OpenAI's AI solves 90 long-open math problems
OpenAI says an internal model generated 722 papers and closed 90 of the field's 500 hardest open problems, with each proof formalized in Lean so it can be machine-checked rather than taken on faith — a different kind of claim than a benchmark score, because a skeptic can verify it line by line instead of trusting a leaderboard. That's the real test of whether 'AI does research' means anything, and it's a genuine shift from AI applying known math to AI generating math a human hadn't yet produced. If you've ever had to defend an experimental result against reviewers who didn't trust your pipeline, the appeal of a formally checkable proof over a trust-me result will feel familiar.
What’s Lean-formalized proof?
Lean is a proof assistant — a language and checker for writing mathematical proofs so that every logical step can be verified by a computer, rather than reviewed and trusted by a human mathematician reading prose.
Pairing an LLM with Lean closes the main hole in 'AI solved a math problem' claims: a model can generate plausible-sounding proofs that are actually wrong, but a Lean-checked proof has been confirmed step by step against formal logic, so the output isn't just confident-sounding text.
The live debate is about what '90 of 500 open problems' actually means — open problems vary enormously in significance, and some of these formalized proofs may restate known techniques in Lean's syntax rather than discover new mathematical insight. Whether this is a watershed or a very well-documented version of existing math is still being argued.