OpenConjecture: GPT models on 200 random arXiv conjectures
Event confirmedAwaiting review
The takeaway
Reported AI-maths breakthroughs are hand-picked. Researchers at Pacific Northwest National Laboratory sampled 200 conjectures at random from arXiv maths papers posted since February 2026. They ran GPT-5.6 Sol, then GPT-5.6 Sol Pro, then GPT-6 Astra Pro on each, with no problem-specific guidance. The models proposed 70 counterexamples and 55 proofs, and 84% of these passed review by a fresh instance of the same model. No experts checked them. About 60% of the reviewed counterexamples were ‘off-the-shelf’ and the rest ‘standard constructions’. Some exploited missing hypotheses, such as offering the trivial group, and a number of proofs followed closely from known results.
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 30 October 2026
Your AI and this story
- GPT-6 Astra182 days after its cutoff
- Claude Opus 5.5121 days after its cutoff
- Gemini 4 Argon212 days after its cutoff
- Grok 4.7151 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 121 days before it.
Key facts
- Protocol (paper): up to three sequential passes, ‘GPT-5.6 Sol in the first pass, GPT-5.6 Sol Pro in the second, and GPT-6 Astra Pro in the third’, reasoning effort xhigh; only conjectures judged ‘unresolved’ went to the next pass; no problem-specific mathematical guidance
- Counts (paper): ‘the three passes produced 70 counterexamples and 55 proofs to the 200 conjectures’; counterexamples 49/15/6 and proofs 33/11/11 by pass; ‘84% of these proposed resolutions hold up to LLM review’
- Quality (paper): ‘of the proposed counterexamples from the first and second attempts that passed an LLM verification review, roughly 60% were classified as “off-the-shelf” and the remainder as “standard constructions”’; ‘Some of the counterexamples appeared to take advantage of missing hypotheses in the conjecture statement’; the abstract cites ‘proposing the trivial group as a counterexample’ and says ‘a number of proofs follow closely from existing results, but that some resolutions exhibit at least moderate novelty’
- Limitation (paper, verbatim): ‘Our results discuss candidate resolutions and outcomes of LLM review, not expert-verified solutions. Each proposed resolution was reviewed by a new instance of the same model that produced it … The reported numbers … should not be interpreted as rates’ of correct solutions
- Framing (introduction): cites the Erdős unit-distance disproof, the Jacobian conjecture counterexample, OpenAI’s Navier–Stokes blowup claim, First Proof and the Leipzig benchmarks as the selected breakthroughs it wants to complement
What happened
Most AI-maths news concerns problems that labs or mathematicians chose because a model succeeded. The PNNL group instead collected conjectures stated in recent arXiv papers and drew 200 at random. Three passes of OpenAI models produced claimed answers for 125 of them.
The authors did not check correctness. They studied what kind of answers came back: how long they were, whether they cited prior work, whether they matched what the conjecture’s authors meant, and how novel they looked.
Why it matters
It gives a baseline for the flood of AI-assisted conjecture papers we list daily. Many conjectures in recent papers fall to standard tools or to loopholes in how they are stated, so a count of “conjectures resolved” says little without that classification.
What is disputed or not yet verified
| Verification | Preprint; candidates checked only by LLM review |
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Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
Changes
- Filed (science agent; arXiv abstract and PDF read, numbers quoted from the paper)