Anthropic claims its Claude agent swarm produced a substantive numerical advance toward the Riemann Hypothesis — a claimed 50% result, since pushed to 67.25 under attempts to break it — now passing through Lean and expert-mathematician checking; verified acceptance of the bound establishes frontier agent teams as credible attackers of top-tier open problems, while a broken or retracted proof deflates the claim.

state: corroboratedheat: mediumuncertainty: mediumconvergesscott: highai-assisted-mathematics anthropic frontier-capability-claimsAnthropicEllie Sleightholm

What is this?

On 2026-08-10 Anthropic published its own research note (anthropic.com/research/riemann-zeta, now among the results — superseding the case's Sleightholm-commentary anchor) reporting that an unreleased research version of Claude, while attempting and failing to prove the Riemann Hypothesis, raised the best lower bound on the proportion of zeta zeros lying on the critical line from 41.6% to 67.2% — per AI Weekly, the largest single-step improvement ever recorded for this bound. The result came out of a Claude Code agent swarm: roughly 60 subagents over ~36 hours, ~31M output tokens, ~650 candidate approaches, with the winning argument synthesizing a 2000 Bombieri paper with results of Baluyot–Goldston–Suriajaya–Turnage-Butterbaugh; subagents reviewed proofs, searched for counterexamples, downloaded 54 arXiv papers for novelty checks, and independently re-proved the finding. Verification is layered but not peer review: Anthropic mathematicians Levent Alpöge and Ralph Furman validated the manuscript, a Lean 4 formalization (with Eric Easley) passed the standard checker, and outside experts Brian Conrey and Dan Goldston reviewed on short notice, with independent community review only beginning as of the August announcement. Conflict flag for the case record: the hypothesis's '50% → 67.25%' framing does not match the sources — all give 41.6% as the prior bound, and 67.25% appears only in Kingy AI's writeup while Anthropic itself says 67.2%.

Why it matters to Scott

Anthropic's swarm independently operationalised the verification architecture Scott's own dev wiki codifies — subagent proof review, counterexample search and independent re-proof (review-until-clear loop, adversarial expert panel), a Lean 4 checker as the hard authority underneath free machine-native exploration, and claim-bounded adversarial challenge of a validated AI finding — so the community review now beginning is a live, resolvable test of patterns he argues for, with a dated-receipts publishing opportunity ('the frontier lab built the stack I documented'). The grounding's number drift (41.6%→67.2% per Anthropic; '67.25' only in secondary writeups) is itself a fresh instance of the capability-claim mutation his evidence–inference–falsifier-reporting pattern exists to catch. Continues the radar's Claude-vs-open-problems lineage (Borsuk, Jacobian, Hopf — with Alpöge now on the validation side at Anthropic).

dev:concept.review-until-clear-loopdev:concept.claim-bounded-adversarial-verificationdev:concept.adversarial-agent-panelip:framework.agent-native-computingdev:concept.evidence-inference-falsifier-reportingradar:claude-borsuk-counterexampleradar:claude-fable-jacobian-counterexampleradar:hopf-proof-codex-lean-formalizationradar:anthropic-multiagent-patterns-validationradar:concept.ai-assisted-mathematicsradar:concept.formal-verificationradar:concept.leanradar:concept.agent-verificationradar:concept.multi-agent-orchestrationradar:concept.long-horizon-agentsradar:concept.frontier-labs

queries asked of Scott's wikis

multi-agent orchestration subagent swarm harness patterns
formal verification Lean checker as agent reward loop
agent self-review counterexample search cross-examination quality gates
frontier lab capability claims evidence standards unreleased models
long-horizon agent research tasks token cost economics
run provenance transcripts reproducibility as product pattern

Measured heat

now 0 pts/hpeak 9 pts/hcomments 0/hpeers p0momentum: steady2 platformsage 1514h

points/hour across evidence · reading as of 2026-10-12 02:59:37.977291+11:00 · deterministic, not a model opinion

