A new paper details an AI agent, built on OpenAI's GPT-5.5 Pro, that autonomously generated proofs for the falsity of the Erdős--Szemerédi sum-product conjecture over $\mathbb R$. The agent successfully produced correct proofs in 7 out of 8 independent trials using a three-stage prompting pipeline: proof-plan proposal, construction, and review. These proofs varied in their approaches, with some resembling existing unit-based methods and others employing algebraic integer regions. The system utilized an average of 132.4k reasoning tokens per trial, and the associated code, intermediate outputs, and proofs are being released as a reproducible case study. AI
IMPACT Demonstrates advanced autonomous reasoning capabilities in AI, potentially accelerating mathematical discovery.
RANK_REASON Academic paper detailing AI model's capability in mathematical proof generation. [lever_c_demoted from research: ic=1 ai=1.0]
- alphaXiv
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- Erdős unit distance conjecture
- Gotit.pub
- GPT-5.5 Pro
- Hugging Face
- $\mathbb R$
- OpenAI
- ScienceCast
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