{
  "id": 5641046,
  "title": "Anthropic says Claude worked \"largely autonomously\" over 11 days to formalize the proof of Fermat's Last Theorem in the Lean programming language (Anthropic)",
  "url": "https://urgent.news/2026/09/04/anthropic-says-claude-worked-largely-autonomously-over-11-days-to",
  "topic": "ai",
  "section": "AI",
  "published": "2026-09-04T20:35:10.000Z",
  "source": {
    "name": "Techmeme",
    "slug": "techmeme",
    "url": "https://www.anthropic.com/research/formalizing-fermats-last-theorem"
  },
  "original_language": "en",
  "account": "Anthropic has revealed the first complete computer-checked proof of Fermat’s Last Theorem, which was generated by Claude, an AI system, over the course of 11 days. Claude worked largely autonomously to write the proof in the Lean programming language. The proof consists of 13 million lines of Lean code and includes the verification of 29,500 intermediate theorems.\n\nFermat's Last Theorem, proposed by Pierre de Fermat in the 17th century, states that no positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. The theorem remained unproven for over three centuries, with Andrew Wiles finally presenting a proof in 1995. However, this proof was highly complex, running to 129 pages and requiring years of painstaking verification.\n\nAnthropic's researchers, led by Tianyi Peng from Columbia University, set out to test whether Claude could formalize the proof. The AI system not only succeeded but did so in just 11 days, producing a fully computer-checked proof of the theorem. The resulting proof is layered, covering algebra, harmonic analysis, geometry, and number theory, and relies on concepts such as the Jacobian as a scheme and the Mazur theorem.\n\nThe achievement demonstrates that AI-driven autoformalization can now produce robust mathematical proofs, paving the way for increased verification of mathematical results. This could potentially ease the burden of evaluating new mathematical theorems, making mathematical knowledge more trustworthy. Unlike previous AI-driven work on mathematical conjectures, such as the Riemann hypothesis, Claude's proof does not introduce novel mathematics but instead verifies an existing proof with the same rigor as one would apply to a mathematical computation conducted with a calculator.",
  "summary": "We are sharing the first complete computer-checked proof of Fermat's Last Theorem. Claude worked largely autonomously over 11 days …",
  "key_points": [
    "Claude AI generated 11-day proof of Fermat's Last Theorem in Lean programming language",
    "Proof consists of 13 million lines of code with verification of 29,500 intermediate theorems",
    "Achievement demonstrates AI-driven autoformalization can produce robust mathematical proofs"
  ],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 4,
    "also_reported_by": [
      {
        "outlet": "MacRumors",
        "title": "Anthropic's Claude is Coming to CarPlay",
        "url": "https://urgent.news/2026/09/04/anthropics-claude-is-coming-to-carplay",
        "published": "2026-09-04T20:43:40.000Z"
      },
      {
        "outlet": "Dev.to",
        "title": "Fermat’s Last Theorem in Lean: The Community Project and Claude’s Real Role",
        "url": "https://urgent.news/2026/09/04/fermats-last-theorem-in-lean-the-community-project-and-claudes-real",
        "published": "2026-09-04T21:00:30.000Z"
      },
      {
        "outlet": "Techmeme",
        "title": "Sources: Anthropic is expected to make its IPO prospectus public late September and complete the listing days before the US midterm elections in November (Echo Wang/Reuters)",
        "url": "https://urgent.news/2026/09/04/sources-anthropic-is-expected-to-make-its-ipo-prospectus-public-late",
        "published": "2026-09-04T22:55:01.000Z"
      }
    ]
  },
  "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."
}