Disproof of the Erdős unit-distance conjecture
Disproof of the Erdős unit-distance conjecture is graded independently checked on whataifound.org, with the AI's role graded ai-led.
A reasoning model produced the core construction disproving a 1946 conjecture in discrete geometry, finding point configurations with more unit-distance pairs than the conjecture permitted.
- Verification
- Independently checked
- Autonomy
- AI-led
- Lab
- OpenAI
- Model
- GPT-5 series reasoning model
- Field
- Mathematics
- Date
- 2026-05-20
- Problem posed
- 1946 · open 80 yrs
- Notability
- 10 Wikipedia language editions
What was found
The model found configurations showing the unit-distance count can grow at least as fast as n^1.014, exceeding the conjectured bound. Checked by external mathematicians including Fields Medalist Timothy Gowers, who called it 'the first example of a result produced autonomously by an AI that I find exciting in itself.'
Novelty check
The unit-distance problem dates to Erdős (1946). Prior bounds were well documented; the construction is new.
Caveats
Human mathematicians shaped the problem framing and verified the construction. The strength of the endorsement from Gowers is notable but is a judgment, not a formal check.
Sources
How this is graded
whataifound.org grades every entry on two axes: verification (how solid the result is, from a machine-checked proof down to refuted) and autonomy (how much the AI did versus its human collaborators). This finding is independently checked and ai-led. Full definitions are in the methodology.
Cite this entry
whataifound.org (2026). Disproof of the Erdős unit-distance conjecture. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-05-erdos-unit-distance