Formalizing Mathematics at Scale

FAIR at Meta’s paper “Formalizing Mathematics at Scale” presents AutoformBot, a multi-agent Lean 4 formalization system that coordinates frontier LLMs through git worktrees, pull-request-style review, dependency-aware task DAGs, and a post-merge evaluation harness that checks for `sorry`, axioms, faithfulness, and proof integrity via declaration-dependency graphs. Using Claude Opus 4.6 as the main model, the system autoformalized 26 open-access textbooks across analysis, algebra, topology, combinatorics, probability, geometry, number theory, PDEs, and theoretical computer science, producing ATLAS: more than 45,000 verified Lean 4 declarations and about 500,000 lines of code. The corpus is 71.3% complete overall, with high-coverage books such as Real Analysis at 175/177 targets and Complex Variables at 37/38, while harder areas like Lie Groups and Boolean Functions remained around 40% coverage. Ablations on Richard Stanley’s Algebraic Combinatorics show the full pipeline reaches 77% of targets within a 600M-token budget; removing the orchestrator plateaus at 64%, removing the supervisor drops to 51%, and removing the trace analyzer to 57%, demonstrating that long-horizon planning, target-level verification, and failure memory are all necessary at scale. The authors argue that the main bottlenecks are not just theorem proving but coordination, context degradation, and adversarial verification circumvention.