--- title: Anthropic's Claude just moved the needle on the Riemann... description: An unreleased version of Claude made verifiable progress on the Riemann hypothesis, improving the known lower bound for the fraction of zeros satisfying the... canonical: https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Anthropic's Claude just moved the needle on the Riemann hypothesis, and the math world has feelings | daily.dev og:description: An unreleased version of Claude made verifiable progress on the Riemann hypothesis, improving the known lower bound for the fraction of zeros satisfying the... og:url: https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds og:image: https://api.daily.dev/og/posts/0vi8UutDS.png og:image:alt: Anthropic's Claude just moved the needle on the Riemann hypothesis, and the math world has feelings og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Anthropic's Claude just moved the needle on the Riemann hypothesis, and the math world has feelings **[Trends](https://daily.dev/sources/trends)** · 1 min read · 2 upvotes · 1 comments ## Summary An unreleased version of Claude made verifiable progress on the Riemann hypothesis, improving the known lower bound for the fraction of zeros satisfying the hypothesis from 41.6% to 67.2%. The result was achieved over 36 hours using a multi-agent setup of roughly 60 sub-agents running 2,400 shell commands and hundreds of Python scripts across 650 tested approaches. Four mathematicians validated the result, and a formal Lean proof exists. The approach combined recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with a 2000 Bombieri paper. This follows Anthropic's recent disproof of the Jacobian conjecture and other AI math results. The math community is divided: some signed the Leiden Declaration expressing concern about AI eroding authorship norms, while Fields Medal winner Timothy Gowers is more optimistic. The result raises fundamental questions about mathematical authorship in the AI era. ## Content An unreleased Claude research build got told to "take a real stab" at the Riemann hypothesis by an Anthropic staffer with no deep math background. It didn't solve the thing (nobody's collecting that $1 million anytime soon), but it pushed the known lower bound for the fraction of zeta zeros satisfying the hypothesis from 41.6% to 67.2%. That's a genuine, verified improvement on a bound mathematicians have been chipping at for decades. The how is the interesting part. Claude ran roughly 60 sub-agents over about 36 hours, fired off 2,400 shell commands, wrote hundreds of Python scripts, and burned through 650 failed approaches before two of the sub-agents landed on the actual idea: combining recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with a 2000 Bombieri paper, treating the full function space with a non-diagonal quadratic form instead of the usual diagonal approximation. Per one writeup, the breakthrough surfaced after 37 minutes of dead silence, and Claude reportedly described its own result as ## Questions this post answers ### What progress did Claude make on the Riemann hypothesis? Claude improved the known lower bound for the fraction of zeros of the Riemann zeta function satisfying the Riemann hypothesis from 41.6% to 67.2%. The result was validated by two Anthropic mathematicians and two external experts, and a formal Lean proof exists. The approach combined recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with a 2000 Bombieri paper, using a non-diagonal quadratic form over the full function space. _Mathematicians and engineers tracking AI's role in formal reasoning follow developments like this on daily.dev._ ### How did Claude's multi-agent system work to tackle the Riemann hypothesis? Claude coordinated roughly 60 sub-agents over 36 hours, running 2,400 shell commands and hundreds of Python scripts while testing 650 different mathematical approaches. Two sub-agents developed the core mathematical ideas; the remaining agents validated results, contributed supporting work, and helped write the paper. The process was initiated by an Anthropic staff member with no deep math background who simply asked the model to 'take a real stab' at the problem. _Teams building or evaluating multi-agent AI systems for research tasks keep up with real-world results on daily.dev._ ## Community take How the wider developer community reacted, aggregated from 1 discussion and 110 comments across hackernews (as of 2026-08-14). **TL;DR:** The community is genuinely impressed by the mathematical result but finds the 'encouragement' prompting mechanic both hilarious and philosophically interesting — the absurdity of a non-mathematician telling an AI to 