For more than 150 years, the Riemann hypothesis has remained one of the biggest open problems in mathematics, a mystery about the distribution of prime numbers that carries a $1 million reward for a general proof. No one has yet claimed it — and today's AI models haven't either. But, as Anthropic announced this week, they can get much further than one might expect.
The feat came from a research model that has not yet been released. An Anthropic staff member with no significant mathematical training asked the model to "take a real stab" at proving the hypothesis — then left it coordinating the task for a day and a half. In that time, the system tested 650 different ideas for solving the problem, orchestrating 60 subagents and spending 31 million output tokens.
"Out of the 60 subagents, two were responsible for developing the key mathematical ideas," a note in the paper explains, "13 contributed ideas to these agents, 30 attempted (but were unable) to develop new ideas, 13 served as validators to check the correctness of the arguments, and the final two helped to write the initial paper." The result: the model raised the known lower bound for the fraction of zeros of the Riemann zeta function satisfying the hypothesis from 41.6% to 67.2%. It is not the proof — Anthropic itself says it doesn't expect the techniques used to get there — but it is a striking leap on a problem that has defied mathematics since 1859.
The finding was confirmed by two in-house mathematicians and formalized using the open source proof assistant Lean, an important step for the credibility of the result. Not coincidentally, the researchers invited outside experts, such as Brian Conrey and Dan Goldston, to examine the paper on short notice. The transparency here is not a detail: in a field that values verifiability, an AI-generated result needs to survive the scrutiny of those who understand the subject.
The case is the latest in a string of mathematical breakthroughs led by large language models. Erdős problems have been solved by AI over the course of this year; OpenAI published ten major results proved by its internal "Astra" model; and a separate Anthropic effort disproved the long-standing Jacobian conjecture. With each release of more powerful models, the results grow more impressive.
That growth, however, divides the community. In June, a group of prominent mathematicians signed a public declaration warning that AI could undermine core values of the field — above all the expectation that proofs be "attributable to specific authors who take credit for their discovery and assume responsibility for their correctness." On the other side, Fields Medal winner Timothy Gowers questioned whether AI's influence might change mathematics in a more complex and positive way.
The Riemann hypothesis episode doesn't settle that debate, but it makes it concrete. If a model, guided by a staff member without formal math training, can improve a result researchers spent decades building, the question stops being whether AI will take part in mathematics — and becomes how the community will give credit, validate, and above all trust demonstrations that no human truly "thought through" from start to finish. Perhaps this week's biggest discovery is not the technical advance, but the proof that this dilemma is already urgent.
Sources: TechCrunch, Anthropic, SaveDelete
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