Erdős's Planar Unit Distance Conjecture
Erdős problem #90 · erdosproblems.com/90
Conjectured upper bound on how many pairs among n points in the plane can be exactly one unit apart.
- Result
- Disproved
- Field
- Combinatorial Geometry
- Posed by
- Paul Erdős
- Year posed
- 1946
- Years open
- 80y
- Solved
- 2026-05
- Model
- OpenAI frontier model (specific version not disclosed)
- Vendor
- OpenAI
- Collaborators
- Noga Alon, Thomas Bloom, Timothy Gowers, Daniel Litt, Will Sawin, Jacob Tsimerman, Melanie Matchett Wood
- Verification
- Expert-verified
- Notability
- 10 Wikipedia languages
What the AI did
Model-assisted construction of a point configuration with more than n^1.014 unit-distance pairs, beating the conjectured bound.
Verification
Independently checked by nine mathematicians and reported as meeting the bar for publication in a top journal.