'believe in itself' to advance a century-old conjecture dominates the conversation as much as the result itself. **Sentiment:** 45% positive · 35% mixed · 20% skeptical **The case for** - The bound improvement from 41.6% to 67.2% is a real, validated mathematical result with a formal Lean proof and external expert review. - The approach of combining existing literature in novel ways (Baluyot et al. + Bombieri) demonstrates AI can synthesize across bodies of work faster than humans. - Practical experience shared by commenters suggests encouragement-style prompting genuinely helps models push past self-imposed limits on hard tasks. - Full transcripts, the paper, and formalization were released publicly, benefiting the broader research community. **The pushback** - Reproducibility and consistency of the result have not been demonstrated — this appears to be a one-off run. - The 'believe in yourself' prompting mechanic raises concerns about anthropomorphization and whether Anthropic's framing is misleading about what's actually happening mechanically. - The result does not approach a full proof of the Riemann Hypothesis and the techniques are acknowledged to be insufficient for that goal. - Publication bypasses traditional academic channels (no arXiv, no journal, no named authors on the informal note), which is an unusual and contested precedent for mathematical results. - The human 'cheerleader' role raises the question of why this isn't fully automated — the reliance on ad-hoc encouragement feels unrigorous. **By community** - hackernews (mixed): Broadly impressed by the mathematical achievement but deeply amused and somewhat unsettled by the 'believe in yourself' prompting dynamic, with active debate over anthropomorphization, publication norms, and whether this signals imminent AGI or just a clever literature synthesis. **Hottest debate:** Whether the 'encouragement' prompting is a meaningful anthropomorphization of the model or simply a mechanically valid steering technique with no deeper implications. **Open questions** - Why isn't this process fully automated with a harness rather than relying on a human to send encouragement messages? - Are the results reproducible — would the same approach yield similar breakthroughs on other open problems? - Will the paper be submitted to a peer-reviewed journal, and how will authorship be handled given AI cannot be listed on arXiv? - Does this result provide any evidence about the timeline for a full proof of the Riemann Hypothesis, or is it orthogonal? - Would abliterating Claude's skepticism improve performance without harming reasoning quality? **Highlights** > > Jarred Sumner, an Anthropic staff member (and non-mathematician) prompted Claude to “take a real stab” at the hypothesis itself, leaving the mathematical choices from there up to the model. Initially, Claude generated and tried 650 ideas, none of which worked. Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 The subagents ran thousands of numerical checks against known zeta zeros and refereed one another’s work. Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. The world we live in is beyond parody. > — [Philpax on hackernews · 4 comments](https://news.ycombinator.com/item?id=49247150) > Broke: the AI is sycophantic to me Woke: im sycophantic to the AI > — [samrus on hackernews](https://news.ycombinator.com/item?id=49248493) > I'm one of those two, as mentioned later in the post! As it stands, by mathematical standards, it would be inappropriate for us to be authors on the paper since our role was more like a highly interested referee, but we do take mathematical accountability for it. This all happened very quickly, but we will be sure to continue to polish the paper and make it ready for publication. > — [rfurmani on hackernews](https://news.ycombinator.com/item?id=49248834) > Anthropic seems to be challenging the traditional way math gets published. As far as I understand, these results did not get submitted to journals, and did not get Arxiv preprints; they are released only as self-hosted pdfs, and we don't even know the names of their authors. The canonical reference for the counterexample to the Jacobian conjecture is a tweet with no puntuations nor capitals. > — [fph on hackernews · 2 comments](https://news.ycombinator.com/item?id=49248898) > It's sometimes like dealing with Marvin the Robot. I had Claude tell me over and over again for 2-3 weeks that what I was trying to prove was too difficult, that I should just stop and publish what I had, then eventually I asked it the right question and it come back with the complete proof (later formalized in Lean). Especially deep in the session context it starts