Formal verification

Plain English. Formal verification is having a machine check a proof or a program line by line, so that correctness is guaranteed rather than merely asserted. The check is exhaustive: if it passes, there is no untested case left. It is how you get reliable output from an unreliable generator — the model can hallucinate all it likes, because nothing unproven survives the checker. (Getting informal mathematics or a specification into checkable form, autoformalisation, is the translation step that feeds it, usually into Lean.)

Why it moves money. This is the claimed escape from hallucination in high-stakes domains, and it has become a funded startup category rather than an academic niche. The economic frame: verification does for AI output what mass production's quality control did for manufactured goods — it makes the output tradeable by strangers. Software, mathematics and eventually safety-critical engineering get a tier of AI work that can be certified, insured and sold, while unverifiable domains stay on the slower trust curve.

What to watch. The cost curve of formalisation — machine-checked results are landing at scales unthinkable two years ago — and whether verification moves from mathematics into the mainstream software supply chain.

From the signals. Claude formalised Fermat's Last Theorem in 11 days and 13 million lines of Lean. OpenAI claimed a Lean-certified Navier–Stokes proof; a priority dispute erupted. Formal verification is to the AI era what mass production was to industry.

Further reading. The Lean theorem prover