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.

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.

Andrej Karpathy's 'Software 2.0' framework posits that AI automates tasks that are easily *verifiable*. This explains the 'jagged frontier' of AI progress: fields like math and code, where correctness is verifiable, advance rapidly. In contrast, creative and strategic tasks, where success is subjective and hard to verify, lag significantly behind.

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's creative process mirrors Karl Popper's model of science. A generative model 'conjectures' plausible hypotheses (or hallucinates), and a verifier then attempts 'refutation' by testing them against hard criteria. This explains why AI currently excels in verifiable domains like code and mathematics, where correctness can be proven.

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.

Defining AGI as 'human-equivalent' is too limiting because human intelligence is capped by biology (e.g., an IQ of ~160). The truly transformative moment is when AI systems surpass these biological limits, providing access to problem-solving capabilities that are fundamentally greater than any human's.

Harmonic, co-founded by Vlad Tenev to build mathematical superintelligence, has seen its model 'Aristotle' advance faster than anticipated. Initially targeting competition-level math, Aristotle is already assisting with or solving previously unsolved 'Erdős problems,' accelerating the timeline towards tackling foundational scientific challenges.