LLMs generate mathematical proofs

LLMs are revolutionizing the generation of mathematical proofs. OpenAI released 350 results on October 6, 2026. The manuscripts are on GitHub.

The manuscripts are on GitHub, organized into 372 research families spanning number theory, computational complexity, algebraic geometry and mathematical physics. The proofs are formalized in Lean for automatic verification, which allows researchers to quickly validate the ideas. OpenAI released a repository with 722 mathematical manuscripts generated by an undisclosed internal model.

Among the results are solutions to problems such as Navier-Stokes and a weakened version of the Riemann hypothesis. But the release drew criticism. The Association of Human Mathematics criticized the abrupt publication of 700 files, calling it a disregard for scientific norms. OpenAI withdrew three papers after identifying problems. Terence Tao defends AI as a valuable tool, but warns about the risks of losing mathematical knowledge by relying on it too heavily. The integration of LLMs into mathematics and science is generating debate about their effectiveness and limits. While some mathematicians see potential in generating proofs and publishing manuscripts, others warn about the risk of losing control over scientific knowledge.

For researchers, this may speed up discoveries, but it also raises doubts about validation. The publication was criticized for not following scientific norms, with some papers removed after problems were identified. The release may change the way proofs are validated, but there is still room for discussion. OpenAI is developing new mathematical techniques that increase the efficiency of language models. The release was made in a GitHub repository, where the proofs are formalized in Lean for automatic verification. The initiative surprised the scientific community, which is still working to understand the impact of this new form of knowledge production. But the reaction was not unanimous. OpenAI, which has already stood out for models such as GPT, is once again at the forefront of using LLMs for research, but the path is uncertain.

With information from exame.com, terrytao.wordpress.com and xataka.com.