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The TWIML AI Podcast

Building an AI Mathematician with Carina Hong - #754

55 min episode · 2 min read
·

Episode

55 min

Read time

2 min

Topics

Startups, Fundraising & VC, Artificial Intelligence

AI-Generated Summary

Key Takeaways

  • Data Scarcity Challenge: Formal math has only 10 million Lean tokens versus one trillion Python tokens, creating a 100,000x data gap that requires auto-formalization and synthetic generation to bridge for effective model training.
  • Three Convergence Factors: AI mathematicians become viable now through post-training reinforcement learning advances, Lean 4 adoption since September 2023, and code generation techniques crossing performance thresholds that transfer to mathematical proving.
  • Self-Play Architecture: Acxiom builds systems where provers and conjecturers interact, with provers providing reward signals for conjectures, creating self-improving loops that expand mathematical knowledge bases through verification and proposal cycles.
  • Auto-Formalization Limitations: Current models struggle to convert natural language proofs longer than five lines into Lean without human intervention, with no established benchmarks for measuring statement formalization accuracy beyond syntax checking.

What It Covers

Carina Hong, founder of Acxiom, explains building AI mathematicians through formal verification using Lean programming language, combining auto-formalization, theorem proving, and self-play systems to achieve mathematical reasoning with provable guarantees.

Key Questions Answered

  • Data Scarcity Challenge: Formal math has only 10 million Lean tokens versus one trillion Python tokens, creating a 100,000x data gap that requires auto-formalization and synthetic generation to bridge for effective model training.
  • Three Convergence Factors: AI mathematicians become viable now through post-training reinforcement learning advances, Lean 4 adoption since September 2023, and code generation techniques crossing performance thresholds that transfer to mathematical proving.
  • Self-Play Architecture: Acxiom builds systems where provers and conjecturers interact, with provers providing reward signals for conjectures, creating self-improving loops that expand mathematical knowledge bases through verification and proposal cycles.
  • Auto-Formalization Limitations: Current models struggle to convert natural language proofs longer than five lines into Lean without human intervention, with no established benchmarks for measuring statement formalization accuracy beyond syntax checking.

Notable Moment

Hong reveals research mathematicians typically spend months stuck on single problems with nothing to report, contrasting sharply with Olympiad training's constant dopamine hits, explaining her motivation to build AI systems that accelerate mathematical intuition.

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Episode Transcript

Math and coding are two important or perhaps the two biggest part of, digital world, and coding is heavily invested. Math is not not that math is not tractable, but that math has not been turned into programming language yet, and there will be new markets and new use cases that get unlocked because of this. Alright, everyone. Welcome to another episode of the Twinmo AI podcast. I am your host, Sam Charrington. Today, I'm joined by Karina Hong. Karina is founder and CEO at Acxiom. Before we get going, be sure to take a moment to hit that subscribe button wherever you're listening to today's show. Karina, welcome to the podcast. Thank you for having me. Great to be here. I'm excited to dig into our conversation. We'll be talking about mathematical reasoning, which is what you are working on there at Acxiom. And, it is a very timely topic. Before we dig in, I'd love to have you share a little bit about your background. I love math since as long as I can remember, when most people don't. And I feel like Olympiad math training gives you this sense of, like, constant dopamine hit. Like, you solve a problem, and then you feel so good about yourself, and then you move on to the next one. A bit later, I went to MIT and started research mathematics career, and that was a lot more pain and suffering. You usually are stuck on a problem for months. And I remember I was working on a really hard problem for about, like, half a year, and I would meet with my adviser every week and have nothing to report. That's kind of the life of a research mathematician. What particular field in mathematics? Yeah. So I work on numbers theory and combinatorics. Lot of people who work in combinatorics come from the Olympiad math background. So they can solve problems, yeah, a lot faster than than other combinatorics researcher. But number theory, hopefully, is is better. It's you can read a lot of literature and, make really interesting contributions without having this sort of outlier problem solving skill. Nice. I took a real analysis class in grad school, and I think that was about enough for me. I love graduate analysis. Yeah. I remember back then at the graduate analysis class, I don't know if it's because no one is quite following. We were just, like, passing note and saying that the professor looks like Winnie the Pooh. That must mean that the class was a lot easier for you than it was for me. Or maybe we're just completely lost. I don't know. Nice. So, so you're working on the this hard problem at MIT. It took you half a year. Yeah. And then I think I realized at one point that wouldn't it be great if you can just let your intuitions take you? You have some lemma that you want to prove instead of being stuck …

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  • Three Convergence Factors: AI mathematicians become viable now through post-training reinforcement learning advances, Lean 4 adoption since September 2023
  • building AI mathematicians through formal verification using Lean programming language, combining auto-formalization, theorem proving, and self-play systems

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