Autonomous Disproof of the Erdős Unit Distance Conjecture by a GPT-5.5 Pro Agent

OpenAI's recent disproof of the Erdős unit distance conjecture represents a milestone in using artificial intelligence to solve important open mathematical problems. However, this achievement relied on an internal model with undisclosed computational costs, limiting independent reproduction and analysis by the broader research community. In this paper, we present a simple autonomous agent built upon the publicly available GPT-5.5 Pro. Using a problem-agnostic, three-stage prompting pipeline—brainstorm, execute, and review—the agent consistently disproved the conjecture, generating a correct proof in 8 out of 8 independent trials. These 8 proofs differ from existing AI-generated proofs. The system operates efficiently, consuming an average of approximately 107k reasoning tokens per trial. We open-source our code and outputs, providing the first publicly accessible AI agent to autonomously resolve this conjecture.