Unreleased Anthropic model makes progress on $1 million math problem
An unreleased artificial intelligence model from Anthropic has made progress toward proving the Riemann hypothesis, one of the most famous unsolved problems in mathematics, which carries a $1 million reward. The result has been confirmed by the company's in-house mathematicians, though a full proof remains far off.
Bernhard Riemann's hypothesis, formulated more than 150 years ago, concerns the distribution of prime numbers and remains open to this day. Anthropic said a lab employee without strong mathematical training asked the model to "take a crack" at the problem and left it to coordinate the work for a day and a half. During that time, the system tried 650 solution approaches, managing 60 subagents and consuming 31 million output tokens.
According to the company, of the 60 subagents, two were responsible for developing core mathematical solutions, 13 generated new solution variants for those agents, 30 failed to produce new ideas, 13 acted as validators checking the correctness of arguments, and the remaining two helped write the initial paper. The final result was formalized using the Lean proof-checking platform, and two of Anthropic's staff mathematicians confirmed its correctness.
The model's achievement lies in significantly raising the lower bound of cases for which the hypothesis holds — a step forward from what was previously known. Still, a complete proof of the Riemann hypothesis remains elusive for both humans and artificial intelligence.
Over the past year, AI systems have already solved several difficult problems by Pál Erdős, and more powerful models have shown even more impressive results. OpenAI reported solving ten problems with its Astra model, while another Anthropic model disproved the long-standing Jacobian hypothesis. The mathematical community has mixed feelings about these successes: on one hand, there is excitement about AI's capabilities; on the other, concern, since professional standards require proofs to be attributed to specific authors who take responsibility for their discovery and correctness. Some argue, however, that mathematical theorems need not be tied to individual researchers — most stars in the universe have no names at all.