How the heat travelled

08-09 14:00	⭐ origin echo-reconstructed	Anthropic's research post "Learning more about Claude's mathematical capabilities": "Recently, a member of staff at Anthropic gave Claude an Anthropic on blog (echo) · attributed from reddit.post.1wwzje5	—
10-03 22:15	first on r/singularity · published · +1328.3h	Anthropic Took On the Riemann Hypothesis. Here’s What Actually Happened \| Ellie Sleightholm SammaVaco	—
10-05 21:49	first on r/ClaudeAI · published · +1375.8h	Claude and I beat Claude's previous proof of the proportion of online zeta zeros. It's now 67.348%. Just_Shallot_6755	—
10-03 22:15	amplified on r/singularity	reddit.post.1wwzje5 SammaVaco	peak 0 · 10 comments · 23% of case engagement
10-05 21:49	amplified on r/ClaudeAI 👑	reddit.post.1wylch8 Just_Shallot_6755	peak 26 · 7 comments · 77% of case engagement
10-03 22:20	our radar first saw it · +1328.3h	discovery anchor: reddit.post.1wwzje5	—

Evidence (3) — ⭐ canonical anchor

source	object	author	score	comments
🟠 reddit	Anthropic Took On the Riemann Hypothesis. Here’s What Actually Happened \| Ellie Sleightholm singularity Retrieved article excerpt Open article · Retrieved 2026-10-03T22:25:42.498235+00:00 # # Back AU Skip navigation Search Search with your voice [Sign in](https://accounts.google.com/ServiceLogin?service=youtube&uilel=3&passive=true&continue=https%3A%2F%2Fwww.youtube.com%2Fsignin%3Faction_handle_signin%3Dtrue%26app%3Ddesktop%26hl%3Den%26next%3Dhttps%253A%252F%252Fwww.youtube.com%252Fwatch%253Fv%253DkvLOiTxYSzA&hl=en&ec=65620) Anthropic Took On the Riemann Hypothesis. Here’s What We Found Tap to unmute 2x ## Anthropic Took On the Riemann Hypothesis. Here’s What We Found Ellie Sleightholm 593,395 views 6 days ago Copy link Info Shopping If playback doesn't begin shortly, try restarting your device. • You're signed out Videos you watch may be added to the TV's watch history and influence TV recommendations. To avoid this, cancel and sign in to YouTube on your computer. 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Body Language Analyst Reacts to Elizabeth Holmes Secret Documentary!The Behavioral Arts 1.1M • 3w agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=BjKWQ22SgXM)[15:23 Why Almost NOBODY Lives On Australia's West CoastGeography By Geoff783K • 4d agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=I5QMtbO-DNk)[21:22 How AI Solved a 90-year old Math Problem in 88 hoursStarTalk2.1M • 2d agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=s7KhLuc3Mck)[33:35 Turkey's $20 Billion Fund Collapse ExplainedPatrick Boyle577K • 11h agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=LF8kY5BLe_o)[29:28 Like Sabine Hossenfelder, I Was Offered Money to Tell You AI Will Kill UsHouse of El: AI532K • 11d agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=claxN4oxDuY)[20:40 Meet The World's Smartest WomanTuring180K • 3d agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=MsprnXFSILQ)[51:56 The last IMO problem AI could not solve3Blue1Brown and PolyaMath2.7M • 2w agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=Nbwv5wHQoj0)[30:12 The paradox at the heart of AI and science \| Terence TaoBig Think Clips and Big Think2.2M • 1mo agoLivePlaylist ()Mix (50+)](https://www.youtube.com/watch?v=svl_1upFpQo) Sign in to confirm you’re not a bot This helps protect our community [Sign in](https://accounts.google.com/ServiceLogin?service=youtube&uilel=3&passive=true&continue=https%3A%2F%2Fwww.youtube.com%2Fsignin%3Faction_handle_signin%3Dtrue%26app%3Ddesktop%26hl%3Den%26next%3D%252Fwatch%253Fv%253DkvLOiTxYSzA&hl=en)[Learn more](https://support.google.com/youtube/answer/3037019#zippy=%2Ccheck-that-youre-signed-into-youtube) # Anthropic Took On the Riemann Hypothesis. Here’s What We Found [Ellie Sleightholm](https://www.youtube.com/@elliesleightholm) [Ellie Sleightholm](https://www.youtube.com/@elliesleightholm) Ellie Sleightholm 165K subscribers Join Subscribe Subscribed 6.7K Share Download Download Save 593K views 6 days ago 593,395 views • Sep 27, 2026 Claude Didn’t Solve the Riemann Hypothesis. So What Did It Do? Get 10% off OutsideIn’s range with code 'ELLIE10' at checkout: [https://www.weareoi.com?sca\_ref=11725...](https://www.youtube.com/redirect?event=video_description&redir_token=QUZZTVljSEFBZEk3WEVodDRSRktHX3ZPZ3VQbnxBSTVJdTVzNWpqb2EtX0xUUnhMaW5rVmNSeS1EUEZiRHVjUTM2NWlMeVhWSzlPUG9sZ1hjSHY2VXBGQVBoZFVkU0xvVGI1bXhYVi1tQ3BJeE5NLXJIMXYtUmdHMFZhRkFFV1Zw&q=https%3A%2F%2Fwww.weareoi.com%2F%3Fsca_ref%3D11725872.7Z91mEpVN0Do1%26sca_source%3DYouTube&v=kvLOiTxYSzA) …...more ...more How this was made Auto-dubbed Audio tracks for some languages were automatically generated. [Learn more](https://support.google.com/youtube/answer/15569972?hl=en) ## Chapters View all [### AI and the crisis in mathematics ### AI and the crisis in mathematics 0:00](https://www.youtube.com/watch?v=kvLOiTxYSzA&pp=0gcJCSoDDuyUWbzu) [### AI and the crisis in mathematics](https://www.youtube.com/watch?v=kvLOiTxYSzA&pp=0gcJCSoDDuyUWbzu) 0:00 [### Prime numbers and the prime counting function ### Prime numbers and the prime counting function 1:38](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s) [### Prime numbers and the prime counting function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s) 1:38 [### From the Basel problem to the zeta function ### From the Basel problem to the zeta function 3:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s) [### From the Basel problem to the zeta function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s) 3:24 [### Euler’s product: connecting zeta to primes ### Euler’s product: connecting zeta to primes 5:01](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s) [### Euler’s product: connecting zeta to primes](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s) 5:01 [### A quick fleece interlude ### A quick fleece interlude 8:12](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s) [### A quick fleece interlude](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s) 8:12 [### Riemann’s paper and complex numbers ### Riemann’s paper and complex numbers 9:05](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s) [### Riemann’s paper and complex numbers](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s) 9:05 [### Zeros, the critical strip and the Riemann hypothesis ### Zeros, the critical strip and the Riemann hypothesis 12:09](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s&pp=0gcJCSoDDuyUWbzu) [### Zeros, the critical strip and the Riemann hypothesis](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s&pp=0gcJCSoDDuyUWbzu) 12:09 [### A history of progress on the critical line ### A history of progress on the critical line 14:18](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s) [### A history of progress on the critical line](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s) 14:18 Transcript Follow along using the transcript. Show transcript [### Ellie Sleightholm 165K subscribers](https://www.youtube.com/@elliesleightholm) [Videos](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/videos)[About](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/about)[YouTube Member](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/join)[Patreon](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljR1c5dlZfczhtaktDQi0wa1dpbVgwMnxBSTVJdTV1a2ZjbTg5cWt3YWZSUi1IS1FrYmVrNnpsU213UHpVbjRkZV9WdHFaNXhEVDVlajE2OEVMQ1d5Z0hvUDhQNDFCMnVjWWo0Tnh2VnBpNmFlSDl4OWRjaGNMbjlGNjVB&q=https%3A%2F%2Fpatreon.com%2Felliesleightholm)[Instagram](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljRUVrVTBJUEFYdEVKZjBtcEd4eWRvOXxBSTVJdTV0NUJkSnRKc1RBVG02VXZjTUFLejVDSmh1OUhHMC15T1g2eVFvdTRlZldGY0I0Zzh4b3YxTVVuQUt5NmJMVlJwa2JaOTBFd2U2TkNqOWhLNmpKcmRxcVpwOUk1MGk5&q=https%3A%2F%2Fwww.instagram.com%2Fellieinstem%2F)[TikTok](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljR043QmEyMVA1amF5TUw2dlE5RjY0M3xBSTVJdTV2VFVMbDhxcXFJZVdrS1Ffb3hibzBZN1JhbWxDLW5HSmlvRnFhT3NCTUpxUzduR0NOQVdWMklNNWxLbnoxZUVaR1pjNExHSzJySXR1dVBHczlRcXprMnVxeWN3V2Rl&q=https%3A%2F%2Fwww.tiktok.com%2F%40elliesleightholm)[Facebook Page](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljSFZBdmFsOENtVkcxaGlrS3hoeVplNHxBSTVJdTV2MTNtelJzRmNUeGhMTFdjeGRkZHJXeldXLUFQMG1iR3VydXFKTEozbzI3VzF6bGN6R3ExdkRWS01YU3VZNUw3WGF5MjhQS0RUNjhzMEhqUEhLdG1RbjlRcUR3Y1ZX&q=https%3A%2F%2Fwww.facebook.com%2Fp%2FEllie-Sleightholm-61573036557417) Show less # Anthropic