Do all nontrivial zeros of the Riemann zeta function lie on the critical line?
The source trail 12
Findings, with context
DiscussionSep 4, 2026
A source discussing Riemann
note.com contains the excerpt below in a discussion related to Riemann. Read the source for the surrounding context.
“the final proposition required is a general proof that ζ(ρ)=0 → Re(ρ)=1/2 holds for all non-trivial zeros.”
This excerpt is evidence of what the linked page says, not verification of its claims. Source reports an update on 2026-09-04; this is not necessarily the original posting date.
arxiv.org contains the excerpt below in a discussion related to Riemann. Read the source for the surrounding context.
“We prove unconditionally that at least two thirds of the nontrivial zeros of the Riemann zeta function”
A linked paper is a research claim, not confirmation that the problem is solved. Source reports an update on 2026-08-19; this is not necessarily the original posting date.
groundtruth.day contains the excerpt below in a discussion related to Riemann. Read the source for the surrounding context.
“The model did not solve the Riemann Hypothesis, which is what it was actually asked to attempt.”
This excerpt is evidence of what the linked page says, not verification of its claims. Source reports an update on 2026-08-12; this is not necessarily the original posting date.
Anthropic reports Claude's advance on the proportion of zeta zeros on the critical line
Anthropic describes an unreleased Claude model improving a lower bound from 41.6% to 67.2%, with its mathematicians checking the argument and a linked Lean formalization. The company explicitly says this does not solve the Riemann hypothesis.
“it has increased this bound from 41.6% to 67.2%.”
The announcement was published August 10 and updated August 13. This is relevant earlier context for the September follow-up work. A proportion of zeros on the critical line is not a percentage of a completed proof of RH. ProofWatch has not independently checked the mathematics.
Lamzouri publishes a simpler proof of the 67.25% zeta-zero bound
Youness Lamzouri presents a shorter argument for more than 67.25% of nontrivial zeta zeros being simple and on the critical line. The September 8 revision also states two additional unconditional estimates, including a bound on zeros that are simple or on the critical line.
First submitted September 2; revised September 8. The additional 88.76% estimate concerns zeros that are simple OR on the critical line, not 88.76% known to lie on the line. None of these statements proves RH. The abstract and submission history were checked; the proof has not been independently reviewed by ProofWatch.
A follow-up paper applies Lamzouri's method to zeros in short intervals
Biao Wang studies lower bounds for simple critical zeros and distinct zeros of the Riemann zeta function in short intervals, building on Lamzouri's approach and earlier pair-correlation work. The abstract explicitly connects the paper to the Claude and Lamzouri results.
A September 7 preprint about related zero-counting bounds, not a claim to solve the Riemann hypothesis. The abstract and submission date were checked; ProofWatch has not independently verified its proof.
A Reddit commenter explains what a larger critical-line proportion leaves open
In the r/slatestarcodex discussion, u/fractalspire distinguishes increasing the proportion of zeros on the critical line from restricting where the remaining zeros may lie. The comment supplies context for why the announced bound does not settle RH.
“without giving any new bound on how big Re(s) can be for the rest”
The exact comment, author and permalink were read on Reddit and checked in its public feed. The feed gives an August 10 source-update timestamp, not a separate comment publication time. This older discussion is included as context; the commenter's expertise and mathematical claims have not been independently verified.
A comment points to the intermediate bounds in Claude's write-up
u/chkno directs readers to section C.5 of the linked paper and describes intermediate improvements before the final bound near 0.6725. It is a specific lead into the research process, rather than another claim that RH was solved.
“Claude first found intermediate improvements of ½ and then 0.5066 before arriving at this 0.6725007... bound”
The comment's wording and author were checked directly and in Reddit's public feed, which gives an August 11 update timestamp without a separate publication timestamp. This reports the commenter's reading of the paper; ProofWatch has not independently verified that section.
A Reddit reply examines what the Lean formalization actually states
u/hattusili-the-third says they read the relevant formalization and focuses on whether its theorem statement matches the reported result. They describe its use of zero-counting functions and mathlib's zeta definition.
“you might accidentally be proving something different than what is being claimed in the paper”
A pseudonymous commenter's assessment, not an independent ProofWatch verification of Lean or RH. The exact entry was checked on Reddit and in its public feed, which supplies an August 12 update date without a separate publication timestamp.
u/hattusili-the-thirdOriginal source · Found Sep 19
Lamzouri advertises a shorter proof of a related zeta-zero bound
An MPIM seminar listing describes a shorter, conceptually simpler proof of a reported bound on zeros on the critical line. It is relevant follow-up work, rather than a proof of the Riemann hypothesis.
September 3 is the listed seminar date, not a verified publication date. The listing alone does not confirm that the event occurred.