Gwern Publishes Deep Dive on Lean Software Scaling Laws

Gwern has published a substantial research essay exploring scaling laws specifically applied to Lean, the interactive theorem prover and formal verification language increasingly used in AI-assisted mathematics. The piece examines how compute, data, and model size interact in the formal proof domain, which behaves differently from natural language because correctness is verifiable and the search space is combinatorial. This is highly relevant for developers and researchers working on AI for formal verification, automated theorem proving, or any application where outputs need hard guarantees rather than statistical accuracy. Scaling laws research in this domain is still early, and a rigorous Gwern-style analysis can meaningfully shape which bets are worth making. Developers building coding assistants or proof assistants on top of LLMs should read this to calibrate expectations about what scale alone can and cannot solve.