Took On the Riemann Hypothesis. Here’s What We Found 593,395 views593K views Sep 27, 2026 6.7K Share Download Download Save ## Comments 855 Top Show featured comments Newest Show recent comments, including potential spam ## In this video Chapters Transcript ## Chapters [### AI and the crisis in mathematics ### AI and the crisis in mathematics 0:00](https://www.youtube.com/watch?v=kvLOiTxYSzA) [### AI and the crisis in mathematics](https://www.youtube.com/watch?v=kvLOiTxYSzA) 0:00 [### Prime numbers and the prime counting function ### Prime numbers and the prime counting function 1:38](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s) [### Prime numbers and the prime counting function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s) 1:38 [### From the Basel problem to the zeta function ### From the Basel problem to the zeta function 3:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s) [### From the Basel problem to the zeta function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s) 3:24 [### Euler’s product: connecting zeta to primes ### Euler’s product: connecting zeta to primes 5:01](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s) [### Euler’s product: connecting zeta to primes](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s) 5:01 [### A quick fleece interlude ### A quick fleece interlude 8:12](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s&pp=0gcJCSoDDuyUWbzu) [### A quick fleece interlude](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s&pp=0gcJCSoDDuyUWbzu) 8:12 [### Riemann’s paper and complex numbers ### Riemann’s paper and complex numbers 9:05](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s) [### Riemann’s paper and complex numbers](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s) 9:05 [### Zeros, the critical strip and the Riemann hypothesis ### Zeros, the critical strip and the Riemann hypothesis 12:09](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s) [### Zeros, the critical strip and the Riemann hypothesis](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s) 12:09 [### A history of progress on the critical line ### A history of progress on the critical line 14:18](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s) [### A history of progress on the critical line](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s) 14:18 [### What Anthropic actually announced ### What Anthropic actually announced 16:07](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=967s) [### What Anthropic actually announced](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=967s) 16:07 [### Inside Claude’s team of AI agents ### Inside Claude’s team of AI agents 17:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1044s) [### Inside Claude’s team of AI agents](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1044s) 17:24 [### Failed approaches and a new direction ### Failed approaches and a new direction 19:23](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1163s) [### Failed approaches and a new direction](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1163s) 19:23 [### The claimed 50% result, and attempts to break it ### The claimed 50% result, and attempts to break it 20:43](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1243s) [### The claimed 50% result, and attempts to break it](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1243s) 20:43 [### Pushing the bound to 67.25 ### Pushing the bound to 67.25 21:39](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1299s) [### Pushing the bound to 67.25](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1299s) 21:39 [### Checking the proof: AI, mathematicians and Lean ### Checking the proof: AI, mathematicians and Lean 22:54](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1374s&pp=0gcJCSoDDuyUWbzu) [### Checking the proof: AI, mathematicia	SammaVaco	0	8
🟧 echo.blog ⭐	Anthropic's research post "Learning more about Claude's mathematical capabilities": "Recently, a member of staff at Anthropic gave Claude an	Anthropic	—	—
🟠 reddit	Claude and I beat Claude's previous proof of the proportion of online zeta zeros. It's now 67.348%. ClaudeAI	Just_Shallot_6755	26	7

