Complete resultmathematics · discrete geometry
AI model disproves the planar unit-distance conjecture
An internal OpenAI model produced an infinite family contradicting Erdős's conjectured upper-bound behavior, followed by human simplification, context, and extensions.
Editorial context
What happened
This is one of the most completely documented headline cases: the initial prompt, original response, long abridged trace, proof, and external mathematical commentary are all public.
Keep in view
The internal model identity, hidden system prompt, attempt count, and compute budget were not disclosed; the public trace is abridged.
Chronology
Timeline
Proof, prompt, and run materials releaseddisclosure · day date
External expert remarks releasedverification · month date
Trust boundaries
Validation
Multiple independent mathematicians reviewed and contextualized the construction.
System
AI and tools
- Undisclosed OpenAI internal model
People
Human contributors
- Mehtaab Sawhney
- Mark Sellke
- External mathematical reviewers
Organizations
Affiliations
- OpenAI
Primary materials