An AI proves a conjecture open for 100 years

Where things stand (14 Oct 2026)

AI can already do this. Journal publication is the bottleneck.

• Recent AI results.
  • May 2026: an OpenAI model disproved Erdős's 80-year-old unit-distance conjecture.
  • July 2026: Claude disproved the 87-year-old Jacobian conjecture.
  • 8 Sep 2026: OpenAI posted an AI-generated, Lean-formalized Navier–Stokes blowup.
  • 6–7 Oct 2026: OpenAI released 719–722 manuscripts covering 372 result families from an unreleased internal model (blog; repo).
  • Several of these are under 100 years old and don't count: Navier–Stokes (~92 years, from Leray 1934), Jacobian (1939), and Artin's primitive-root conjecture (1927, so 99 years at disclosure).
• Century-old candidates already on the table. I scanned the repo's CONTENTS.md and checked keywords and paper introductions.
  • Koebe's circle-domain conjecture. The paper states the problem was "posed in 1908" and that this "proves Koebe's conjecture in its unrestricted form." The Lean documentation says the formalization covers every domain. This is a clean 118-year-old target.
  • Hilbert's 16th problem, uniform boundedness assertion (1900). Not formalized. Whether "uniform boundedness" counts as the stated conjecture is arguable.
  • Weaker candidates. Partition Principle vs. Choice (Lean-formalized, but its age as a stated conjecture is unclear). Hilbert–Smith (could be dated to Hilbert 1900 or to Smith's later formulation). Catalan's constant (no documented 100-year-old conjecture).
  • Maxwell's conjecture (1873). Disproved on arXiv on 29 Jul 2026 (2607.27197). It probably fails two tests:
    • The disclosure says only that the construction's "idea… was suggested by an LLM," and the authors "have written the argument in their own words."
    • The precise conjecture was formulated in 2007, as commentary notes.
• No journal route yet for OpenAI's results. OpenAI released on GitHub rather than in journals (Decoder). The IAS advisory group's Sept 29 guidelines send papers nobody yet understands to repositories, with human understanding to follow. Community hostility is high: Retraction Watch reported three withdrawals and an open letter from Fields medalists.
• Precedents that journals will publish AI-produced main proofs, quickly.
  • Alexeev–Mixon, "featuring a human-assisted proof": arXiv Oct 2025, published in PNAS on 26 May 2026.
  • Axiom told Axios (26 May 2026) that its AI proofs had appeared in several peer-reviewed journals within months.
  • OpenAI publicly attributes its arguments to its model (its Aug 1 statement).

I found no qualifying journal article published since 16 Sep.

Reference class and hazard

• Reference class: the lag from an AI result appearing to a refereed journal version, about 3–12 months (PNAS took about 7). On top of that, someone outside OpenAI has to produce, or write up, a clean result on a conjecture at least 100 years old with explicit attribution to the AI.
• Near term (low hazard).
  • Nothing that clearly qualifies is in the pipeline.
  • Maxwell would need fast publication and a generous reading of both its age and its attribution.
  • Koebe or Hilbert-16 would need OpenAI to change its practice, or experts to write and referee a digested version, which is likely a late-2027 to 2028 timescale.
• Middle (peak hazard, 2027–28). Public models already solve decades-old problems, and OpenAI plans to release the stronger model. Startups such as Axiom, academics using AI, and DeepMind (which publishes in Nature) all want "century-old conjecture" papers in journals. Lean proofs make refereeing easier. The pool of documented pre-1927 conjectures is large, including many obscure ones.
• Late (declining hazard). The hazard tapers off. If nothing has happened by 2030, that more likely reflects lasting norms, such as journals refusing AI main proofs or authors downplaying AI's role.

The computed cumulative series is 3% (end-2026), 37% (end-2027), 67% (end-2028), 80% (end-2029), and 89% (end-2031).

