Lean was created by Leonardo de Moura at Microsoft in 2013 and released as open‑source software. Its companion library, mathlib, now contains nearly 300,000 theorems, over 100,000 definitions and about 2.5 million lines of code, contributed by more than 700 mathematicians, allowing users to cite existing results rather than reprove them. (Source: primary)
Autoformalization—using AI to generate formal proofs from informal sources—has become practical in 2025‑2026. Milestones include a quasi‑autoformalization of the prime number theorem by Math Inc. in September 2025, J. Urban's arXiv preprint of 130 k lines of formal topology in early 2026, Math Inc.’s sphere‑packing proof in 24 dimensions that produced ~500 k SLOC later reduced to 200 k lines, Meta/Facebook’s ATLAS project covering large parts of 26 mathematical textbooks, Anthropic’s autoformalization of Fermat’s Last Theorem yielding 13 million Lean lines in 11 days, and OpenAI’s autoformalization of the Navier‑Stokes blowup theorem in September 2026. (Source: primary)
Despite these advances, Lean’s kernel has faced reliability challenges. A soundness bug traced to an overflow error was reported in May 2025, and the summer of 2026 saw multiple such bugs, including one that produced an illicit disproof of the Collatz conjecture and another that gave a short false proof of the Kepler conjecture. These bugs were discovered with the help of frontier‑model AI used by security researchers such as Ramana Kumar and Dan Selsam of OpenAI, promptly patched, and mathlib was re‑verified with the corrected kernel, underscoring the importance of both automated checking and human audit of statement fidelity. (Source: primary)