AI Solves a Major Unsolved Math Problem. Not Everyone Is Happy

At the Heidelberg Laureate Forum in Germany, math wasn’t the only thing on people’s minds. The talk all week was AI — specifically the way OpenAI, Anthropic and Google are pushing their models into territory that used to belong to humans with blackboards and patience. In a field built on proof, that matters. Math gives AI a rare test: the answers can be checked, step by step, without anyone having to take the model’s word for it.

That is why this summer landed so hard. AI systems moved from being clumsy on research-level problems to tackling a stream of famous puzzles, from Erdős problems to a verified proof of Fermat’s Last Theorem, and then to OpenAI’s claim that it had solved the Navier–Stokes existence and smoothness problem. That one sits among the seven Millennium Prize Problems set out by the Clay Mathematics Institute in 2000, and only the Poincaré conjecture has been solved by humans so far. If OpenAI’s claim holds up, it is not just another demo. It is a milestone for automated reasoning.

Not everyone is celebrating. Jacob Tsimerman said the pace has been faster than many expected, while Peter Scholze dismissed the big problem hunts as little more than benchmark-chasing and public relations. Others were more sharply critical of OpenAI’s conduct around the Navier–Stokes announcement. Geordie Williamson and Michael Harris said the company’s behavior cut against the norms of the math community, and Harris repeated claims that correspondence with Tristan Buckmaster felt coercive, censorious and even threatening. OpenAI did not respond before publication.

The deeper worry is bigger than one company’s manners. Williamson’s point was that math’s usual goal — understanding — is getting harder to measure when an AI can spit out an answer without producing methods humans can absorb or reuse. That leaves universities and researchers in a bind: how to judge people, how to train them, and what counts as real progress when the machine may have done the headline work but not the thinking people actually build on.

For younger researchers, that pressure is already personal. Mita Ramabulana said two of OpenAI’s August math advances overlapped with his own work, and he is not thrilled about problems he has spent time on being solved by someone else’s model. Ailsa Robertson said many of her colleagues are using LLMs so heavily that some are paying thousands of euros for extra tokens, even as OpenAI offers 100,000 free licenses to academics. Her own PhD has shifted away from pure math and toward quantum-safe cryptography’s social consequences, because she does not want a career spent verifying LLM output.