Mathematicians face months of reading to judge whether OpenAI's hundreds of proofs contain new ideas

OpenAI says each result solves, or moves substantially toward solving, a major unsolved problem in math or theoretical computer science ^[1]. Lean, the tool behind the verified share, is a programming language that validates a proof's logic ^[19]. Scientific American does not say how many of the hundreds have passed through it ^[19].

For those that have, correctness is close to settled, and the open question becomes whether a proof contains anything new ^[19]. Mathematicians will need months to decide whether the proofs carry novel and important ideas or are mostly mash-ups of existing techniques, according to Scientific American ^[2]. Lean checks logic, so it cannot make that call ^[19]. OpenAI's spokesperson said many of the new results are not yet understood by the company's own mathematicians ^[13].

How the results were produced is a second question, and a Lean check does not reach it. A verified proof shows its steps, but not how many attempts the model made or how much computing it spent ^[19]. The spokesperson who described the single-prompt workflow also said some results might have taken multiple attempts ^[18]. Cost per result is what separates the Navier-Stokes swarm from a tool an individual mathematician could run ^[7]. If the single-agent account is true, Scientific American notes, that kind of mathematical power could soon be accessible to anyone ^[20].

Scientific American reports considerable skepticism among mathematicians, given OpenAI's reputation in the field for bold claims and little transparency ^[6]. "Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified," said Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology. "We should ask for receipts." ^[17]

The release falls short of the standard OpenAI's own advisory group wrote. Of the three per-result items the group recommended, none arrives in the requested form: the model stays internal, the prompts are withheld, and compute time comes only as an average ^[15]. An average across hundreds of problems cannot show which results came on the first try and which took several ^[3][18]. The recommendations are particularly critical of proprietary internal models that mathematicians cannot broadly access ^[14]. The spokesperson said the team takes the guidelines seriously and is doing its best to comply, but that the company is not bound by them ^[10]. OpenAI also said it is working to release the model as quickly and responsibly as possible ^[11].

Two prominent mathematicians differ on whether the volume helps. "If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us," said Daniel Litt, a mathematician at the University of Toronto. "To me, it's going to be a good thing for mathematics." ^[12] Terence Tao has criticized OpenAI and other frontier labs for the "insane" pace of their AI-generated results ^[4].

OpenAI says it cannot slow down because these problems are an indispensable test of whether its AI is getting smarter ^[5]. That test counts problems solved. It does not measure what limits mathematicians: the months of reading needed to find what is new ^[2]. Nor does it capture what limits a would-be user, a per-result compute cost that OpenAI reports only as an average ^[3]. In my view the Lean checks have moved the hard part of this release from correctness to novelty, for the verified share and only for it ^[19].