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GPT-5.5 Pro autonomously proves sum-product conjecture over R

By PulseAugur Editorial · [1 sources] ·

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]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

GPT-5.5 Pro autonomously proves sum-product conjecture over R

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Academic paper detailing AI model's capability in mathematical proof generation. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Yichen Huang ·

    Autonomous disproofs of the sum-product conjecture over $\mathbb R$ with GPT-5.5 Pro

    arXiv:2607.20525v1 Announce Type: new Abstract: OpenAI's recent disproof of the Erd\H{o}s unit distance conjecture marked a milestone for AI in mathematics. It also inspired another breakthrough: a human disproof of the Erd\H{o}s--Szemer\'edi sum-product conjecture over $\mathbb …

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