{"schema":"postcutoff/event@1","as_of":"2026-10-17T02:25:00+02:00","url":"https://postcutoff.com/e/2026-10-16-lean-leaders-how-to-formalize-all-of-mathematics/","md":"https://postcutoff.com/e/2026-10-16-lean-leaders-how-to-formalize-all-of-mathematics/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":"2026-10-16-lean-leaders-how-to-formalize-all-of-mathematics","date":"2026-10-16","date_precision":"day","short_title":"Lean leaders: how to formalize all of mathematics","deck":null,"takeaway":"On Oct 16, 2026 Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz published \"How to Formalize All of Mathematics\" on the Xena blog, responding to calls from \"AI enthusiasts\" to auto-formalize the whole literature.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":[{"n":1,"title":"Xena blog: How to Formalize All of Mathematics (Avigad, Buzzard, Commelin, Degenne, Morrison, Nash, Topaz; Oct 16, 2026)","url":"https://xenaproject.wordpress.com/2026/10/16/how-to-formalize-all-of-mathematics/","type":"official","group":"primary","domain":"xenaproject.wordpress.com"},{"n":2,"title":"Terence Tao: How to Formalize All of Mathematics (pointer post)","url":"https://terrytao.wordpress.com/2026/10/16/how-to-formalize-all-of-mathematics/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"}],"official":1,"filed":"2026-10-16","updated":"2026-10-16","orgs":["Lean community","Mathlib"],"title":"Buzzard, Avigad, Morrison and other Lean leaders answer AI 'formalize everything' pushes: most of mathematics could be formalized within three years, but only with curated, reviewed libraries","summary":"On Oct 16, 2026 Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz published \"How to Formalize All of Mathematics\" on the Xena blog, responding to calls from \"AI enthusiasts\" to auto-formalize the whole literature. They criticise AI dumps such as Anthropic's 13-million-line Fermat formalization and OpenAI's math release, set out ten shared values (defer to human-curated Mathlib, public review, open publication, standards met before release), and say most of mathematics could be formalized \"within three years, and possibly much sooner\". Terence Tao amplified it the same day.","key_facts":["Examples criticised: Math, Inc.'s attempted takeover of the 8-dimensional sphere-packing Lean project (the original team rewrote the AI code); Anthropic's Fermat's Last Theorem formalization (13 million lines in 11 days); OpenAI's Navier–Stokes blow-up with Lean formalization and its large GitHub math release (retractions, informal/formal mismatches, hard-to-read write-ups)","Examples praised: OpenAI's unit-distance conjecture work and Anthropic's Riemann zeta zeros work","Main argument: a formal artifact has value only if people use it to do more mathematics; poor formalization could waste millions of dollars and set the field back","Projects described: Mathlib (65 reviewers, 950 contributors; 2026 Jean-Pierre Demailly Prize), DeepMind's Formal Conjectures, the Annals Challenge (statements of recent Annals theorems), Tau Ceti (AI-written and AI-reviewed, ~3M lines), Formal Frontier (41 libraries, ~200k lines), Palomar registry","Asks: contribute to Mathlib; scale Tau Ceti and Formal Frontier tenfold within months; expert roadmaps and blueprints; keep autoformalization tools under mathematicians' control; non-profit or academic hosting","Tao (Oct 16): questions about formal mathematics mirror those about informal mathematics, a tradeoff between speed, scale and understanding"],"key_numbers":[],"tags":["math","lean","formalization","autoformalization","mathlib","ai-for-math"],"science":null,"body_md":"## What happened\n\nThe leading maintainers of Lean's mathematical library wrote a joint position paper on how AI-scale formalization should be done.\nThey do not oppose AI formalization; they want it, and set a three-year horizon. Their objection is to unreviewed, unaudited code\nreleased on the promise of later cleanup, and to libraries that duplicate Mathlib instead of building on it.\n\n## Why it matters\n\nAfter Anthropic's Fermat formalization and OpenAI's mass release, the Lean community's leaders set out the standards they expect AI\nformalization to meet. They also named the projects (Tau Ceti, Formal Frontier) they think should be scaled up.","disputed":[],"related":[{"id":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":84,"official":13,"filed":"2026-10-07","updated":"2026-10-15","orgs":["OpenAI"]},{"id":"2026-09-18-sair-open-math-model-initiative","url":"https://postcutoff.com/e/2026-09-18-sair-open-math-model-initiative/","date":"2026-09-18","date_precision":"day","short_title":"SAIR launches the Open Math Model initiative for community-governed open-weight math AI, plus Lean Kernel and Andrews–Curtis challenges","deck":null,"takeaway":"It is the most concrete attempt by leading mathematicians to build an open, independent alternative to frontier labs' math AI, with governance and data-consent rules written in from the start.","category":"open-source","category_label":"Open source","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":10,"official":9,"filed":"2026-09-29","updated":"2026-10-16","orgs":["SAIR Foundation","Lean FRO","Caltech"]},{"id":"2026-09-08-openai-navier-stokes-blowup","url":"https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/","date":"2026-09-08","date_precision":"day","short_title":"OpenAI claims a Millennium Prize problem","deck":"10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts","takeaway":"It is the first credible AI claim on a Clay Millennium Prize problem, even if only a technically permitted variant.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"disputed","labels":["Disputed"]},"sources":37,"official":4,"filed":"2026-09-29","updated":"2026-10-13","orgs":["OpenAI"]},{"id":"2026-09-04-claude-formalizes-fermats-last-theorem","url":"https://postcutoff.com/e/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":"Formalising FLT had been a flagship multi-year human project.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":4,"official":2,"filed":"2026-09-29","updated":"2026-10-07","orgs":["Anthropic"]},{"id":"2026-08-18-palomar-lean-registry","url":"https://postcutoff.com/e/2026-08-18-palomar-lean-registry/","date":"2026-08-18","date_precision":"day","short_title":"Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claims","deck":null,"takeaway":"Formal verification became the main way to trust AI mathematics in 2026.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":5,"official":5,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Lean FRO","ICARM"]},{"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":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"},{"id":"kevin-buzzard","name":"Kevin Buzzard","url":"https://postcutoff.com/person/kevin-buzzard/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-16","type":"filed","text":"Created (read the Xena post)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-16","run":null,"sources_read":"Read the Xena post","updated":"2026-10-16","human_review":null,"version":{"date":"2026-10-16"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":169,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":108,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":199,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":138,"in_training_data":false}],"short_url":null}