Breaking·First-hour kit
Learning more about Claude's mathematical capabilities
A paper on arXiv and a Lean formalisation, rebuilt here. Read the announcement.
The first hour
What is claimed, and how much can be inspected?
A higher proven proportion of zeta zeros on the critical line. Of 1 result announced, 1 is named, 1 written up and 1 published with an artifact anyone can check.
Has anyone independent checked it?
The result held here is machine-checked.
- Proportion of zeta zeros proved to lie on the critical line: Machine-checked by qed.bot.
Does the formal statement say what is claimed?
The authors declare how their formal statement matches the claim; no independent statement anchors it.
- Proportion of zeta zeros proved to lie on the critical line: No formal statement is held. F2 declared: The correspondence is declared through a Comparator challenge, an alignment table and written divergences. Flags: declares divergences from its source.
Who did the work?
Graded A3 autonomous for who did the mathematics.
- Claude: A3 autonomous. The prompt was to attempt the Riemann hypothesis; the mathematical choices were the model's, the paper states the proof was discovered autonomously by Claude, and the accompanying formalization.yaml records the work as autonomous. Humans validated the result rather than contributing to it.
Who got there first?
No precursor, concurrent work or dispute is recorded against these results.
What would move the grades
- Fidelity rises from F2 with a Comparator check against a statement from a separate corpus.
AI activity
How grades workProved that at least two thirds of the zeta zeros are simple and on the critical line, 67.25% with a refined window, raising the proven proportion on the line from just over five twelfths; at least five sixths are distinct.
Reasoning and sources
Autonomy
The prompt was to attempt the Riemann hypothesis; the mathematical choices were the model's, the paper states the proof was discovered autonomously by Claude, and the accompanying formalization.yaml records the work as autonomous. Humans validated the result rather than contributing to it.
Autonomy declared autonomous in the project's formalization.yaml.
Details
method: Two Claude Code sessions, 31 million output tokens, roughly 60 subagents
review: Examined by Brian Conrey and Dan Goldston; formalisation author-verified by Ralph Furman
Sources
Citing this kit
qed.bot, “Learning more about Claude's mathematical capabilities: first-hour kit”, https://qed.bot/a/anthropic-2026-08-10, as of 30 Sep 2026.