Speaker unverified: belief

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…ause, you know, there's a lot of false positives," and all this kind of stuff. And all of this is just feels to me like kind of fighting the last war, sort of a, a scarcity mindset on multiple levels. From the body to mathematics. Karina Hong founded Axiom Math, and her bet runs directly against the entire frontier lab playbook. Not bigger models, but formally verified ones, where a machine checks every step of a proof. She explains what that even means, why it matters, and the milestone that just quietly fell. For the first time, a formal system beat an informal one on a real math Olympiad. What is Lean? How is this paradigm that you're developing different from the paradigm that the frontier companies are developing? And obviously we're hearing pretty amazing things in terms of math results from them too. What makes your Bet and the paradigm you're working in diff- Yeah. So I'll, I'll start with the story. This is about January 2025, the joint math meetings, I believe it was in Seattle. So, um, I was there, I think for the first time, the topic is AI. Um, it's the American Mathematical Society, and you would not expect AI to be in the front and center of the largest annual mathematicians gathering. And, and wherever I go for that, I think like three-day period, I heard people whisper one thing, Lean. And so, so like, kind of like, what is Lean? This is a formal language for math proofs. It has been started, like, in specifically 2013 by Leo de Moura at Microsoft. In 2019, people start building Mathlib, the largest math library in Lean. And the dream of AI for math started, predated the, uh, deep learning era of using basically va- various forms of formal languages, Lean included, to try and close out theorem. That's called automated theorem proving. And what's today AI for math would have been called interactive theorem proving, with the human being replaced by an AI. So that's kind of the historical context. Now, obviously, large language models, um, various, like frontier labs, are also pursuing AI for math. But they generally have taken an informal approach, which is the idea of using natural language reasoning and train on really large, um, volume of data train of thought to try to, and also scaling test time, scaling inference, to get to a very sort of strong computing power to be able to not rely on the verifiable output. We're obviously taking a different approach here. We believe in Lean, the power of Lean. Uh, it is at the Putnam Exam in December, which is four months after we start operating, we realized the first time that a, a formal system actually beat the informal system on a math Olympiad. That was never the case. So Econ 101, there's this famous theorem, Agree to Disagree, by Nobel Prize winner Robert Aumann, and that is a 50-year-old theorem since 1976. Everyone's been teaching it for 50 years. There's an implicit assumption that was never made explicit that Axiom Prover was able to catch in the auto-formalization process and was also able to patch the f- the proof, and that- One big question I have about math in general is, like-…

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