Human Designed Proof

Human-designed proof, the process of formally verifying mathematical theorems and software correctness, is increasingly aided by artificial intelligence. Current research focuses on improving the automation of proof generation and optimization, leveraging large language models and automated theorem provers to create more concise, readable, and modular proofs, often incorporating techniques like symbolic context analysis and growing theorem libraries. This work aims to bridge the gap between human-readable mathematical arguments and machine-verifiable formal proofs, ultimately enhancing the reliability and efficiency of mathematical reasoning and software verification. The resulting improvements in proof automation have significant implications for both mathematical research and software engineering.