An unreleased research version of Anthropic’s Claude raised the longstanding lower bound on the fraction of nontrivial zeros of the Riemann zeta function lying on the critical line from 41.6 percent to 67.2 percent, a jump Anthropic describes as the largest single-step advance on record. The Riemann hypothesis itself, first stated in 1859 and one of the seven Clay Mathematics Institute Millennium Prize Problems carrying a $1 million bounty each, remains unproven.

The paper, dated August 10 and titled “More Than Two Thirds of the Zeros of the Riemann Zeta Function Lie on the Critical Line,” lists Claude as author. The problem was posed by Jarred Sumner, a non-mathematician on Anthropic’s staff, who prompted the model to “take a real stab” at the hypothesis. Anthropic mathematicians Ralph Furman and Levent Alpöge communicated the write-up. At Anthropic’s request, outside number theorists Brian Conrey and Dan Goldston examined the paper on short notice.

The compute choreography is the story underneath the story. Claude generated and discarded 650 ideas before the productive run. It then executed roughly a day and a half of agentic work across two Claude Code sessions, coordinating about 60 subagents that fired off 2,400 shell commands and wrote hundreds of Python scripts, consuming 31 million output tokens. Two subagents produced the key mathematical ideas; 13 contributed supporting ideas, 13 served as validators, and two handled formalization in the Lean proof assistant.

Mathematically, the argument fuses recent unconditional techniques from Siegfred Baluyot, Daniel Goldston, Ade Irma Suriajaya, and Caroline Turnage-Butterbaugh with a 2000 paper by Enrico Bombieri, read through a Weil quadratic form. Anthropic said it doesn’t expect the methods to extend to a full proof of the hypothesis. Claude also produced a formally verifiable Lean version of the argument.

Independent scrutiny is where the release strains against its own framing. According to the AI Weekly newsletter, Anthropic hasn’t released the model checkpoint or the process transcripts, and the research post carries no direct correctness verdict from Dr. Conrey or Dr. Goldston beyond the acknowledgment that they looked at the work. What’s on the table is a claim about a machine’s mathematical output, communicated through the machine’s makers, with the artifacts of verification still inside the lab.

The result sits in a familiar register for frontier-lab publication: a genuine analytic advance, priced in tokens, staged for maximum narrative lift, and released ahead of the peer-review timeline that would ordinarily discipline the framing.

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