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Anthropic Took On the Riemann Hypothesis. Here’s What Actually Happened | Ellie Sleightholm

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Anthropic Took On the Riemann Hypothesis. Here’s What We Found

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## Anthropic Took On the Riemann Hypothesis. Here’s What We Found

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# Anthropic Took On the Riemann Hypothesis. Here’s What We Found

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Claude Didn’t Solve the Riemann Hypothesis. So What Did It Do?
Get 10% off OutsideIn’s range with code 'ELLIE10' at checkout: [https://www.weareoi.com?sca\_ref=11725...](https://www.youtube.com/redirect?event=video_description&redir_token=QUZZTVljSEFBZEk3WEVodDRSRktHX3ZPZ3VQbnxBSTVJdTVzNWpqb2EtX0xUUnhMaW5rVmNSeS1EUEZiRHVjUTM2NWlMeVhWSzlPUG9sZ1hjSHY2VXBGQVBoZFVkU0xvVGI1bXhYVi1tQ3BJeE5NLXJIMXYtUmdHMFZhRkFFV1Zw&q=https%3A%2F%2Fwww.weareoi.com%2F%3Fsca_ref%3D11725872.7Z91mEpVN0Do1%26sca_source%3DYouTube&v=kvLOiTxYSzA)  …...more

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## Chapters View all

[### AI and the crisis in mathematics

### AI and the crisis in mathematics

0:00](https://www.youtube.com/watch?v=kvLOiTxYSzA&pp=0gcJCSoDDuyUWbzu)

[### AI and the crisis in mathematics](https://www.youtube.com/watch?v=kvLOiTxYSzA&pp=0gcJCSoDDuyUWbzu)

0:00

[### Prime numbers and the prime counting function

### Prime numbers and the prime counting function

1:38](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s)

[### Prime numbers and the prime counting function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s)

1:38

[### From the Basel problem to the zeta function

### From the Basel problem to the zeta function

3:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s)

[### From the Basel problem to the zeta function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s)

3:24

[### Euler’s product: connecting zeta to primes

### Euler’s product: connecting zeta to primes

5:01](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s)

[### Euler’s product: connecting zeta to primes](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s)

5:01

[### A quick fleece interlude

### A quick fleece interlude

8:12](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s)

[### A quick fleece interlude](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s)

8:12

[### Riemann’s paper and complex numbers

### Riemann’s paper and complex numbers

9:05](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s)

[### Riemann’s paper and complex numbers](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s)

9:05

[### Zeros, the critical strip and the Riemann hypothesis

### Zeros, the critical strip and the Riemann hypothesis

12:09](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s&pp=0gcJCSoDDuyUWbzu)

[### Zeros, the critical strip and the Riemann hypothesis](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s&pp=0gcJCSoDDuyUWbzu)

12:09

[### A history of progress on the critical line

### A history of progress on the critical line

14:18](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s)

[### A history of progress on the critical line](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s)

14:18

Transcript

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[### Ellie Sleightholm

165K subscribers](https://www.youtube.com/@elliesleightholm)

