{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-09-04-claude-formalizes-fermats-last-theorem/","md":"https://postcutoff.com/e/2026-09-04-claude-formalizes-fermats-last-theorem/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-09-04-claude-formalizes-fermats-last-theorem","date":"2026-09-04","date_precision":"day","short_title":"Claude produces the first complete machine-checked proof of Fermat's Last Theorem in Lean, in 11 days","deck":null,"takeaway":null,"category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Anthropic: Formalizing Fermat's Last Theorem","url":"https://www.anthropic.com/research/formalizing-fermats-last-theorem","type":"official","group":"primary","domain":"anthropic.com"},{"n":2,"title":"Anthropic on X: first formalized proof of Fermat's Last Theorem","url":"https://x.com/AnthropicAI/status/2095947707605266436","type":"official","group":"primary","domain":"x.com"},{"n":3,"title":"AI Weekly: Claude formalized Fermat's Last Theorem in 11 days","url":"https://aiweekly.co/alerts/claude-formalized-fermats-last-theorem-in-11-days-anthropic","type":"press","group":"press","domain":"aiweekly.co"},{"n":4,"title":"Kevin Buzzard (Xena Project): FLT: Anthropic has beaten me to it","url":"https://xenaproject.wordpress.com/2026/09/04/flt-anthropic-has-beaten-me-to-it/","type":"discussion","group":"reactions","domain":"xenaproject.wordpress.com"}],"official":2,"filed":"2026-09-29","updated":"2026-11-09","orgs":["Anthropic"],"title":"Claude produces the first complete machine-checked proof of Fermat's Last Theorem in Lean, in 11 days","summary":"Anthropic reported that a Claude model (roughly comparable to Claude Fable 5.1), running for 11 days (7–18 Aug 2026) using the Prove2Me multi-agent platform, produced a complete Lean formalisation of Fermat's Last Theorem using only Lean's three standard axioms: about 13 million lines and 30,300 theorems, over 5× the size of Mathlib.","key_facts":["Run 7–18 Aug 2026; published 4 Sep 2026","~13M lines of Lean; 30,300 theorems (29,500 used); ~6 billion output tokens","Only occasional high-level instructions from Anthropic researcher Tianyi Peng (e.g. 'Jacobian as a scheme sounds high priority')","Checked against Mathlib's statement of FLT with a comparator; no axioms beyond Lean's standard three","Kevin Buzzard (who leads the human FLT formalisation project): 'This extraordinary autoformalization achievement ... proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics.'"],"key_numbers":[],"tags":["math","lean","formalization","fermat","claude"],"science":{"field":"mathematics","subfield":"number theory / formal verification","problem":"Formal verification of Fermat's Last Theorem (Wiles 1995)","result":"First complete machine-checked proof of FLT from the axioms, in Lean 4.","open_since":"","ai_system":["Claude (research model comparable to Fable 5.1)"],"human_role":"Near-autonomous; occasional high-level guidance","verification":{"key":"lean","label":"Lean-verified","text":"Formal proof in Lean"},"status":"confirmed","shock":"Buzzard's human-led project had expected to need many years to reach a full formalisation; an AI did it in 11 days.","kind":"formalization"},"body_md":"## What happened\n\nAn agentic Claude, orchestrated through the Prove2Me platform, wrote the missing chain of Lean on top of Mathlib, through the modularity-lifting machinery of the Wiles–Taylor proof, up to FLT itself.\n\n## Why it matters\n\nFormalising FLT had been a flagship multi-year human project. Its completion by AI shows that even the deepest modern proofs can now be machine-checked at AI speed.","disputed":[],"related":[{"id":"2026-11-09-claude-fable-5-2-mythos-5-2","url":"https://postcutoff.com/e/2026-11-09-claude-fable-5-2-mythos-5-2/","date":"2026-11-09","date_precision":"day","short_title":"Anthropic releases Claude Fable 5.2 and Claude Mythos 5.2","deck":null,"takeaway":"A new frontier claim from Anthropic on coding, robotics and formal mathematics at a lower price, and the clearest public statement so far of how close a lab's own measurements put it to its automated-AI-R&D threshold.","category":"model-release","category_label":"Model releases","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":26,"official":11,"filed":"2026-11-09","updated":"2026-11-13","orgs":["Anthropic"]},{"id":"2026-09-01-claude-fable-5-1-mythos-5-1","url":"https://postcutoff.com/e/2026-09-01-claude-fable-5-1-mythos-5-1/","date":"2026-09-01","date_precision":"day","short_title":"Anthropic releases Claude Fable 5.1 and Claude Mythos 5.1","deck":null,"takeaway":"Fable/Mythos 5.1 was Anthropic's capability frontier until Opus 5.5 matched it three weeks later at less than half the price.","category":"model-release","category_label":"Model releases","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":9,"official":5,"filed":"2026-09-29","updated":"2026-10-19","orgs":["Anthropic"]},{"id":"2026-03-01-gauss-sphere-packing-formalization","url":"https://postcutoff.com/e/2026-03-01-gauss-sphere-packing-formalization/","date":"2026-03-01","date_precision":"month","short_title":"Math Inc's Gauss formalises Viazovska's sphere-packing proofs in dimensions 8 and 24, fixing errors in the originals","deck":null,"takeaway":"AI autoformalization reached Fields-Medal-level proofs, strengthening the case that formal verification can keep up with the flood of AI-generated mathematics.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":2,"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Math Inc"]}],"people":[{"id":"kevin-buzzard","name":"Kevin Buzzard","url":"https://postcutoff.com/person/kevin-buzzard/"}],"posts":[{"id":"2026-09-04-anthropicai-fermat-last-theorem-formalized","title":"Anthropic: Claude completes first formalized proof of Fermat's Last Theorem","url":"https://postcutoff.com/p/2026-09-04-anthropicai-fermat-last-theorem-formalized/"},{"id":"2026-09-04-xenaproject-flt-anthropic-beaten-me","title":"FLT: Anthropic has beaten me to it","url":"https://postcutoff.com/p/2026-09-04-xenaproject-flt-anthropic-beaten-me/"}],"videos":[],"models":[],"changes":[{"date":"2026-11-10","type":"edit","text":"Checked for a public artefact of the Fable 5.2 re-formalization: the Anthropic research page (still the 4 Sep text) and github.com/anthropics/fermats-last-theorem (last commit 24 Sep, README only) contain none; the 30-hour, ~1,000-agent figures come only from the Fable 5.2 launch material."},{"date":"2026-11-09","type":"edit","text":"Anthropic reports that ~1,000 Claude Fable 5.2 agents redid the full formalization in 30 hours (vs 11 days here) with a proof seven times shorter; see [Anthropic releases Claude Fable 5.2 and Claude Mythos 5.2](https://postcutoff.com/e/2026-11-09-claude-fable-5-2-mythos-5-2/)"},{"date":"2026-10-07","type":"edit","text":"Science block: kind: formalization (formal proof of a theorem already proved) (not a long-open problem; listed with other AI science results, not in the open-problems count)"},{"date":"2026-09-29","type":"edit","text":"Added post link(s) (1) from Anthropic posts cluster"},{"date":"2026-09-29","type":"edit","text":"Added post link(s) (1) from Google/DeepMind + math posts pass"},{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-11-09","human_review":null,"version":{"date":"2026-11-10"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":127,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":66,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":157,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":96,"in_training_data":false}],"short_url":"https://postcutoff.com/s/claude-produces-first-complete"}