OpenAI's math proofs fall short of a Princeton panel's verification standards

The standard the mathematicians emphasized most was the plainest one: a human should be able to understand the proof ^[4]. The group behind it, nine researchers at Princeton's Institute for Advanced Study, had published guidelines for frontier labs at the end of September ^[13]. OpenAI said it consulted the panel to avoid repeating an earlier controversy ^[12], and on that measure it fell short; it is not clear the lab is taking responsibility for ensuring human understanding follows ^[4]. The reasoning behind the proofs was mostly withheld, and the chain of thought came with about 1.4 percent of the manuscripts ^[3][17].

Terence Tao, who has criticized the lab's approach, put the worry plainly after the release. "Problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is 'solved', and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field," he wrote on social media ^[15].

The second gap is mechanical. A model writes a proof in ordinary language, then restates it in Lean, a programming language that checks a proof by compiling it as code ^[7]. If the restatement drifts from the prose, the Lean file can compile cleanly while proving something other than what the English claimed. The Cambridge and King's College authors say the gaps they found do not disprove either version, but they do question whether a model can be trusted to formalize its own work ^[10].

That risk is why the authors want the usual scrutiny applied. "Because of the phenomenon of mistranslations ... the NL proof by OpenAI and other autoformalised Lean proofs should not prima facie be trusted without the same peer review process and scrutiny that other proofs are subjected to," they conclude ^[8].

OpenAI did follow some of the group's requests, releasing results quickly and describing how the models reached them ^[9]. The group has not graded the release itself. "It is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully," it said ^[16]. Until that community has read these proofs and can stand behind them, a lab's claim to have solved a problem is a submission waiting for review.