Lean 4 software scaling laws
The article proposes scaling laws for Lean 4 software development, suggesting that simply adding more computational resources can increasingly automate theorem proving, potentially leading to fully self-improving AI systems that write and verify their own code.
Background
Gwern Branwen is a well-known independent AI and statistics researcher who publishes extensive online essays. This post relates to **scaling laws** — the empirical finding that performance of large AI models improves predictably with more compute, data, or parameters. The post focuses on training "Lean 4" (a modern version of the Lean interactive theorem prover — software that lets mathematicians write machine-verified proofs). Gwern applies scaling-law methodology to the problem of training neural networks to generate formal proofs in Lean 4, analyzing how performance changes with model size and training compute. Lean is significant because it enables computers to rigorously check mathematical reasoning; training AI to write Lean proofs could automate parts of mathematics. The post builds on recent work (like AlphaProof and DeepSeek-Prover) that uses LLMs to generate formal proofs, extending the scaling-laws framework to this domain.