OpenAI paper claims first fixed zero-free strip for zeta, pushing boundary to Re(s)>7/8
Around October 7, OpenAI released a 199-page paper claiming a proof of the "quasi-Riemann hypothesis": the zeta function has no zeros for Re(s)>7/8. Alex Kontorovich, chair of Rutgers University's mathematics department and a number theorist, publicly said that if this were human work, it would unquestionably win the Fields Medal; the math community reacted with excitement.
Confirmed
- The paper's core claim is ζ(s)≠0 for Re(s)>7/8 — the first "fixed zero-free band," meaning the boundary does not vary with the imaginary part's height (per @PTenigma and @imjustnewatai relaying the paper's contents).
- The classical zero-free region's boundary approaches Re(s)=1 as the imaginary part grows, so zeros at Re(s)=0.99 at any height could not be ruled out by older results; the new result provides a height-independent fixed gap, qualitatively far beyond prior expectations (@PTenigma's reading).
- Kontorovich called the result Fields Medal-caliber work (@burnytech relaying his post).
- One user had "Claude Fable 5.5" explain the paper, and the model generated a roughly 2-minute 3D animated walkthrough on the spot (@imjustnewatai).
Why it matters
- If the proof holds, this is the first fixed zero-free strip in Riemann hypothesis research — a qualitative leap from a "shrinking exclusion zone" to a "constant exclusion zone."
- Produced by an OpenAI frontier model, the work is seen as a landmark case of AI-assisted pure mathematics research; @PTenigma also suggests using LLMs in tutorial-style sessions to unpack the paper's multi-branch mathematical structure layer by layer.
Not yet confirmed
- The posts above are secondhand accounts and interpretations of the paper; the completeness and correctness of the proof itself await formal review by the mathematics community.
2026-10-07 ~ 2026-10-08 · 5 related posts
- Episode 1: Debate flares over how OpenAI should release AI-generated math proofs(2026-10-06, 5 posts)
- Episode 2: Rumor: Unreleased OpenAI Model Proves Quasi-Riemann Hypothesis(2026-10-07, 3 posts)
- Episode 3: OpenAI paper claims first fixed zero-free strip for zeta, pushing boundary to Re(s)>7/8(2026-10-07, 5 posts)
- Episode 4: Rumor: OpenAI Has Two More Batches of Math Results Unreleased(2026-10-07, 3 posts)
- Episode 5: OpenAI's Mass Release of Math Manuscripts Sparks Backlash and Boycott Calls from Mathematicians(2026-10-07, 23 posts)
- Episode 6: Report: OpenAI's Hidden Model Makes Progress on 4 Millennium Prize Problems(2026-10-08, 2 posts)
Primary sources
- AI turns OpenAI's 199-page zeta proof into a 2-minute 3D animation claiming first zero-free strip past 7/8 — imjustnewatai · 2026-10-07
- Rutgers math chair on OpenAI's quasi-RH proof: a human would get an instant Fields Medal — burny_tech · 2026-10-07
- Mathematicians stun over claimed quasi-Riemann proof: a zero-free strip for zeta, 'instant Fields Medal' — burny_tech · 2026-10-07
- OpenAI paper extends zeta zero-free region to Re(s)>7/8, a fixed gap toward Riemann hypothesis — PTenigma · 2026-10-08
- [source] New OpenAI paper extends Riemann zeta zero-free region to Re(s) > 7/8 — PTenigma · 2026-10-08