Autonomous disproofs of the Erdős unit distance conjecture with GPT-5.5 Pro
- 1Santa Clarita, CA 91350
Abstract
OpenAI’s disproof of the Erdős unit distance conjecture marks a milestone in AI for mathematical research. However, the result relied on an internal model with undisclosed test-time compute, hindering independent reproduction and analysis by the community. Here we present a simple autonomous agent built on the publicly available GPT-5.5 Pro. The agent uses a problem-agnostic three-stage prompting pipeline: brainstorm, execute, and review. We ran eight independent trials with web search disabled. In each trial, the agent produced a correct or essentially correct disproof of the conjecture. The resulting proofs are diverse and do not merely reproduce earlier AI-generated proofs. Since GPT-5.5 Pro was released nearly a month before OpenAI published its disproof, our evaluation is free from data contamination. The system operates efficiently, using an average of 106.7 k reasoning tokens per trial. We release our code and all outputs, providing a publicly accessible AI agent to resolve this conjecture autonomously.
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BibTeX
@article{huang2026autonomous,
title = {{Autonomous disproofs of the Erdős unit distance conjecture with GPT-5.5 Pro}},
author = {Yichen Huang},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {2026},
month = oct,
doi = {10.1073/pnas.2621541123},
url = {https://doi.org/10.1073/pnas.2621541123},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Autonomous disproofs of the Erdős unit distance conjecture with GPT-5.5 Pro
AU - Yichen Huang
PY - 2026
DA - 2026/10/26
JO - Proceedings of the National Academy of Sciences of the United States of America
DO - 10.1073/pnas.2621541123
UR - https://doi.org/10.1073/pnas.2621541123
AB - OpenAI’s disproof of the Erdős unit distance conjecture marks a milestone in AI for mathematical research. However, the result relied on an internal model with undisclosed test-time compute, hindering independent reproduction and analysis by the community. Here we present a simple autonomous agent built on the publicly available GPT-5.5 Pro. The agent uses a problem-agnostic three-stage prompting pipeline: brainstorm, execute, and review. We ran eight independent trials with web search disabled. In each trial, the agent produced a correct or essentially correct disproof of the conjecture. The resulting proofs are diverse and do not merely reproduce earlier AI-generated proofs. Since GPT-5.5 Pro was released nearly a month before OpenAI published its disproof, our evaluation is free from data contamination. The system operates efficiently, using an average of 106.7 k reasoning tokens per trial. We release our code and all outputs, providing a publicly accessible AI agent to resolve this conjecture autonomously.
SN - 0027-8424
SN - 1091-6490
ER -