Claude research model raises Riemann zeta zero bound from 41.6% to 67.2%
The Riemann hypothesis has been open for roughly 150 years and carries a $1 million prize. Forbes described the advance as the largest single advance in the hypothesis's 165-year history, achieved in 1.5 days against 37 years of minimal human progress on the same measure.
An unreleased research version of Claude produced a paper claiming at least 67.250% of nontrivial Riemann zeta zeros are both simple and on the critical line, raising the prior proven lower bound of 41.6%. The paper also claims at least 83.625% of zeros are distinct, with analogous results for fixed primitive Dirichlet L-functions. Anthropic confirmed the result, noting it drew on extensive prior research by mathematicians over past decades, but stated it does not expect the techniques to lead to a full proof of the Riemann hypothesis. The result has not undergone conventional peer review and cannot be reproduced end-to-end because the model used is unreleased.
An Anthropic mathematician claimed August 23 to have used Claude to show that the 6-sphere (S^6) admits a complex structure, a problem open since 1948, describing the result as 'a beautiful new geometric object'.
No independent verification has been reported, and the claim arrives alongside the still-unreviewed result in which an unreleased Claude model raised the proven lower bound on nontrivial Riemann zeta zeros from 41.6% to 67.250%.
Anthropic mathematician claimed to have used Claude to resolve the S^6 complex structure problem
An unreleased Anthropic research model raised the lower bound for nontrivial Riemann zeta zeros on the critical line from 41.6% to 67.250%, Anthropic announced August 19; the paper also claims 83.625% of zeros are distinct.
Forbes called it the largest advance in the hypothesis's 165-year history, achieved in 1.5 days. Two Anthropic mathematicians and external experts Brian Conrey and Daniel Goldston reviewed the proof, and Lean checked the formal derivation, but the result cannot be reproduced end-to-end and has not passed peer review because the model is unreleased.
Forbes reported August 19 that an unreleased Anthropic model's improvement of the Riemann zeta zeros bound from 41.6% to 67.250% is the largest advance in the hypothesis's 165-year history, achieved in 1.5 days against 37 years of prior human progress; kingy.ai flagged the result cannot be reproduced end-to-end and has not passed peer review.
Researcher Gavin Crooks also reported that Claude closed an entire class of open problems in stochastic thermodynamics over a few days of dialogue, work he estimated at months for a graduate student.
Researcher Gavin Crooks reported Claude closed an open problem class in stochastic thermodynamics over a few days of dialogue
Anthropic announced on August 17 that an unreleased research version of Claude raised the proven lower bound for the fraction of Riemann zeta zeros satisfying the Riemann hypothesis from 41.6% to 67.2%, stating "it did make strides on a related problem" while adding it does not expect the techniques used will lead to a full proof. The Riemann hypothesis is a 150-year-old problem with a $1 million prize still unclaimed.
The Neuron Daily reported the advance, noting the $1 million prize remains unclaimed
Zvi newsletter noted Anthropic does not expect the techniques to lead to a full proof
Anthropic announced Claude raised the Riemann zeta zero lower bound from 41.6% to 67.2%
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