{
  "id": 8261417,
  "title": "I Vibed a Proof of Conway's Conjecture",
  "url": "https://urgent.news/2026/09/18/i-vibed-a-proof-of-conways-conjecture",
  "topic": "ai",
  "section": "AI",
  "published": "2026-09-18T14:36:10.000Z",
  "source": {
    "name": "Hacker News",
    "slug": "hacker-news",
    "url": "https://overreacted.io/how-i-vibed-a-proof-of-conways-conjecture/"
  },
  "original_language": "en",
  "account": "In a recent development, an artificial intelligence approached the task of solving a mathematical conjecture posed by John Conway 50 years ago. The AI, through a series of prompts and interactions, managed to devise a proof of Conway's refinement conjecture, which concerns the omnific integers within the surreal number system. While the proof has not yet been independently verified by mathematicians, it has passed certain mechanical checks and been deemed plausible by those familiar with Lean and the field. The AI's approach was driven by a curiosity to find an open problem in the field of surreal numbers, which it ultimately identified as Conway's arithmetic problem: the conjecture that every irreducible in K((ℝ^≤0)) with infinite support is prime. This conjecture is equivalent to Conway's 1976 conjecture and is the last of his own conjectures about the surreal numbers remaining unresolved.",
  "summary": null,
  "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."
}