[Videos](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/videos)[About](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/about)[YouTube Member](https://www.youtube.com/channel/UCylqgu2ojsCxojFpQogowOA/join)[Patreon](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljR1c5dlZfczhtaktDQi0wa1dpbVgwMnxBSTVJdTV1a2ZjbTg5cWt3YWZSUi1IS1FrYmVrNnpsU213UHpVbjRkZV9WdHFaNXhEVDVlajE2OEVMQ1d5Z0hvUDhQNDFCMnVjWWo0Tnh2VnBpNmFlSDl4OWRjaGNMbjlGNjVB&q=https%3A%2F%2Fpatreon.com%2Felliesleightholm)[Instagram](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljRUVrVTBJUEFYdEVKZjBtcEd4eWRvOXxBSTVJdTV0NUJkSnRKc1RBVG02VXZjTUFLejVDSmh1OUhHMC15T1g2eVFvdTRlZldGY0I0Zzh4b3YxTVVuQUt5NmJMVlJwa2JaOTBFd2U2TkNqOWhLNmpKcmRxcVpwOUk1MGk5&q=https%3A%2F%2Fwww.instagram.com%2Fellieinstem%2F)[TikTok](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljR043QmEyMVA1amF5TUw2dlE5RjY0M3xBSTVJdTV2VFVMbDhxcXFJZVdrS1Ffb3hibzBZN1JhbWxDLW5HSmlvRnFhT3NCTUpxUzduR0NOQVdWMklNNWxLbnoxZUVaR1pjNExHSzJySXR1dVBHczlRcXprMnVxeWN3V2Rl&q=https%3A%2F%2Fwww.tiktok.com%2F%40elliesleightholm)[Facebook Page](https://www.youtube.com/redirect?event=Watch_SD_EP&redir_token=QUZZTVljSFZBdmFsOENtVkcxaGlrS3hoeVplNHxBSTVJdTV2MTNtelJzRmNUeGhMTFdjeGRkZHJXeldXLUFQMG1iR3VydXFKTEozbzI3VzF6bGN6R3ExdkRWS01YU3VZNUw3WGF5MjhQS0RUNjhzMEhqUEhLdG1RbjlRcUR3Y1ZX&q=https%3A%2F%2Fwww.facebook.com%2Fp%2FEllie-Sleightholm-61573036557417)

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# Anthropic Took On the Riemann Hypothesis. Here’s What We Found

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Sep 27, 2026

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## In this video

Chapters

Transcript

## Chapters

[### AI and the crisis in mathematics

### AI and the crisis in mathematics

0:00](https://www.youtube.com/watch?v=kvLOiTxYSzA)

[### AI and the crisis in mathematics](https://www.youtube.com/watch?v=kvLOiTxYSzA)

0:00

[### Prime numbers and the prime counting function

### Prime numbers and the prime counting function

1:38](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s)

[### Prime numbers and the prime counting function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=98s)

1:38

[### From the Basel problem to the zeta function

### From the Basel problem to the zeta function

3:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s)

[### From the Basel problem to the zeta function](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=204s)

3:24

[### Euler’s product: connecting zeta to primes

### Euler’s product: connecting zeta to primes

5:01](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s)

[### Euler’s product: connecting zeta to primes](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=301s)

5:01

[### A quick fleece interlude

### A quick fleece interlude

8:12](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s&pp=0gcJCSoDDuyUWbzu)

[### A quick fleece interlude](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=492s&pp=0gcJCSoDDuyUWbzu)

8:12

[### Riemann’s paper and complex numbers

### Riemann’s paper and complex numbers

9:05](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s)

[### Riemann’s paper and complex numbers](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=545s)

9:05

[### Zeros, the critical strip and the Riemann hypothesis

### Zeros, the critical strip and the Riemann hypothesis

12:09](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s)

[### Zeros, the critical strip and the Riemann hypothesis](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=729s)

12:09

[### A history of progress on the critical line

### A history of progress on the critical line

14:18](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s)

[### A history of progress on the critical line](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=858s)

14:18

[### What Anthropic actually announced

### What Anthropic actually announced

16:07](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=967s)

[### What Anthropic actually announced](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=967s)

16:07

[### Inside Claude’s team of AI agents

### Inside Claude’s team of AI agents

17:24](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1044s)

[### Inside Claude’s team of AI agents](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1044s)

17:24

[### Failed approaches and a new direction

### Failed approaches and a new direction

19:23](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1163s)

[### Failed approaches and a new direction](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1163s)

19:23

[### The claimed 50% result, and attempts to break it

### The claimed 50% result, and attempts to break it

20:43](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1243s)

