Learning more about Claude's mathematical capabilities

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Claude increased the proven lower bound of Riemann zeta zeros on the critical line from 41.6% to 67.2%.

Anthropic gave an unreleased research version of Claude an open-ended prompt to tackle the Riemann hypothesis. Over two sessions using Claude Code, the model coordinated about 60 sub-agents, ran 2,400 shell commands, and performed thousands of numerical checks. While it did not prove the hypothesis, Claude combined recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with a 2000 paper by Bombieri to raise the proven lower bound for zeros on the critical line from 41.6% to 67.2%. Anthropic mathematicians validated the result, and Claude produced a Lean formalization of its proof.

What commenters are saying

Commenters were split between amazement at the outcome and skepticism about Anthropic's framing. Several found the process-a non-mathematician repeatedly telling the model to "believe in yourself"-absurd or beyond parody. Others argued this is simply effective stochastic prompting, not actual anthropomorphization. One commenter noted the result is a genuine contribution to analytic number theory, linking to the paper and formalization. A minor thread discussed whether companies would delay releases to exploit such capabilities internally.