Among the most notable achievements is a disproof of Connes’s rigidity conjecture and new results for multicolor Ramsey numbers, resolving questions originally posed by mathematician Paul Erdős.
These breakthroughs suggest that AI infrastructure is evolving from a conversational tool into a sophisticated engine for scientific discovery.
The results have direct implications for technical fields such as post-quantum cryptography—encryption methods designed to remain secure against future quantum computers—and coding theory.
OpenAI noted that the computational work required to find these solutions would cost roughly $2,000 at current API rates, indicating that high-level theoretical research may become significantly faster and more cost-effective as AI models scale.
To ensure the accuracy of the findings, the model formalized its arguments into Lean certificates, which are digital files used to verify the logical correctness of a mathematical proof.
While human researchers assisted in preparing the final manuscripts, OpenAI stated that the core arguments were generated entirely by the AI.
The company is now sharing these results and the model's thinking processes with the broader academic community to encourage further research and to navigate the ethical questions of attribution in AI-assisted science.