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.

Expert mathematicians adopt formal tools like Lean not primarily to catch errors, but to offload tedious, low-level deductions. This automation allows them to operate at a higher level of abstraction and focus their cognitive energy on creative intuition and problem-solving strategy.

Writing formally verified code, which can be mathematically proven to be secure, has been a niche practice due to its extreme difficulty for humans. Because AI agents don't get bored or frustrated, they could be tasked with writing code in these secure languages, making high-assurance programming practical for the first time.

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.

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.

The market for formal verification isn't limited to niche, safety-critical sectors. The true opportunity is providing an optional but powerful verification layer for the massive and growing volume of code produced by AI agents, making it a horizontal utility for the entire AI economy.

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.

Simply generating a mathematical proof in natural language is useless because it could be thousands of pages long and contain subtle errors. The pivotal innovation was combining AI reasoning with formal verification. This ensures the output is provably correct and usable, solving the critical problems of trust and utility for complex, AI-generated work.

With AI generating complex formulas and proofs, the most challenging part of scientific research is no longer solving the core problem. Instead, the primary human task becomes verifying the AI-generated results and writing them up, fundamentally changing the research workflow.