{
  "id": "fermat-formal-proof",
  "org": "Anthropic",
  "topic": "Formal verification",
  "published": "2026-09-04",
  "status": "external-expert-comment",
  "method": "Lean proof; external expert commentary",
  "math": "aⁿ + bⁿ ≠ cⁿ, n > 2",
  "source": "https://www.anthropic.com/research/formalizing-fermats-last-theorem",
  "source_kind": "provider_announcement",
  "checked": "2026-10-29",
  "translations": {
    "en": {
      "title": "Fermat's Last Theorem, checked by a machine",
      "simple": "There are no positive whole numbers a, b and c with aⁿ + bⁿ = cⁿ for n bigger than two. Humans proved this in the 1990s. Claude's new achievement is turning the proof into instructions a computer can check.",
      "research": "Anthropic reports that Claude produced an end-to-end Lean formalization in 11 days, with approximately 29,500 intermediate theorems. Mathematician Kevin Buzzard publicly commented on the resulting artifact.",
      "academic": "This is an autoformalization result, not a newly discovered proof of an open conjecture. In Lean, each proof term is checked against axioms and library definitions by a small kernel. Trust still depends on the assumptions, formal statement and checker; it is not evidence that the model's private reasoning has been revealed.",
      "impact": "Demonstrates a possible path to auditing long mathematical arguments at scale, reducing verification labor while shifting attention to specifications and dependencies.",
      "caution": "The theorem was already proved by Andrew Wiles. Formal verification does not establish that every explanatory step in natural language is correct."
    },
    "nl": {
      "title": "De laatste stelling van Fermat, machinaal gecontroleerd",
      "simple": "Voor n groter dan twee bestaan geen positieve gehele a, b en c met aⁿ + bⁿ = cⁿ. Mensen bewezen dit al; Claude formaliseerde het.",
      "research": "Anthropic meldt dat Claude in elf dagen een volledig Lean-bewijs met circa 29.500 tussenstellingen maakte; Kevin Buzzard gaf commentaar.",
      "academic": "Dit is formalisering, geen oplossing van een nog open probleem. De Lean-kernel toetst bewijster­men tegen expliciete definities en axioma's; correcte specificaties blijven essentieel.",
      "impact": "Maakt grootschalige controle van ingewikkelde bewijzen voorstelbaar.",
      "caution": "De stelling was eerder door Andrew Wiles bewezen; formele controle verklaart niet hoe het model intern dacht."
    },
    "de": {
      "title": "Fermats letzter Satz, maschinell geprüft",
      "simple": "Für n größer als zwei gibt es keine positiven ganzen a, b, c mit aⁿ + bⁿ = cⁿ. Der Satz war bereits bewiesen; Claude formalisierte ihn.",
      "research": "Anthropic berichtet über eine vollständige Lean-Formalisation in elf Tagen; Kevin Buzzard kommentierte das Artefakt.",
      "academic": "Dies ist eine Autoformalisierung, keine neue Lösung eines offenen Problems. Der Lean-Kernel prüft Beweisterme relativ zu Axiomen und Definitionen.",
      "impact": "Weniger manueller Aufwand bei der Überprüfung langer Beweise.",
      "caution": "Der Satz wurde bereits von Andrew Wiles bewiesen."
    },
    "fr": {
      "title": "Le dernier théorème de Fermat, vérifié par machine",
      "simple": "Pour n supérieur à deux, aucun entier positif a, b, c ne satisfait aⁿ + bⁿ = cⁿ. Le théorème était déjà démontré ; Claude l'a formalisé.",
      "research": "Anthropic annonce une formalisation Lean complète en onze jours, commentée par Kevin Buzzard.",
      "academic": "Il s'agit d'autoformalisation, non de la résolution d'une conjecture ouverte. Le noyau Lean vérifie des termes de preuve relativement à leurs axiomes et définitions.",
      "impact": "Vers une vérification plus accessible des longues démonstrations.",
      "caution": "Le théorème avait déjà été prouvé par Andrew Wiles."
    },
    "es": {
      "title": "El último teorema de Fermat, verificado por máquina",
      "simple": "Para n mayor que dos no existen enteros positivos a, b, c con aⁿ + bⁿ = cⁿ. Ya estaba demostrado; Claude lo formalizó.",
      "research": "Anthropic comunica una formalización completa en Lean realizada en once días y comentada por Kevin Buzzard.",
      "academic": "Es un logro de formalización automática, no la solución de una conjetura abierta. El núcleo de Lean comprueba pruebas frente a axiomas y definiciones.",
      "impact": "Potencial para acelerar la revisión de demostraciones largas.",
      "caution": "Andrew Wiles ya había demostrado el teorema."
    },
    "it": {
      "title": "L'ultimo teorema di Fermat, verificato da una macchina",
      "simple": "Per n maggiore di due non esistono interi positivi a, b, c con aⁿ + bⁿ = cⁿ. Il teorema era già noto; Claude lo ha formalizzato.",
      "research": "Anthropic riporta una formalizzazione completa in Lean realizzata in undici giorni e commentata da Kevin Buzzard.",
      "academic": "È un risultato di autoformalizzazione, non la soluzione di una congettura aperta. Il kernel Lean controlla le prove rispetto ad assiomi e definizioni.",
      "impact": "Possibile riduzione del lavoro di verifica dei grandi teoremi.",
      "caution": "Il risultato matematico era già stato dimostrato da Andrew Wiles."
    }
  },
  "translation_method": "AI-assisted explanatory translations; not native mathematical peer review",
  "url": "https://appliedfrontier.nl/en/discoveries/fermat-formal-proof/",
  "as_of": "2026-10-29"
}