{
  "id": 59777,
  "title": "OpenAI’s Astra solves 10 long-open math problems and publishes the proofs",
  "url": "https://urgent.news/2026/08/02/openais-astra-solves-10-long-open-math-problems-and-publishes-the",
  "topic": "ai",
  "section": "AI",
  "published": "2026-08-02T22:21:10.000Z",
  "source": {
    "name": "SiliconANGLE",
    "slug": "siliconangle",
    "url": "https://siliconangle.com/2026/08/02/openais-astra-solves-10-long-open-math-problems-publishes-proofs/"
  },
  "original_language": "en",
  "account": null,
  "summary": "OpenAI's Astra, the company's next major release of its AI model family, has reportedly solved 10 long-standing mathematical problems and published machine-checkable proofs for each. The 249-page manuscript collection, along with model-written reasoning walkthroughs and Lean 4 certificates for all 10 results, is available on GitHub under an Apache 2.0 license. The most significant achievement is the construction of a non-sofic group, a question left open since Mikhail Gromov introduced soficity in 1999. Other notable results include disproving Connes's rigidity conjecture and proving Ehrhart's volume conjecture. Additionally, Astra has provided counterexamples in extremal graph theory, resolving two more Erdős problems. The Lean certificates ensure the proofs are machine-checkable, reducing trust in the model to a simple binary verdict.",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "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."
}