Autonomous sum-product disproofs
| Field | Additive combinatorics / AI-math methodology |
|---|---|
| Researcher | Yichen Huang |
| Model | GPT-5.5 Pro |
| Date | Jul 9, 2026 |
| Status | Strong AI-math result / methodology |
| Prompts | system, plan, construct, review |
Result
An autonomous three-stage plan, construction, and review pipeline produced correct proofs in 7 of 8 independent trials for a disproof of the Erdős–Szemerédi sum-product conjecture over the reals. The repository releases the code, all eight transcripts, and generated proofs; the one failed trial contains an honestly identified unresolved gap.
This entry is primarily methodological: the underlying mathematical result was already known, while the contribution is the autonomous proof-production and review workflow.
Provenance
The setup disabled web search and used a public GPT-5.5 Pro model. The prompts below are transcribed from the released paper and repository.
Prompt techniques
The first round forces an explicit proof plan and gap assessment. The second round asks for completion, and the third independently audits the constructed proof and requires every gap to be resolved.