Yang-Hui He: How AI Is Reshaping Pure Mathematics Right Now
episodePreviously titled “The AI Math That Left Number Theorists Speechless” — renamed by the publisher on Aug 3, 2026
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What new paradigm is AI introducing to pure mathematics and physics?
What the hell this is bizarre that this patent exists. It went from zero to almost a hundred percent immediately. I was amazed.
I'm extremely excited. Today we're going to be talking about a new paradigm of science, AI research in particular for math and physics, as well as do a deep dive into Professor Yang Hui He's murmuration conjecture. Professor, what am I leaving out?
Um, I think uh well thank you very much for having me again. I had so much fun talking to you last time. And uh it's uh it's great fun. So got so excited about this new uh field of AI assisted uh theoretical discovery, you know, in pure mathematics and theoretical physics, that it really we're really entering a new era of hum of of discovery. And and it's it's amazing. It's happening every week. Uh you know, there's something new that's that could trans potentially be transformative in the way we do science.
Yes, you said it shocked the math world, maybe even the physics world and the science world in general.
Yeah, absolutely. So Um um and I I'm gonna I'm gonna talk about a little bit more details about about this, but just you know, just priv private companies like uh uh g Deep Mind, you know, the fact that they're getting Nobel prizes. And you know, I know these various A uh AI companies, Open AI, Epoch AI, uh they're actually doing fundamental research uh with uh with their models and that are that are beginning to solve problems uh in in in real research and you know at the real research level. So this is uh quite exciting, quite exciting times.
Why don't you talk about how the landscape of research has changed with the advent of these new AI models? Now there's a large class, like there's L LMs, but then there's also new machine learning techniques in general that you have uncovered and other people have uncovered. So why don't you just talk about that?
Yeah, absolutely. So You know, eve when you know, as I as I said, I I think I mentioned uh in the in the in our first long uh conversation, I think I got into this thing as a complete novice. You know, my background was in the interface between algebraic geometry and string theory. And in twenty seventeen, I was just beginning to learn from Cossera. А часто верить базикс о машине лені. And So since then I I I personally have evolved and I've seen the field evolve. uh of of how far we can we can go, you know, because you know, twenty seventeen was pre chat GPT. So this was just really machine learning of data from from pure from you know from from pure mathematics. But now we're we're much more advanced than this.
Uh we're we're beginning to benchmark benchmark, you know, of uh uh deep minds alpha geo two, alpha deep minds alpha proof. They're beginning to show, you know, the signs of reasoning. Whether whether they are reasoning, it's is a purely philosophical uh question, which I'm I have no right to to answer. But what I'm seeing is that they're certainly beginning to outperform your typical undergraduate. And and now um Epoch AI, which is another company, um ha have uh has launched this tier one, two, three uh problems which are research level mathematics. The kind of problems you would give to a graduate student or to give a collaborator or a colleague. And I can show you some of that later, some of some of the stuff.
Yeah, I'd love that. And they're they're entering their uh they're entering their tier four phase. And in fact I'm flying to to Berkeley on um Thursday to have a meeting with a bunch of other mathematicians. to benchmark how far that their tier four reasoning machine can go. So this is really rather you know, it's happening. It's happening As we speak. How th how the landscape of research can be changed. Yeah, sorry, yeah.
Yeah, I think that's in part why firstly it's an honor to speak with you again. Our last conversation went viral. I think that's this whole AI assisted research in math and physics is part of the reason because our last conversation was quite specialized in in nature. It just means the audience loves you, loves hearing from you.
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Chapters
8 chapters
1
What new paradigm is AI introducing to pure mathematics and physics?
0:00–15:11
2
How are DeepMind, OpenAI and Epoch AI changing research workflows?
15:11–29:12
3
Why do mathematicians compare themselves to birds and hedgehogs?
29:12–42:48
4
What role does visual thinking play in modern mathematical discovery?
42:48–56:08
5
How did the Murmuration conjecture reveal AI‑assisted breakthroughs?
56:08–1:11:20
6
What is the Memoration phenomenon and why does it matter for BSD?
1:11:20–1:25:34
7
How is AI reshaping the future of proofs and theorem‑proving?
1:25:34–1:38:59
8
What does the ‘Brave New World of Discovery’ look like for mathematicians?
1:38:59–1:53:25
Speakers
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