Building an AI Mathematician with Carina Hong

**SPEAKER_1** (0:01)
This podcast is sponsored by Google. Hey folks, I'm Amar, Product and Design Lead at Google DeepMind. We just launched a revamped vibe coding experience in AI Studio, that lets you mix and match AI capabilities to turn your ideas into reality faster than ever. Just describe your app and Gemini will automatically wire up the right models and APIs for you. And if you need a spark, hit I'm feeling lucky and we'll help you get started. Head to ai.studio slash build to create your first app.

**Carina Hong** (0:32)
Math and coding are two important, perhaps the two biggest part of digital world. And coding is heavily invested. Math is not. Not that math is not trackable, 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.

**Sam Charrington** (1:08)
All right, everyone, welcome to another episode of The TWIML AI Podcast. I am your host, Sam Charrington. Today, I'm joined by Carina Hong. Carina is founder and CEO at Axiom. Before we get going, be sure to take a moment to hit that subscribe button wherever you're listening to today's show. Carina, welcome to the podcast.

**Carina Hong** (1:27)
Thank you for having me, great to be here.

**Sam Charrington** (1:29)
I'm excited to dig into our conversation. We'll be talking about mathematical reasoning, which is what you are working on there at Axiom. And it is a very timely topic. Before we dig in, I'd love to have you share a little bit about your background.

**Carina Hong** (1:47)
I love math since as long as I can remember, what most people don't. And I feel like Olympian 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 advisor every week and have nothing to report. That's kind of the life of a research mathematician.

**Sam Charrington** (2:27)
What particular field in mathematics?

**Carina Hong** (2:29)
Yeah, so I work on number theory and combinatorics. A lot of people who work in combinatorics come from the Olympiad math background, so they can solve problems a lot faster than other combinatorics researchers. But number theory hopefully is better. You can read a lot of literature and make really interesting contributions without having this sort of outlier problem-solving skill.

**Sam Charrington** (2:53)
Nice, I took a real analysis class in grad school, and I think that was about enough for me.

**Carina Hong** (2:57)
I love graduate analysis. 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 notes and saying that the professor looks like Winnie the Pooh.

**Sam Charrington** (3:15)
That must mean that the class was a lot easier for you than it was for me.

**Carina Hong** (3:20)
Or maybe we were just completely lost. I don't know.

**Sam Charrington** (3:24)
Nice, so you're working on this hard problem at MIT. It took you half a year.

**Carina Hong** (3:32)
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 there constantly verifying the details, wouldn't it be great to just think that there's a high chance if your intuitions is right that the lemma is correct and move on to the next one? A bit like those creative AI arts startups like Pika. You want to put a fox on the cartoon and then have the fox talk to a bunny instead of actually sketching it out like the cartoon creators.

**Sam Charrington** (4:08)
Like say it and let it be so.

**Carina Hong** (4:09)
Yeah, exactly. I think that might be the difference between, say, Terry Tao and Carina Hong, which is perhaps both can have some sort of lemma they want to prove. But Terry can just move on to the next one, and Carina need to be stuck there for about six months before moving to the next one.

**Sam Charrington** (4:28)
One thing that strikes me about what you're doing is that we seem to be in a particular moment with regards to math and AI, and this confluence of math and reasoning. I recently had Christian Zeggity on the podcast. Like a week after we talked, he left to start another, or he started another startup, Math Inc, to focus in this area. There's also Harmonic working on this area and probably Untold Others. I think the first thing I want to get your take on is why now? Why is so much investment and effort more broadly going into mathematics and AI?