OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training (list released 6 Oct: 722 manuscripts)
Awaiting review
The takeaway
On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep).
Status
- Claim
Awaiting review
- Our reporting
- Low confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 10 October 2026
Your AI and this story
- GPT-6 Astra144 days after its cutoff
- Claude Opus 5.583 days after its cutoff
- Gemini 4 Hydrogen174 days after its cutoff
- Grok 4.7113 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 83 days before it.
Key facts
- Claim: 100+ open problems resolved in ~24 days of training; no evidence released as of 29 Sep 2026
- Released 6 Oct 2026: github.com/openai/math, 722 manuscripts in 372 families from ~4,000 posed problems (~3 h ChatGPT Pro compute per result), with Lean formalizations for 162 manuscripts (review ‘unchecked’); claims include the quasi-Riemann hypothesis, Unique Games, Hodge for CM abelian varieties and free group factor isomorphism
- Advisory Group on Mathematics and AI (9 members) at the Institute for Advanced Study; per its own announcement (Tao blog) it formed after OpenAI approached members, but it is independent of any AI company and unpaid
- Sober counterpoint: Epoch’s ‘FrontierMath Erdős’ benchmark (68 open Erdős problems, Lean, $300/problem): GPT-6 Astra 3%, all others 0% (arXiv 2609.25050)
- OEIS Open benchmark: models resolved 147 of 492 formalised open OEIS conjectures (30%) at $50/attempt (arXiv 2608.11941)
- Side effect: on 22 Sep Francesco Deangelis posted an unchecked ChatGPT Astra proof of the Mumford–Shah conjecture to document priority, explicitly because of this announcement (arXiv 2609.26732)
- The Verge (28 Sep): AGMAI member Martin Hairer said ‘We don’t work for OpenAI, are not paid by them, and it’s totally independent’, and that the group had begun talks with other frontier labs. Asked about plans: ‘we, well, you know, started two days ago’. Hairer also described OpenAI altering manuscripts ‘sneakily’ after criticism
- Critics quoted by The Verge: Álvaro Lozano-Robledo (UConn) on OpenAI’s ‘almost solved another Millennium problem’ line, ‘That sentence makes no sense in mathematics’; Colva Roney-Dougal (St Andrews) said it is ‘somewhat agonizing’ to know a large number of results may soon be announced
What happened
OpenAI made a sweeping claim about a model still in training while announcing an advisory body of leading mathematicians.
Update, 6 Oct 2026: the list is out
OpenAI published the promised results as a GitHub repository with 722 manuscripts in 372 families, far more than “100+”. Many come with Lean proofs, and it released reasoning summaries and compute estimates, as AGMAI had recommended. See OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems and the separate entries for the most famous claims.
Why it matters
If substantiated, it would mean open problems are being resolved at industrial scale. Until a list and proofs appear it is an unverified claim, and it contrasts with independent benchmarks where most open Erdős problems still resist all models.
What is disputed or not yet verified
| Verification | List and manuscripts released 6 Oct 2026; partly Lean-formalized, mostly not yet independently verified |
|---|
Sources
11 sources from 8 sites. Numbers match the chips in the text.
11 sources: 5 primary, 4 press, 2 reactions
Primary
- GitHub: openai/math (the released list, 6 Oct 2026)github.com, code
- OpenAI: Sharing AI progress in mathematics (6 Oct 2026)openai.com, official
- FrontierMath Erdős benchmark (arXiv 2609.25050)arxiv.org, paper
- OEIS Open benchmark (arXiv 2608.11941)arxiv.org, paper
- OpenAI: Advisory Group on Mathematics and Artificial Intelligenceopenai.com, official
Press
- TechCrunch: OpenAI forms math advisory group as its AI resolves more than 100 open problemstechcrunch.com, press
- The Decoder: OpenAI says internal model solved over 100 long-standing math problemsthe-decoder.com, press
- The Verge (23 Sep): OpenAI wants to consult elite mathematicians about how to not fumble againtheverge.com, press
- The Verge (28 Sep): OpenAI keeps bulldozing mathematicians (Hairer interview)theverge.com, press
Reactions
- Terence Tao blog: Announcing the Advisory Group on Mathematics and Artificial Intelligenceterrytao.wordpress.com, discussion
- Thomas Bloom on X: FrontierMath Erdős threadx.com, discussion
Changes
- Linked Google DeepMind’s AlphaProof Nexus paper published in Science (AlphaProof Nexus, published in Science 8 Oct 2026)
- List released on 6 Oct (openai/math); retitled, linked the release entry, updated verification status
- Added The Verge’s Sept 23 and Sept 28 AGMAI pieces (Hairer interview, critics’ quotes)
- Linked the Mumford–Shah priority posting and the FrontierMath Erdős resolutions
- Added post link(s)
- Added post link(s) (2) from Google/DeepMind + math posts pass
Show all 7 changes
- Filed