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.

Wet lab experiments are slow and expensive, forcing scientists to pursue safer, incremental hypotheses. AI models can computationally test riskier, 'home run' ideas before committing lab resources. This de-risking makes scientists less hesitant to explore breakthrough concepts that could accelerate the field.

Kepler's method of testing numerous, often strange, hypotheses against Tycho Brahe's precise data mirrors how AIs can generate and verify countless ideas. This uncovers empirical regularities that can later fuel deeper theoretical understanding, much like Newton's laws explained Kepler's findings.

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.

Scientists constrained by limited grant funding often avoid risky but groundbreaking hypotheses. AI can change this by computationally generating and testing high-risk ideas, de-risking them enough for scientists to confidently pursue ambitious "home runs" that could transform their fields.

The ultimate goal isn't just modeling specific systems (like protein folding), but automating the entire scientific method. This involves AI generating hypotheses, choosing experiments, analyzing results, and updating a 'world model' of a domain, creating a continuous loop of discovery.

Traditional science failed to create equations for complex biological systems because biology is too "bespoke." AI succeeds by discerning patterns from vast datasets, effectively serving as the "language" for modeling biology, much like mathematics is the language of physics.

AI's key advantage isn't superior intelligence but the ability to brute-force enumerate and then rapidly filter a vast number of hypotheses against existing literature and data. This systematic, high-volume approach uncovers novel insights that intuition-driven human processes might miss.

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.