AI Is Cracking Maths' Hardest Problems. The People Who Devoted Their Lives to Them Are Not Celebrating.

Key points

• A peer-reviewed proof posted to arXiv in August 2026 shows that at least two thirds of the nontrivial zeros of the Riemann zeta function are simple and lie on the critical line, beating the previous record of five twelfths, and it has been formally verified in the Lean 4 proof-checking language.
• OpenAI claimed this summer to have solved the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems.
• Mathematician Tristan Buckmaster alleged that OpenAI's conduct during the announcement was coercive and threatening toward researchers working on the same problem; OpenAI did not respond to requests for comment.
• Young researchers say they feel financially and professionally pressured into using large language models (AI systems trained on vast text datasets) just to stay competitive for jobs.
• The verified arXiv proof, by Ralph Furman, is separate from any AI company claim on the Riemann hypothesis.

Mathematics has always moved slowly, on purpose. A result must be checked and then checked again by people who are actively trying to break it. This summer, that norm ran headlong into a very different culture.

The collision was on full display at the Heidelberg Laureate Forum in September 2026, where, as IEEE Spectrum AI reported, conversations kept returning to one subject: the speed at which AI companies are claiming to solve problems the field has guarded for generations.

What exactly has been solved, and by whom?

Two things happened this summer, and keeping them separate matters.

First, a human mathematician. In August 2026, Ralph Furman posted a proof to arXiv showing that at least two thirds of the nontrivial zeros of the Riemann zeta function (a specific mathematical object whose behaviour, according to the century-old Riemann hypothesis, governs the distribution of prime numbers) are simple and sit on the critical line, meaning the strip of the complex plane where mathematicians expect all the action to be. The previous unconditional record was five twelfths. Lean 4, a computer program that checks mathematical arguments line by line, has formally verified the proof. This is not a solution to the Riemann hypothesis itself, but it is the strongest unconditional progress on it in decades.

Then came the AI companies. OpenAI announced it had solved the Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute's seven Millennium Prize Problems, each carrying a million-dollar prize and each representing a question mathematics had not been able to answer since 2000. We first reported OpenAI's claim on 8 September, when a rival mathematician also alleged the company had raced ahead after learning of his own progress. Anthropic separately used an unreleased version of its Claude model to work on the Riemann hypothesis, reportedly making progress on a related question without cracking the central one. OpenAI is said to be targeting the Hodge conjecture next.

Should mathematicians be worried?

Many already are, and their concern goes beyond professional pride.

Fields Medalist Geordie Williamson (University of Sydney) put the structural problem plainly: AI solutions can produce an answer without generating the new methods or conceptual understanding that let mathematicians build further knowledge. Solving a problem and understanding it are not the same thing. Those two yardsticks are, in Williamson's words, becoming "very, very quickly uncorrelated."

The human cost is already showing up. Mita Ramabulana, a young mathematician at the University of Cape Town, found that two of the ten results OpenAI announced in August overlapped with his own research. Ailsa Robertson, a PhD student in quantum-safe cryptography at the University of Amsterdam, says colleagues are spending thousands of euros they don't have on AI tokens. Robertson has restructured her PhD away from core mathematics toward policy and societal implications, partly because she doesn't want a career that consists of checking AI output.

The conduct around OpenAI's Navier-Stokes announcement added its own layer of alarm. Mathematician Michael Harris (Columbia University) said he trusted accounts from Tristan Buckmaster (New York University) describing correspondence with OpenAI that Buckmaster characterised as coercive and threatening. Harris noted that most media coverage was consistent with that characterisation. OpenAI has not commented.

AI2Day has followed rising tensions inside OpenAI closely this month, including a safety writer's public resignation.

What strikes me most, having watched this beat for months, is that the verification crisis is the real story. Fields Medalist Peter Scholze called these efforts "some kind of PR stunt" at the Forum, and he may be right about the motive. If OpenAI's Navier-Stokes proof can't be independently checked in full, the million-dollar prize isn't the point: trust is. And mathematics runs entirely on trust.