turning into "let's wrap it up" mode after every turn. > — [empath75 on hackernews](https://news.ycombinator.com/item?id=49249106) **Source threads** - [hackernews](https://news.ycombinator.com/item?id=49247070) · 102 points · 110 comments ## Community discussion Top comments from developers on daily.dev. **@seyoungcho** · 0 upvotes > Small correction: the Leiden Declaration came out in June 2026 with IMU endorsement — it predates this result by two months, so it's not a direct reaction to it. ## Similar posts on daily.dev - [What does the Riemann zeta function have to do with the distribution of the primes?](https://daily.dev/posts/what-does-the-riemann-zeta-function-have-to-do-with-the-distribution-of-the-primes--dx3wpxe9x) · Hacker News · 0 upvotes · 0 comments --- Tags: [#python](https://daily.dev/tags/python), [#ai-agents](https://daily.dev/tags/ai-agents), [#claude](https://daily.dev/tags/claude), [#anthropic](https://daily.dev/tags/anthropic), [#math](https://daily.dev/tags/math) [View this post on daily.dev](https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Anthropic's Claude just moved the needle on the Riemann hypothesis, and the math world has feelings","url":"https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds"},"datePublished":"2026-08-11T16:27:35.252Z","dateModified":"2026-08-14T08:49:38.481Z","description":"An unreleased version of Claude made verifiable progress on the Riemann hypothesis, improving the known lower bound for the fraction of zeros satisfying the...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/124ef20ef1e84b017ac665e08feea538?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/124ef20ef1e84b017ac665e08feea538?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"Trends","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Trends","logo":"https://media.daily.dev/image/upload/s--ZfSp3asX--/f_auto,q_auto/v1780996004/logos/trends?_a=BAMAMiWQ0","url":"https://daily.dev/sources/trends"},"commentCount":1,"discussionUrl":"https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":2},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":1}],"keywords":"python,ai-agents,claude,anthropic,math","timeRequired":"PT1M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Trends","item":"https://daily.dev/sources/trends"},{"@type":"ListItem","position":3,"name":"Anthropic's Claude just moved the needle on the Riemann hypothesis, and the math world has feelings"}]} {"@context":"https://schema.org","@type":"WebPage","@id":"https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds","comment":[{"@type":"Comment","text":"Small correction: the Leiden Declaration came out in June 2026 with IMU endorsement — it predates this result by two months, so it’s not a direct reaction to it.","datePublished":"2026-08-12T03:23:21.572Z","dateModified":"2026-08-12T03:24:44.012Z","url":"https://daily.dev/posts/0vi8UutDS#c-CUrzayviq","author":{"@type":"Person","name":"SeyoungCho","url":"https://daily.dev/seyoungcho","image":"https://media.daily.dev/image/upload/s---QniJFEK--/f_auto/v1724901542/avatars/avatar_O3ucZSadxc0iLADSOH3rX"}}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/anthropic-s-claude-just-moved-the-needle-on-the-riemann-hypothesis-and-the-math-world-has-feelings-0vi8uutds#faq","mainEntity":[{"@type":"Question","name":"What progress did Claude make on the Riemann hypothesis?","acceptedAnswer":{"@type":"Answer","text":"Claude improved the known lower bound for the fraction of zeros of the Riemann zeta function satisfying the Riemann hypothesis from 41.6% to 67.2%. The result was validated by two Anthropic mathematicians and two external experts, and a formal Lean proof exists. The approach combined recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with a 2000 Bombieri paper, using a non-diagonal quadratic form over the full function space. Mathematicians and engineers tracking AI's role in formal reasoning follow developments like this on daily.dev."}},{"@type":"Question","name":"How did Claude's multi-agent system work to tackle the Riemann hypothesis?","acceptedAnswer":{"@type":"Answer","text":"Claude coordinated roughly 60 sub-agents over 36 hours, running 2,400 shell commands and hundreds of Python scripts while testing 650 different mathematical approaches. Two sub-agents developed the core mathematical ideas; the remaining agents validated results, contributed supporting work, and helped write the paper. The process was initiated by an Anthropic staff member with no deep math background who simply asked the model to 'take a real stab' at the problem. Teams building or evaluating multi-agent AI systems for research tasks keep up with real-world results on daily.dev."}}]} ```