Wispr Flow turns your voice into clean, ready-to-send writing — speak naturally, it strips the filler and fixes the punctuation. I've used it daily since February 2026 to build this newsletter. Read the full review →
A member of Anthropic's staff who is not a mathematician typed a request to an unreleased version of Claude: take a real stab at the Riemann hypothesis.
That problem has been open since 1859 and carries a million-dollar prize. Claude failed at it, exactly as expected. But on the way down it improved a related, entirely real result — the provable minimum share of the zeta function's zeros that sit where the hypothesis says they must. That figure stood at 41.6%. Claude moved it to 67.2%.
Human mathematicians moved the same number roughly seven points in fifty years.
The first attempt died completely
Claude generated and tested 650 ideas. All 650 failed. That is where most operators would close the session and conclude the tool can't do the work. Instead, Jarred Sumner told it to try again.
The second run lasted a day and a half. Claude coordinated about 60 subagents that executed 2,400 shell commands, wrote hundreds of Python scripts, and ran thousands of numerical checks — 31 million output tokens across two Claude Code sessions. Sumner's own contribution was mostly encouragement, variants of keep going and believe in yourself, which Anthropic says helped Claude past its initial skepticism that it could achieve anything here at all.
See how AI delivers fast, secure, personalized experiences
Watch Fin and Plaid now on demand to see how AI can resolve issues directly in customer conversations. This includes everything from reducing bank-linking friction, enabling proactive support, and helping customers complete real financial tasks.
The org chart is the part worth studying
Anthropic published the full breakdown of those 60 agents: 2 developed the key mathematical ideas, 13 fed ideas to those two, 13 validated the arguments, 2 wrote the paper — and 30 tried to develop new ideas and could not.
Half the swarm produced nothing. That is not a bug report, it is the cost of search. Two agents found the idea and there was no way to know in advance which two.
The swarm then attacked its own work: agents refereed each other, hunted counterexamples, downloaded 54 arXiv papers to check nobody had already proved it, and independently re-proved the result from scratch. Claude volunteered to write it up and recommended a human number theorist check it.
What 67.2% does not mean
Nobody checked 67.2% of the zeros. Trillions of zeros have been computed and every one sits on the line — and that proves nothing, because there are infinitely many. The 41.6% and 67.2% figures are a proven floor across the entire infinite set: at least this share must be on the line, however far out you look. That is why a fraction of a point used to be a publishable theorem, and why 25.6 points in thirty-six hours is startling. The hypothesis itself claims the floor is 100%, and Anthropic says plainly it doesn't expect these techniques to get there.
Four things you can use
Budget for failure explicitly — thirty duds out of sixty and the run still worked. Keep validators separate from producers, because an author reviewing their own work doesn't catch their own errors. Ask agents to disprove their answer rather than confirm it. And treat one more attempt as a strategy: the entire result sat on the far side of 650 failures and a human saying try again.
The honest caveats
Brian Conrey and Dan Goldston examined the paper on short notice — a fast informal look by qualified people, not journal peer review, which hasn't happened. The Lean formalization is real and machine-checkable, which isn't the same as the field having accepted the result. And the model is unreleased, so you can't run it.
But the paper, the Lean proof, Claude's own account of how it got there, and the process transcripts are all public. Anthropic withheld the model and handed out the method. You can read Anthropic's write-up here →
The full edition on the site adds the complete subagent allocation table and the copy-paste prompt that designs a swarm structure for your own task.
— Jerry
AI Super Simplified