In this episode, Carina Hong, founder and CEO of Axiom, joins us to discuss her work building an "AI Mathematician." Carina explains why this is a pivotal moment for AI in mathematics, citing a convergence of three key areas: the advanced reasoning capabilities of modern LLMs, the rise of formal proof languages like Lean, and breakthroughs in code generation. We explore the core technical challenges, including the massive data gap between general-purpose code and formal math code, and the difficult problem of "autoformalization," or translating natural language proofs into a machine-verifiable format. Carina also shares Axiom's vision for a self-improving system that uses a self-play loop of conjecturing and proving to discover new mathematical knowledge. Finally, we discuss the broader applications of this technology in areas like formal verification for high-stakes software and hardware. The complete show notes for this episode can be found at https://twimlai.com/go/754.

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