A failed Riemann attempt finds a stronger bound
Progress on how many zeros lie on the line, not a proof that all do.
Anthropic · Levent Alpöge · Alex Furman · earlier analytic number theorists
Start with the question
The problem
The Riemann hypothesis says that every nontrivial zero of the zeta function has real part one half. A related, weaker question asks what fraction of zeros can be proved to lie on that critical line.
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The unreasonable challenge
Anthropic says a staff member challenged an unreleased Claude model to attack the Riemann hypothesis. The attempt did not solve it. Instead, the model combined earlier analytic-number-theory work to improve a lower bound on zeros on the critical line, from 41.6% to 67.2%. [1]
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What the paper actually promises
The Alpöge–Furman paper concerns more than two thirds of zeros being simple and on the critical line. That is a quantitative theorem about a proportion. It still leaves room for zeros off the line and therefore does not settle the universal claim made by the Riemann hypothesis. [2]
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A formal statement to compare
The public formal-math repository identifies zeta23 as the corresponding Lean project. It describes pinned toolchains, comparator challenges, and independent-kernel checks. A reader can follow those verification instructions rather than relying on the percentage in a social-media headline. [3]
Inspect the evidence
The Lean formalization
Public zeta23 Lean development
The original zeta-23-lean link now redirects to anthropics/formal-math. Its project table links zeta23 to the Alpöge–Furman paper. Build and verification instructions are maintained there; no local proof rebuild was performed for this article.
Open the Lean project ↗Sources & further reading
Reviewed 9 Sept 2026. X permalinks were recovered from indexed posts and linked discussions; direct X pages were not consistently accessible. They document the conversation, not proof correctness.
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