A result with more of its working shown
OpenAI says an internal frontier model produced a set of new mathematical results. It has published the collection in a GitHub repository and included formalizations for many proofs in Lean, a language that allows a proof to be checked by computer. The repository also records attempted problems, compute estimates and ten reasoning summaries.
OpenAI says the average result used compute equivalent to roughly three hours of ChatGPT Pro thinking. That is the company’s estimate, included as context for the work rather than a measure that makes the results automatically important.
What verification adds
A formal proof does not replace mathematical judgment about whether a result is significant, novel or well-presented. It can, however, make the logical steps more inspectable and catch errors in the formalized argument. OpenAI says it is consulting an independent advisory group and plans to improve citations and exposition as it shares future results.
The release makes a useful distinction: model-produced mathematical claims can be shared with artifacts that invite scrutiny. Some formalizations are still incomplete, and the repo is expected to grow. Researchers and technically curious readers can review the source, check the formal proofs that exist and see what remains unsupported.
Source published 2026-10-06. Coverage is based on the maker’s announcement and demonstration.