Anthropic said on Tuesday that an unreleased research version of Claude raised the proven lower bound on the fraction of non-trivial Riemann zeta zeros lying on the critical line from 41.6% to 67.2%, a genuine step inside a problem first stated in 1859 and still carrying an unclaimed $1 million Clay Mathematics Institute bounty. The company was explicit that this isn’t a proof of the Riemann hypothesis, and that it doesn’t expect the technique to yield one.

The framing matters as much as the number. The person driving the run, Anthropic staffer Jarred Sumner, is described by the company as a non-mathematician; his prompt was to “take a real stab” at the problem, and his contribution during execution was, per Anthropic, “mostly limited to sending Claude messages of encouragement.”

A first attempt generated 650 ideas and failed. The second run, executed across two Claude Code sessions and consuming roughly 31 million output tokens, had the model self-coordinate about 60 subagents over roughly 1.5 days, firing off 2,400 shell commands and hundreds of Python scripts. Anthropic’s breakdown: 2 subagents produced the key mathematical ideas, 13 supplied supporting work, 30 tried and failed, 13 acted as validators, and 2 wrote the paper.

The 35-page manuscript, dated August 10, 2026, leans on a Weil-induced quadratic form and a rank-trace inequality, extending prior work by Bombieri, Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh. Anthropic mathematicians Ralph Furman and Levent Alpöge studied it internally; Brian Conrey and Dan Goldston reviewed it on short notice. A Lean 4 formalization was published alongside.

The result sits awkwardly between two narratives Anthropic usually keeps apart: the safety-inflected caution about frontier models, and the capability flex. Here the flex is a bounded, checkable, formalized contribution to analytic number theory, produced largely without human mathematical steering. That’s the part worth sitting with.

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