An unreleased Claude model pushes a Riemann Hypothesis bound from 41.6% to 67.2%

9:00 AM PT · August 11, 2026

Anthropic researchers gave an unreleased Claude model what they call an ‘unreasonable challenge’: attempt the Riemann Hypothesis, one of mathematics’ oldest unsolved problems, first posed in 1859. The model did not solve it, but after roughly 650 failed approaches, it found an unexpected path to a related result, raising the known lower bound on the fraction of the zeta function’s nontrivial zeros that lie on the critical line from 41.6% to 67.2%. Anthropic calls it the largest single step advance on that bound in the problem’s history. The breakthrough run used about 60 Claude subagents working in parallel across roughly 31 million output tokens, 2,400 shell commands, and hundreds of Python scripts, building on recent papers by mathematicians Baluyot, Goldston, Suriajaya, and Turnage Butterbaugh alongside a 2000 paper by Enrico Bombieri. Two Anthropic mathematicians reviewed the argument, outside experts examined it, and Claude produced a machine checkable version using the Lean proof assistant. Anthropic is careful to note the result has not yet passed conventional peer review and that the techniques used are unlikely to lead to a full proof of the Hypothesis itself. Even so, it is one of the clearest public examples yet of a language model contributing an original, verifiable advance to open pure mathematics research.