An unreleased research version of Anthropic’s Claude made progress on a problem linked to the Riemann hypothesis. The hypothesis concerns the distribution of prime numbers and has remained unsolved for more than 150 years. A staff member without advanced math training simply asked the model to take a real stab at proving it. The model then worked for about a day and a half, testing 650 ideas across 60 subagents and using 31 million output tokens. It did not prove the hypothesis. Instead it improved a longstanding lower bound on the fraction of zeros of the Riemann zeta function that lie on the critical line, raising the figure from 41.6 percent to 67.2 percent. Two Anthropic mathematicians confirmed the result, and the argument was formalized in the Lean proof assistant. External experts also examined the work. The finding continues a recent run of AI contributions to open mathematical problems.
An unreleased research version of Anthropic’s Claude made progress on a problem linked to the Riemann hypothesis. The hypothesis concerns the distribution of prime numbers and has remained unsolved for more than 150 years. A staff member without advanced math training simply asked the model to take a real stab at proving it. The model then worked for about a day and a half, testing 650 ideas across 60 subagents and using 31 million output tokens. It did not prove the hypothesis. Instead it improved a longstanding lower bound on the fraction of zeros of the Riemann zeta function that lie on the critical line, raising the figure from 41.6 percent to 67.2 percent. Two Anthropic mathematicians confirmed the result, and the argument was formalized in the Lean proof assistant. External experts also examined the work. The finding continues a recent run of AI contributions to open mathematical problems.