Strongest case against

• Many mathematicians are hostile. The Leiden Declaration says credit should not be given to automated systems, and Kra and Cohn's guest posts on Tao's blog note that most journals have policies against fully AI-generated manuscripts and that refereeing is swamped.
• The lab that resolves the famous old problems publishes only on GitHub.
• Strict tests apply: the conjecture's age must be documented, it must be a conjecture rather than a loosely stated problem, and the attribution must be explicit. Commentators already contest the Maxwell case on these grounds.

These keep the near-term probabilities modest and leave about an 11% chance of NO overall. Still, the clean Koebe case and the PNAS precedent make eventual YES likely.

Question. By the last day of each quarter, has a refereed mathematics journal published a resolution of a conjecture that had been open for at least 100 years, with the authors stating that an AI system produced the main proof?

Definitions.

• Refereed mathematics journal: a scholarly periodical whose stated scope includes original mathematical research and whose research articles undergo editorially managed review by independent subject specialists before acceptance. A multidisciplinary journal qualifies for a mathematical research article. Conference proceedings, preprint servers, blogs, and journals offering only post-publication review do not qualify.
• Published: the journal has released the accepted, refereed article on its official publication platform, including an online-first version. Submission, acceptance notices, author-posted accepted manuscripts, and unrefereed advance manuscripts do not count. Later print publication does not restart the clock.
• Resolution: a proof of the conjecture or a rigorous disproof, including a counterexample. The article must present the result as settling the stated conjecture, rather than merely supplying evidence, a special case, or a conditional result. A proof of independence from the conjecture's explicitly stated axiom system counts; a failure to prove it does not.
• Open for at least 100 years: at least 100 calendar years elapsed between the earliest documented public statement of the same mathematical conjecture and the first public disclosure of the resolution ultimately published in the qualifying article. The article or a cited scholarly historical source must establish that the conjecture remained unresolved over that interval. The age of an underlying equation, subject, or related problem does not establish the conjecture's age. Equivalent formulations count; a later strengthening does not inherit the original conjecture's date. When only a year or month is documented, use its last day for the conjecture's statement and its first day for the resolution's disclosure, so the minimum established interval must reach 100 years.
• AI system: any machine-learning-based system, from any developer, including a multi-agent system or one using symbolic tools. Conventional computation, exhaustive enumeration, computer algebra, or proof checking alone does not constitute AI production of a proof.
• Authors stating that AI produced the main proof: an explicit statement presented on behalf of the paper's authors that AI generated the principal mathematical argument establishing the resolution, not merely an auxiliary lemma, calculation, conjecture, or exposition. An AI-generated counterexample counts when the authors credit AI with the decisive construction and argument establishing that it refutes the conjecture. Human prompting, selecting approaches, checking, editing, formalizing, and repairing noncentral details are permitted. The statement must not describe humans as supplying the essential missing argument. AI need not be listed as an author, and raw model transcripts are not required.

Resolves YES if a qualifying journal article is published within the Resolution window and, by the quarter-end, the public record establishes the conjecture's age and contains the qualifying authors' statement. The statement may appear in the article, journal-hosted supplements or corrections, or a dated author-authored companion document on an institutional website or scholarly repository explicitly identifying the article. If the statement appears later than the article, the later publication completes the requirements.

Exclusions (resolve NO).

• An AI-assisted result without explicit author attribution of the main proof to AI; translation into Lean or another formal language of an already supplied human proof; or rediscovery of an already resolved conjecture.
• A younger conjecture, even if described informally as a century-old problem, or a result that reaches its centenary only while awaiting journal publication.
• Press coverage, developer publicity, a model's own attribution claim, or expert endorsements without both journal publication and the qualifying authors' statement.
• Articles already retracted or subject to a journal correction withdrawing the claimed resolution before all requirements are met. Later retractions do not reverse an established YES under the Resolution window convention.

Resolving source. The publishing journal's official article record and peer-review policy establish publication and refereeing; the article and the author-authored documents specified above establish AI attribution; the article and its cited scholarly historical sources establish age and prior open status. These are narrower resolving sources than Public confirmation (A2): third-party publicity alone cannot substitute for them. Apply the Resolution window and Resolution date (A3), using the publication date of the last document needed to establish all requirements. The journal article itself must be published on or after the opening date.