paulsimon
457 posts




In this episode, @CarinaLHong, founder and CEO of @axiommathai, 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. 🗒️ For the full list of resources for this episode, visit the show notes page: twimlai.com/go/754. 📖 CHAPTERS =============================== 00:00 - Introduction 03:56 - Convergence of three fields for mathematics and AI 07:14 - Lean 13:06 - Autoformalization 15:51 - Lean data gap in autoformalization 16:49 - Reinforcement learning in formal math 19:18 - Seed-Prover and Aristotle models 20:17 - Axiom’s approach 23:05 - Self-play 26:45 - Self-supervised in math 29:02 - Axiom team 32:19 - Mathematical discovery 35:25 - Autoformalization of statements and proofs 39:29 - Autoformalization challenges 48:04 - Why math reasoning unlocks AI’s next frontier 51:55 - UI for mathematical reasoning 53:10 - Next steps

















