Heilbronn problem in an arbitrary convex bounding box (AlphaEvolve problem 49)
Heilbronn problem in an arbitrary convex bounding box (AlphaEvolve problem 49). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
For any let be the largest quantity such that in every configuration of points in the plane, there exists a triple of points determining a triangle of area at most times the area of their convex hull. Establish upper and lower bounds on .
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.29 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864.
Progress & source assessment
The repository page records no bounds for this problem.
- [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Heilbronn problem in an arbitrary convex bounding box (AlphaEvolve problem 49) linkApache-2.0 (repository license); problem pages reproduced with attribution.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
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Discussion
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