Claude's math result: 60 subagents, 31M tokens

Anthropic published a result on August 10 that will get read as a headline about math and should be read as a spec sheet for agent orchestration. An unreleased research build of Claude improved a lower bound on the Riemann zeta function from 41.6% to 67.2%. The number that matters to anyone running subagents in production is the receipt underneath it: about 60 subagents, 31 million output tokens, 2,400 shell commands, and 650 ideas that did not work before one did.

What actually happened

Anthropic's write-up is unusually specific about process. Claude was asked to attempt the full Riemann hypothesis. It generated and tried roughly 650 ideas, none of which held. It then spent about a day and a half coordinating a fleet of subagents across two sessions, burning 31 million output tokens and issuing around 2,400 shell commands while writing hundreds of Python scripts.

The subagent roles are the interesting part. Of the ~60, two produced the key ideas, thirteen contributed usable ideas, thirty attempted approaches that failed, thirteen validated results, and two helped draft the paper. Half the fleet produced nothing directly usable, and that was fine — it was how the search got covered.

Then the verification layer. Claude downloaded 54 arXiv papers to check the result was actually new. It produced a Lean formalization that passed standard validation. Two Anthropic mathematicians, Levent Alpöge and Ralph Furman, examined the work, and external number theorists Brian Conrey and Dan Goldston reviewed it. Anthropic is explicit that it does not expect these techniques to prove the hypothesis, and that the bound improvement was a byproduct of asking for the whole thing.

Why the token receipt matters for your business

Every operator we talk to has tried the same experiment: point one agent at a hard task, get a mediocre answer, conclude the tech is oversold. This run is the counterexample, and it is not because the model is smarter than yours. It is because the work was structured as a search with a budget, a failure tolerance, and a verification gate.

Three things to steal:

Budget for the dead ends, not the answer. Thirty of sixty subagents failed and 650 ideas went nowhere. If your agent budget only covers the happy path, you are funding a demo, not a search. Price the run, not the call.

Split roles: generate, validate, write. Anthropic separated idea generation from validation from drafting. Generators that grade themselves grade generously. This is the same reason you do not let the developer who wrote the migration also sign off on it.

Make the verification machine-checkable. The Lean proof is the load-bearing piece — it is what turns "the model claims" into "the claim compiles." Your equivalent is a test suite, a schema check, a reconciliation query against the ledger. If nothing can mechanically say wrong, you have not built a verification step, you have built a second opinion.

The uncomfortable corollary: 31 million output tokens is a real invoice. Fan-out orchestration is not free, and the cost lands whether or not you get a result. That is an argument for scoping agent fleets at tasks where a correct answer is worth four figures — a migration, a reconciliation, an audit — and not at drafting your newsletter.

Sources: Anthropic.