Anthropic published a mathematical result produced with Claude: the proven share of zeta function zeros on the critical line rises from 41.6% to 67.2%. Not a solution to the hypothesis. Something rarer: a verifiable step.
- On August 10 Anthropic published a result on the Riemann hypothesis produced with Claude: the lower bound for the share of zeros on the critical line rises from 41.6% to 67.2%.
- It was achieved by combining known techniques, not by new theory: 60 subagents, 650 generated ideas, 31 million tokens.
- The proof was reviewed by mathematicians and formalized in Lean - a system that machine-checks every step.
The headlines will say artificial intelligence is conquering mathematics. Anthropic's official text says less. Which is exactly why I trust it more.
The Riemann hypothesis is a 167-year-old riddle about where the zeros of one function stand. Nobody has proven it. What gets proven are bounds: what share of the zeros sit where they should. The claim here is exactly that much - a higher bound, not an answer.
And the real news is the method. The model did not invent new theory. It read the literature, glued together pieces from four different authors and did not drop a single step along the way. That is work that costs a human team months of reading.
The most important line in the announcement is about Lean. Formal verification means the model is not trusted - it is checked, step by step, by a machine that does not accept almost right. That habit travels far beyond mathematics. Demand it from every system that promises you truth.