OpenAI's 372 math results outrun the people who must check them

The cost of producing a result fell sharply between OpenAI's two releases. The September Navier-Stokes work used a swarm of 10,000 AI agents and millions of dollars in computing ^[6]. For the October batch, a company spokesperson said nearly every result came from a single prompt to a single agent, though some may have taken several attempts ^[27]. Reading the output got no such reduction. Each family can bundle a main proof with supporting arguments, consequences or alternative proofs ^[24], so the catalogue runs to 719 manuscripts, nearly two per family ^[26].

Machine checking covers part of that load. Lean lets a computer check every step of a proof ^[8], but 419 top-line results still had no Lean proof as of Oct. 7 ^[25]. A passed check is also narrower than understanding. Few people have understood the proofs, including those a computer has verified, implicator.ai reported ^[3]. Scott Aaronson, a UT Austin researcher, wrote on his blog that "it also appears that no human has understood just about any of these proofs yet; the race to do so has just started" ^[4].

Dana Moshkovitz's attempt to read the Unique Games proof shows what that race involves. "It feels like something written by someone who's on psychedelics," she wrote in texts Aaronson published ^[10]. "Basically the paper is so horribly written that it's impossible to read it without AI help," she wrote ^[11]. She asked an AI model to pull together claims scattered across the paper ^[12]. The stakes are concrete. If the conjecture holds, Max Cut and a long list of other optimization problems are NP-hard even when the target is only slightly better than what semidefinite programming already gives ^[13].

OpenAI traded checkability for publication speed. The Institute for Advanced Study's advisory group had asked on Sept. 29 for the model name, prompts, reasoning summary, time and computation cost of each result ^[15]. Without the prompts, I think no outside reader can separate what the model contributed from what the person prompting it supplied. Tristan Buckmaster, a New York University mathematician, raised that problem with the New York Times, saying people prompting the models could be giving them information that helped them reach results ^[17]. "There's likely to be a bunch of results where they take someone's work and then take it to completion," Buckmaster said ^[18].

The Association for Human Mathematics has taken the hardest line, urging mathematicians to stop working with OpenAI ^[23]. The strongest case for that position is the institute's own warning that proprietary models risk "creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline" ^[20]. A boycott has a cost too. It pulls readers away from a backlog in which most top-line results lack even a machine check ^[25].

Two timelines run here. This month's question is whether specific proofs, the Unique Games claim first, survive human reading. The decade's question is the one the institute's statement set out: "It is now the case that AI can output mathematical arguments in situations without the human who prompted it being able to understand the arguments, verify them, or take responsibility for them" ^[19].