OpenAI Drops 722 Math Papers from Secret Frontier Model, Claiming Quasi-Riemann and Kakeya Breakthroughs
机器之心 · wechat · 2026-10-07
OpenAI has published 722 mathematical manuscripts in 372 result families, all produced by an unnamed internal frontier model, in the GitHub repo openai/math. The list claims progress on the quasi-Riemann hypothesis, the 4D Kakeya conjecture, the Unique Games conjecture, Hilbert's Tenth Problem over Q, the Hodge conjecture for CM abelian varieties, Mahler's conjecture, and more. The repo hit 2k stars in three hours; Sam Altman says we're entering "a new era of discovery."
Scale: The model was fed 4,000 research problems; results were filtered to 372 families (top fields: theoretical CS 40, combinatorics 37, algebraic & complex geometry 36, number theory 31). Most results used a fixed pipeline averaging 3 hours of ChatGPT Pro thinking compute each. Manuscript dates cluster between Sept 23 and Oct 5 — the bulk produced in under two weeks. 63% (235 families) include Lean formalization notes; OpenAI admits non-formalized results "may have issues."
Headline results:
- #003: Quasi-Riemann with θ=7/8, uniform for zeta and all Dirichlet L-functions, Lean-formalized, plus a uniform Landau–Siegel zero exclusion.
- #074: Claims the 3D Kakeya maximal function conjecture and the 4D Hausdorff dimension conjecture (3D was proved by Wang–Zahl, earning Wang a Fields Medal).
- #102: Claims a proof of Khot's Unique Games conjecture with optimal hardness thresholds for Max-Cut etc.
- #287: Free group factors are isomorphic (with Lean formalization).
Controversy: After September's Navier-Stokes announcement, friction with mathematicians escalated: an erroneous Connes rigidity counterexample in August, a private meeting with 40 mathematicians, a statement by 25 Fields medalists including Terence Tao criticizing rushed announcements, and accusations from NYU's Tristan Buckmaster of scooping unpublished work. Against the IAS September release guidelines, OpenAI's release is "selectively passing" — it shared reasoning summaries and compute estimates but withheld the model's name and hosts the repo on its own GitHub org.
The piece closes on Tao's framing: the real conflict is between abundant proof output and scarce expert attention — when new theorems are no longer scarce, how the community allocates time to understand them becomes the key question.
More from AGI Musings
- Kevin Roose puts AI apocalypse odds at 10%, publishes new book The AGI Chronicles — kevinroose · 2026-10-08
- The Hard Problem of consciousness as a 'water is wet' meme, mapped to four camps — burny_tech · 2026-10-08
- OpenAI math problem #109 tightened ~570-million-fold via nonadjacent axis swaps — aran_nayebi · 2026-10-08
- 'What EA/AI safety folks miss is…': the tell that you're retreading old literature — JacquesThibs · 2026-10-08
- If AI automates math, the frontier shifts from solving problems to asking deeper ones — xwang_lk · 2026-10-08
- Self-Copying AI Breaks One-Person-One-Vote: Social Theory Needs a Rework — jacyanthis · 2026-10-08