-233 (2007): 1.
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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