{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2025-09-10-math-inc-gauss-strong-pnt/","md":"https://postcutoff.com/e/2025-09-10-math-inc-gauss-strong-pnt/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":"2025-09-10-math-inc-gauss-strong-pnt","date":"2025-09-10","date_precision":"day","short_title":"Math Inc's Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeks","deck":null,"takeaway":"Math Inc (Christian Szegedy) announced that its autoformalization agent Gauss completed Terence Tao and Alex Kontorovich's Strong Prime Number Theorem project in Lean in about 3 weeks, producing ~25,000 lines of Lean and over 1,000 theorems and definitions.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Math Inc: Gauss","url":"https://www.math.inc/gauss","type":"official","group":"primary","domain":"math.inc"},{"n":2,"title":"GitHub: math-inc/strongpnt","url":"https://github.com/math-inc/strongpnt","type":"code","group":"primary","domain":"github.com"},{"n":3,"title":"Math Inc announcement on X","url":"https://x.com/mathematics_inc/status/1966194751847461309","type":"official","group":"primary","domain":"x.com"}],"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Math Inc"],"title":"Math Inc's Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeks","summary":"Math Inc (Christian Szegedy) announced that its autoformalization agent Gauss completed Terence Tao and Alex Kontorovich's Strong Prime Number Theorem project in Lean in about 3 weeks, producing ~25,000 lines of Lean and over 1,000 theorems and definitions. Human experts had worked on the project for 18+ months.","key_facts":["~25,000 lines of Lean, 1,000+ theorems and definitions, code public on GitHub","Human project began in 2024 and had stalled on complex-analysis prerequisites","Announcement day approximate (10–11 Sep 2025)"],"key_numbers":[],"tags":["math","lean","formalization","autoformalization","number-theory"],"science":{"field":"mathematics","subfield":"analytic number theory / formal verification","problem":"Formalising the strong Prime Number Theorem (with error term) in Lean","result":"Complete machine-checked formalisation produced largely by an AI agent in 3 weeks.","open_since":"","ai_system":["Gauss"],"human_role":"AI-assisted: agent wrote most Lean code from the human blueprint; humans supervised","verification":{"key":"lean","label":"Lean-verified","text":"Formal proof in Lean (compiles against Mathlib)"},"status":"confirmed","shock":"Weeks of agent time finished a formalisation that expert humans had been working on for a year and a half."},"body_md":"## What happened\n\nGauss read the human blueprint of the Strong PNT project and wrote the missing Lean formalisations, including a large amount of complex analysis.\n\n## Why it matters\n\nAutoformalization at this scale points to a future where new proofs, including AI-generated ones, are routinely machine-checked. That matters as AI floods mathematics with claimed proofs.","disputed":[],"related":[{"id":"2025-12-06-axiomprover-putnam-2025","url":"https://postcutoff.com/e/2025-12-06-axiomprover-putnam-2025/","date":"2025-12-06","date_precision":"day","short_title":"AxiomProver produces machine-checked Lean proofs for all 12 Putnam 2025 problems","deck":null,"takeaway":"Formal verification removes grading disputes like those around informal IMO proofs, and showed formal provers catching up with informal LLMs on hard competition maths.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":2,"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Axiom Math"]}],"people":[{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"}],"posts":[{"id":"x-mathematics_inc-1966194751847461309","title":"“Today we're announcing Gauss, our first autoformalization agent that just completed Terry…”","url":"https://postcutoff.com/p/x-mathematics_inc-1966194751847461309/"}],"videos":[],"models":[],"changes":[{"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":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":"https://postcutoff.com/s/math-inc-gauss-agent"}