Generative AI can produce the "miraculous" insights needed for formal proofs, like finding an inductive invariant, which traditionally required a PhD. It achieves this by training on vast libraries of existing mathematical proofs and generalizing their underlying patterns, effectively automating the creative leap needed for verification.

The standard for mathematical proofs is shifting from peer-reviewed papers to formally verified code. This makes math more like a large open-source project, where anyone in the world can contribute. Because the contributions can be computationally certified for correctness, collaboration becomes easier and the field becomes more accessible to amateurs.

Languages like Lean allow mathematical proofs to be automatically verified. This provides a perfect, binary reward signal (correct/incorrect) for a reinforcement learning agent. It transforms the abstract art of mathematics into a well-defined environment, much like a game of Go, that an AI can be trained to master.

The purpose of creating a superhuman mathematician is not just to solve proofs, but to establish a system of verifiable reasoning. This formal verification capability will be essential to ensure the safety, reliability, and collaborative potential of all future AI code and superintelligence.

While AI can generate code, the stakes on blockchain are too high for bugs, as they lead to direct financial loss. The solution is formal verification, using mathematical proofs to guarantee smart contract correctness. This provides a safety net, enabling users and AI to confidently build and interact with financial applications.

AI and formal methods have been separate fields with opposing traits: AI is flexible but untrustworthy, while formal methods offer guarantees but are rigid. The next frontier is combining them into neurosymbolic systems, creating a "peanut butter and chocolate" moment that captures the best of both worlds.

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 goal for trustworthy AI isn't simply open-source code, but verifiability. This means having mathematical proof, like attestations from secure enclaves, that the code running on a server exactly matches the public, auditable code, ensuring no hidden manipulation.

We have formal languages like Lean for deductive proofs, which AI can be trained on. The next frontier is developing a language to capture mathematical *strategy*—how to assess a conjecture's plausibility or choose a promising path. This would help automate the intuitive, creative part of mathematical discovery.