A language model receives an informal statement (e.g. a theorem in English) and generates its formal-language equivalent (e.g. Lean), often along with a proof sketch. The generated code is passed to a proof assistant that checks its correctness; errors and verifier messages return to the model as a signal to improve (a generate-verify-repair loop). Training and fine-tuning use informal-to-formal pairs and reinforcement learning based on the verification outcome.
Formalizing mathematics by hand is very labor-intensive, and LLMs can hallucinate in reasoning. Autoformalization automates translation into a formal form that can be machine-verified, combining AI scale with proof certainty.
Generates formal statements and proofs from informal content.
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A verifier (e.g. Lean) checking the generated code.
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Verifier messages guide the repair of subsequent attempts.
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Wu et al. show LLMs can translate mathematics into formal language.
A system combining autoformalization and Lean reaches IMO medal level.