[### The claimed 50% result, and attempts to break it](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1243s)

20:43

[### Pushing the bound to 67.25

### Pushing the bound to 67.25

21:39](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1299s)

[### Pushing the bound to 67.25](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1299s)

21:39

[### Checking the proof: AI, mathematicians and Lean

### Checking the proof: AI, mathematicians and Lean

22:54](https://www.youtube.com/watch?v=kvLOiTxYSzA&t=1374s&pp=0gcJCSoDDuyUWbzu)

[### Checking the proof: AI, mathematicia

SammaVaco

🟧 echo.blog ⭐

Anthropic's research post "Learning more about Claude's mathematical capabilities": "Recently, a member of staff at Anthropic gave Claude an

Anthropic

—

🟠 reddit

Claude and I beat Claude's previous proof of the proportion of online zeta zeros. It's now 67.348%.

ClaudeAI

Just_Shallot_6755

Interpretation history

2026-10-06T01:45:02Z
First independent replication: a non-Anthropic human+Claude pair pushed the zeta-zeros bound to 67.348% via a community-built constrained Lean-verifier leaderboard (riemannzeta.fun) modeled on Anthropic's methodology — moving the case from a lone frontier-lab claim to the early stages of a verification ecosystem, and corroborating the bound's achievability before any verdict lands on Anthropic's own manuscript. Number drift continues (the new post cites '65.25%' for the August result vs Anthropic's 67.2%), reinforcing the claim-mutation thread.
2026-10-05T23:34:20Z
evidence attached: reddit.post.1wylch8 — Independent corroboration: a non-Anthropic human+Claude effort pushed the zeta-zeros proportion to 67.348% via the same Lean-verifier methodology, directly advancing the open case.
2026-10-03T22:39:01Z
origin walked (opencode/cheap-glm, conf 0.87): anchor reddit.post.1wwzje5 -> echo.blog.0b2744e224 by Anthropic
2026-10-03T22:36:52Z
grounded: converges/high — Anthropic's swarm independently operationalised the verification architecture Scott's own dev wiki codifies — subagent proof review, counterexample search and i
2026-10-03T22:27:07Z
case created — The 593K-view breakdown documents a genuinely new Anthropic open-problem announcement — a Claude-agent Riemann Hypothesis attempt with a claimed 50%-to-67.25 bound under Lean and expert verification — distinct from the existing Fermat, amplitude, and elliptic-curve cases, with a crisp resolvable outcome; the Sleightholm video is commentary, not the origin, so it anchors until Anthropic's own announcement surfaces.

Decision trace

10-08 15:34review_screenjev screen: no material development (noul=0.30)
10-06 16:21sensor_dirtycomment_update
10-06 12:45repriceFirst independent replication: a non-Anthropic human+Claude pair pushed the zeta-zeros bound to 67.348% via a community-built constrained Lean-verifier leaderboard (riemannzeta.fun) modeled on Anthrop
10-06 10:34attachIndependent corroboration: a non-Anthropic human+Claude effort pushed the zeta-zeros proportion to 67.348% via the same Lean-verifier methodology, directly advancing the open case.
10-06 10:28propose_attachIndependent corroboration: a non-Anthropic human+Claude effort pushed the zeta-zeros proportion to 67.348% via the same Lean-verifier methodology, directly advancing the open case.
10-05 10:29review_screenNew Reddit comments only add user reactions and questions; the 'reached 6x%' remark restates the already-known ~67% bound, and the 'Ellie' and link-policy comments contain no new f
10-04 14:21sensor_dirtycomment_update
10-04 10:21sensor_dirtycomment_update
10-04 09:39promote_anchororigin walk conf 0.87
10-04 09:36groundAnthropic's swarm independently operationalised the verification architecture Scott's own dev wiki codifies — subagent proof review, counterexample search and independent re-proof (review-un
10-04 09:27createThe 593K-view breakdown documents a genuinely new Anthropic open-problem announcement — a Claude-agent Riemann Hypothesis attempt with a claimed 50%-to-67.25 bound under Lean and expert verification —