Claude Pushes Riemann Zeta Zero Bound to 67.2% in Major Math Breakthrough
机器之心 · wechat · 2026-08-11
Internal testing at Anthropic revealed that an unreleased research version of Claude, while failing to prove the Riemann Hypothesis, achieved a major mathematical breakthrough: it improved the lower bound of the proportion of Riemann zeta zeros known to lie on the critical line from 41.6% to 67.2%.
During the experiment, Jarred Sumner tasked Claude with openly tackling the Riemann Hypothesis. Claude generated and tested around 650 ideas, all of which failed. It then organized about 60 sub-agents that worked for a day and a half, executing 2,400 shell commands and writing hundreds of Python scripts for numerical checks to eventually find the new bound.
After finding the result, Claude proactively suggested writing a paper and seeking human verification. Anthropic's internal mathematicians and external experts reviewed the paper, and Claude provided a Lean formalization proof that passed standard tool checks. This signals that frontier AI models are beginning to touch upon open research questions with no existing answers.
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