Continuing to model the world through long-form podcasts! @CarinaLHong This episode is full of the "beauty of mathematics". She is also our youngest guest to date — Hong Letong, born in 2001, known online as the "Math Girl". This is her first-ever interview in Chinese. We talked about mathematics as invented versus discovered, proofs from the Book of Proofs, the entrepreneurial journey of the most unlikely founder, and of course, AI for Math. ✍🏻✍🏻 A 4-hour Interview with Carina Hong: AI for Math, Lean, Proofs from The ... 来自 @YouTube

Axiom Math's Carina Hong on the undergrad intern who proved Richard Stanley conjectures with her AI: "There's someone who just joined our team, a junior undergrad student and intern, using Axiom Prover to prove a couple of conjectures by Richard Stanley, one of the best combinatorialists, at MIT." "That's very exciting for this person, because the AI basically means you can now reach for the impossible conjectures that would typically take you some time of getting used to that difficulty of problem." @CarinaLHong @axiommathai

Axiom Math's Carina Hong on why verification isn't about catching mistakes, it's how you drive the cost of a proof to zero: "Formal verification is going to make your life slightly better if you're facing a proof with one million lines. Remember the Erdős unit distance problem, the chain of thought being generated? There are actual mathematicians trying to follow it step by step and scrutinize it. That seems very difficult if you're not in that very niche domain of discrete geometry intersecting with algebraic number theory." "But if you have a Lean proof accompanying it, you can just run it. And running the Lean proof gives you that provable guarantee that this proof is sound." "I have a hot take. People think Lean is this library built on the existing Mathlib. I think it's going to grow significantly. A lot of the hurdles where Lean is difficult is that the basic definitions of some mathematical fields are just not in the library." "My hot take is the scaling law, if you go down the formal mathematics path, is going to be a lot steeper than informal mathematics. So it's not just for verification, for trust, it's also for performance, it's also for optimal generation." "Verification is not like insurance. It's not something where, oh, we want to make sure there's no flaw. That's great, but it also helps you generate mathematics, both proofs and conjectures and theories, a lot better." "So imagine the cost of proof goes to zero. Then you can massage the problem statements, and even if it's an open problem, a lot more easily, flexibly, and adaptively." @CarinaLHong @axiommathai