The Odd Area Conjecture for Unit Disks
For a family of an odd number of unit disks in the plane, let be the area covered by an odd number of disks. It was conjectured that , the area of a single disk. False: configurations exist with smaller odd area.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Computation
- Field
- Discrete geometry
- Posed by
- conjectured in the discrete geometry literature
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-06
- Model
- AlphaEvolve
- Vendor
- Google DeepMind
- Collaborators
- Stefan Steinerberger
- Verification
- Site-confirmed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The counterexample configurations, at 51 and 151 disks, were investigated using AlphaEvolve. The author notes the behaviour differs between small and large numbers of disks, which is what the search surfaced.
Verification
The refutation is explicit finite disk configurations, so the odd area is a direct computation. Single-author arXiv note, not peer-reviewed.