OpenAI's frontier model produces solutions to hundreds of open math problems

OpenAI said an internal frontier model, an advanced AI system it has not released publicly, produced new solutions to long-standing open problems in mathematics. The company published the work in 722 manuscripts covering 372 families of problems, in a post titled “Sharing AI progress in mathematics.”

Each manuscript addresses a result mathematicians had previously left unresolved, according to OpenAI. Instead of keeping the work internal, the company published the full set along with supporting material on GitHub, a platform where developers host and share code.

Among that material are formalizations in Lean, software that checks a proof step by step. Writing a proof in Lean forces every logical step to be spelled out in a form the program can check, closing gaps that can hide in a proof written only in prose. OpenAI said it included Lean formalizations for the new results, giving outside mathematicians a way to confirm the model’s work without relying on the model’s own description of it.

The material reviewed for this story does not say which specific problems were solved, who outside OpenAI has checked the results, or how the company verified the model’s output before publishing. Those gaps matter. A claim of solutions to hundreds of open problems is unusual, and the release’s value depends on independent mathematicians being able to reproduce the proofs now that they are public.

The release fits a wider pattern among AI companies of using frontier models, the most capable systems they have built, as research tools and not only as consumer products. Publishing machine-checkable proofs lets a company support claims about a model’s mathematical ability with something other than its own description.

What happens next sits with the mathematics community. Lean formalizations are built to be checked by software rather than taken on trust, so the files OpenAI posted on GitHub can be run and verified independently. Whether mathematicians do that, and whether the 372 result families hold up as genuinely new, is not yet known. The GitHub repository OpenAI linked is where that process will show up first.