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.
Functional analysis
Withdrawn
Green's open problem 54
Let K⊂Rn be a balanced compact set (that is, λK⊆K whenever
∣λ∣≤1
) and suppose that the normalised Gaussian measure
γn(K)≥0.99
.
Does
10K
contain a compact convex set
C
with
γn(C)≥0.01
?
Withdrawn 5 Aug 2026
SOURCE_MISMATCH (Green #54 is per-n on ℝ^n; formalization is a single statement on ℕ → ℝ with Measure.infinitePi gaussian — nonequivalent setting)
Original formulation: M. Talagrand, Are All Sets of Positive Measure Essentially Convex?, in Operator Theory:
No one has attempted this yet.
Formal statement
Lean type
True ↔
∀ (K : Set (ℕ → ℝ)),
IsCompact K →
Balanced ℝ K →
0.99 ≤ Green54.gaussianMeasureInf K →
∃ C, IsCompact C ∧ Convex ℝ C ∧ C ⊆ 10 • K ∧ 1e-2 ≤ Green54.gaussianMeasureInf C
What you must prove
import FormalConjectures.GreensOpenProblems.«54»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Green54.green_54" := by
sorry
end Bounty
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.