Erdős Problem #960
Erdős problem #960 · erdosproblems.com/960
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Geometry
- Posed by
- Paul Erdős
- Year posed
- 1984
- Years open
- 42y
- Solved
- 2026-04-09
- Model
- OpenAI internal model
- Vendor
- —
- Collaborators
- Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant
- Verification
- Site-confirmed
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
From "Short proofs in combinatorics, probability and number theory II": "The proofs in this manuscript are due to an internal model at OpenAI... The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." The authors also re-ran the public model: ChatGPT-5.4 Pro solved this problem in one of five independent attempts, by a similar route through a cyclic subgroup of a real elliptic curve, though slightly weaker in that it did not resolve the r = 3 case.
Verification
Marked solved by erdosproblems.com's official status. Solve credited via Terence Tao's AI-contributions wiki.
Sources
- PaperShort proofs II (Section 2)
- Problem recorderdosproblems.com