Carina Hong is CEO of Axiom Math, where they're building a self-improving superintelligent reasoner, starting with an AI mathematician. She's a Rhodes Scholar, first-gen college grad and mathematics prodigy who earned dual degrees in mathematics and physics from MIT in 3 years. And a joint JD/PhD at Stanford. They just raised a $64M seed round from B Capital, Greycroft, Madrona, and Menlo Ventures.

Carina's favorite books: Proofs from THE BOOK (Author: Martin Aigner, Günter M. Ziegler)

(00:02) Intro
(00:38) What self-improving mathematical superintelligence means
(04:04) Proofs as programs: Lean and the data gap
(06:36) How AI proves: human-style vs. Lean-style reasoning
(10:43) Carina’s journey: from Olympiad problem-solver to theory-builder
(14:47) The engine room: data, infra, and building a math knowledge graph
(17:42) Verifying results: compile checks vs. LLM judges
(18:56) Self-improvement loops: skills libraries, memory, and conjecture↔prover curricula
(21:30) Synthetic data & auto-formalization strategy
(24:00) Benchmarks that matter: miniF2F, CombiBench, miniCTX v2
(26:24) Why combinatorics is uniquely hard for AI
(31:13) Compute footprint & scaling philosophy
(32:20) In-house Lean tooling and productization path
(33:57) Early use cases: formal verification in hardware/software
(36:19) Team blueprint: AI, programming languages, and math
(37:35) Scaling laws, efficiency, and bottlenecks
(38:26) If Axiom works: what becomes cheaper/faster for the world
(40:22) Rapid Fire Round

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Where to find Carina Hong:

LinkedIn: https://www.linkedin.com/in/carina-hong/

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Where to find Prateek Joshi:

Research column: https://www.infrastartups.com
Newsletter: https://prateekjoshi.substack.com
Website: https://prateekj.com
LinkedIn: https://www.linkedin.com/in/prateek-joshi-infinite
X: https://x.com/prateekvjoshi