Yang-Hui He

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1,500 appearances 1 recordings 1 series first heard Jan 2025 last heard Jan 2025

Yang-Hui He’s voice in public audio — every appearance, attributed to the second.

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Theories of Everything with Curt Jaimungal · Yang-Hui He: Why AI Will Permanently Transform How Math Is Done · 3 Jan 2025 podcast

And then so the surface of a donut is exactly the topologically um the what they call topologically homeomorphic to to um uh the the the cup.

And then you got the you know the the pretzel.

No, no, so I think that's a pretzel.

Or maybe um I think this is like the German pretzel, and it gets more and more complicated.

But the Euler Euler's um uh because you know Euler invented the the field of topology.

So he was like he realized this this idea of topological equivalence in the sense that there's a single topological invariant called which we now call the Euler number, which characterizes these things.

Uh another way to and

equivalent way to say is the genus of these surfaces is you know no no handles one handle two handles three handles and so on and so forth it turns out that the Eulen number uh what we can now call the Eulen number is two minus twice the genus so two two two minus two g.

Okay that's great so this is

That's the classic Euler th Euler's theorem.

And then, you know, comes in Gauss, right?

No, you when you when when once you got these three names next to each other, Euler, Gauss and Riemann, you know this is it's gotta be some serious theorem.

Right.

So Euler did this in topology.

And then Gauss did this incredible work, which he calls him he himself calls him the the Theorema Gregium.

the great theorem, which he considers this is his personal favorite.

And this is Gauss, right?

And and Gauss said, you can relate this number to uh to um which is this number is purely topological.

You can relate this number to metric geometry.

So he he he came up with this concept which we now call Gaussian curvature.

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