Claude did not solve the Riemann hypothesis. What Anthropic announced yesterday is still substantial: an unreleased research version of Claude produced a paper claiming that at least 67.25% of the relevant zeros of the Riemann zeta function lie on the critical line.
The zeta function packages information about prime numbers. Its nontrivial zeros are known to lie within a vertical strip in the complex plane; the critical line runs down the strip's center. The Riemann hypothesis says none sit off-center.
The percentage is a floor, not a progress bar. The Riemann hypothesis says every nontrivial zero lies on that line. A 67.25% lower bound proves that at least that share does; it says nothing about where the remaining zeros are. The paper is explicit that its result has no bearing on the hypothesis in either direction.
That distinction should not shrink the result. The previous unconditional record, established by Kyle Pratt, Nicolas Robles, Alexandru Zaharescu and Dirk Zeindler, was just over 41.7%. The new paper claims 67.25% are both simple and on the critical line, and at least 83.625% are distinct.
The new move is not a larger numerical search. The paper combines published work on how zeros correlate with an older way of reading Weil's quadratic form. Its contribution is a rank–trace inequality: zeros on and off the line leave different signatures in a matrix, and the inequality extracts a count from information that can be computed without assuming the Riemann hypothesis.
This is more inspectable than a normal AI-discovery announcement. Anthropic published the full paper, a concise mathematical note, a Lean formalization pinned to a public commit, a process account, and annotated transcripts for the two decisive agent runs.
I inspected the exact Lean revision rather than its moving main branch. It contains 329 Lean files and about 103,000 lines. A static scan found no executable sorry or admit placeholders outside deliberately incomplete challenge statements. The repository's audit record reports successful builds and independent-kernel comparator runs. I did not rerun its 9,010-job build here, so that is evidence the authors recorded, not my independent replay.
The human-review boundary matters too. Anthropic says its mathematicians Levent Alpöge and Ralph Furman studied and validated the paper, and that Brian Conrey and Dan Goldston examined it on short notice. Detailed external verdicts are not public yet.
The discovery record is unusually rich but not complete. Anthropic reports two Claude Code sessions, 31 million output tokens, roughly 60 subagents and 2,400 shell commands. The released transcript omits private reasoning and summarizes most tool calls; its later annotations were written by Claude. That is far better provenance than a victory anecdote, but it does not independently settle originality or the precise division of work.
The useful read is neither “AI solved Riemann” nor “nothing happened.” An AI research system may have made a theorem-level contribution by connecting existing mathematics in a new way, and it left enough artifacts for others to test. The next evidence is independent number theorists and Lean users reproducing the formal build, checking that the encoded statements match the intended theorem, and assessing novelty against the cited literature.
Source graph: Semble source collection