{
  "id": 12482362,
  "title": "Mathematical manuscripts and supporting proof artifacts produced by OpenAI",
  "url": "https://urgent.news/2026/10/06/mathematical-manuscripts-and-supporting-proof-artifacts-produced-by",
  "topic": "ai",
  "section": "AI",
  "published": "2026-10-06T22:22:48.000Z",
  "source": {
    "name": "Hacker News",
    "slug": "hacker-news",
    "url": "https://github.com/openai/math"
  },
  "original_language": "en",
  "account": "OpenAI has released a collection of mathematical manuscripts and supporting proof artifacts generated by an internal model. This repository consists of 722 manuscripts organized into 372 families, each categorized by mathematical discipline. The models were evaluated on open research problems, with performance on existing mathematical evaluations reaching a saturation point that prompted the expansion of these evaluations.\n\nThe model was posed approximately 4,000 problems during the evaluation process, with each result utilizing an average of three hours of ChatGPT Pro thinking compute. A significant number of results were obtained using the same procedure with the unreleased internal OpenAI model. However, some exceptional cases, such as the zero-free region for the Riemann zeta function and the proof of the Hodge Conjecture for CM abelian varieties, did not follow the fixed procedure. These works were human-edited for readability, specifically the writeup for the Re(s) ≥ 11/12 zero-free region for the Riemann zeta function.\n\nNot all manuscripts in this collection have accompanying Lean formalizations, which are formal proofs in the Lean theorem prover. The collection will continue to be updated with these formalizations as they become available. Some unformalized results might contain issues, which the team aims to address promptly. The repository will also explore community-hosted repositories for these materials.\n\nThe catalogue of manuscripts and families generated by the model was compiled by aggregating the output into result families and manuscripts, requiring an appropriate level of significance. Exceptions to the fixed procedure include the aforementioned zero-free region and Hodge Conjecture cases. The public release history of this collection will be preserved, with corrections and revisions recorded as new versions while retaining access to previously released versions.\n\nTo cite individual manuscripts, users can utilize the BibTeX block provided in their respective directories.",
  "summary": null,
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 3,
    "also_reported_by": [
      {
        "outlet": "The Verge",
        "title": "OpenAI drops another batch of mathematical breakthroughs",
        "url": "https://urgent.news/2026/10/06/openai-drops-another-batch-of-mathematical-breakthroughs",
        "published": "2026-10-06T23:26:38.000Z"
      },
      {
        "outlet": "Hacker News",
        "title": "OpenAI just dropped 700 preprints of mathematical proofs and counterexamples",
        "url": "https://urgent.news/2026/10/06/openai-just-dropped-700-preprints-of-mathematical-proofs-and",
        "published": "2026-10-06T23:37:02.000Z"
      }
    ]
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}