What mathematicians should know about Lean: reliability, soundness bugs and AI
In a guest post on Terence Tao's blog, Thomas Hales surveys formalization and the Lean theorem prover, arguing that autoformalization became a practical reality in 2026: milestones cited include Math Inc.'s autoformalization of the 24-dimensional sphere-packing problem, Meta's ATLAS textbook project, Anthropic's 13 million lines of Lean for Fermat's Last Theorem in 11 days, and OpenAI's Lean formalization alongside its Navier-Stokes announcement. He also examines Lean's 2026 "Summer of Soundness Bugs" — one bug yielded an illicit disproof of the Collatz conjecture — which were found by security researchers using frontier models, quickly patched, and followed by re-verification of mathlib. Hales stresses that Lean proofs must be kernel-checked and then human-audited for statement fidelity.
If AI can produce formal proofs at scale, the reliability of proof-assistant kernels and human checking of what a statement actually says become central to trusting mathematics.