Comment by ww520

From the little I know of, language based provers like Lean allow mathematicians to specify the steps of a proof in a precise language format that can be “run” by a machine assisted prover to prove its validity. It automates the verification and makes proofs reproducible.

In the past when proofs were done by hands, little mistakes or little changes could lead to a complete failure of the proof. Mathematicians spent weeks or months to redo the steps and recheck every little detail.

Machine assisted prover basically raises the abstraction level for theorem proving. People don’t need sweat about little details and little changes in the proof steps.

Language based machine provers also enable wider corroboration as a problem can be subdivided into smaller problems and farmed out to different people to tackle, perhaps to different experts for different parts of the problem. Since everyone uses the same language, the machine can verify each part and the overall proof once the parts come together.