The primary barrier to adopting formal verification has been the immense cost (often 10x development time) of maintaining proofs as software changes. AI excels at this tedious and difficult task, rewriting and adapting proofs automatically, which is the key change making the practice scalable and mainstream.

Beyond its academic use for formal verification, Lean is a functional programming language used to build substantial software. Its own tooling is written in Lean, and AWS uses it for a half-million-line compiler for AI accelerators, treating its proof capabilities as a valuable bonus.

A team successfully formalized and simplified a complex proof from Fields Medalist Peter Scholze using Lean. The tool's interactive feedback guided them, allowing them to refactor and improve the mathematics akin to how a programmer refactors code, even without a complete intuitive grasp of the subject.

A project demonstrated an AI successfully translating the zlib C library into the Lean language and proving its core compression/decompression property is correct. This shows AI's capability to handle real-world, complex codebases for formal verification, a task previously deemed infeasible.

Verifying complex systems is bottlenecked by the human inability to specify all requirements. The future of software development is an interactive process where AI helps propose specifications (e.g., via test generation) and then uses a prover to formally verify them.

A major hurdle for formal methods is the effort required to write proofs. Generative AI is becoming capable of producing proofs in formal languages like Lean, which can then be automatically verified by a machine. This could make verified software development scalable for the first time.

Instead of struggling to write an abstract mathematical specification, developers can write a simple, inefficient, but correct version of their program. This 'naive' implementation can then be used as a formal spec for an AI to generate an optimized version, along with a proof of its equivalence.

Formal verification, the process of mathematically proving software correctness, has been too complex for widespread use. New AI models can now automate this, allowing developers to build systems with mathematical guarantees against certain bugs—a huge step for creating trust in high-stakes financial software.

Instead of writing code and then tests, developers could define precise mathematical properties. AI would then synthesize both the program and a formal proof that the program meets those specifications, ensuring correctness by design and flipping the current code-first paradigm.