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

This where computers can help us or AI can help us in these three different uh directions.

Great.

So let me just begin with the this bottom up and just sort of to to summarize uh this this is probably the oldest uh attempt in in in w where computers can can help us.

So so this is where I'm gonna define bottom-up, which is uh you I guess it goes back to um

Where they try to axize axiomatize mathematics, you know, from the very beginning.

You know, it took like 300 pages for them to prove that one plus one is good to two, famously.

Nobody has read this.

So this is this is one of those impenetrable books.

But I mean this but this tradition goes back to you know Leibniz.

or to Euclid even, you know, that the idea that mathematics should be axiomatized, right?

Uh of course this this program uh took took only about twenty years before he was completely killed in some sense because of Goethe and Church and Tyron's incompleteness theorems.

That you know, this I very idea of trying to axiomatize mathematics by constructing, you know, uh layer by layer is proven to be, you know, logically impossible within every order of logic.

Uh but uh I'd like to quote my uh very distinguished uh uh uh colleague uh Professor Mignon Kim.

He says the practice of mathematician hardly ever worries about Girdle.

Because if you have to worry about whether your axioms are are or your are are are valid to your day-to-day, you know, if if an algebraic geometer has to worry about this, then you're sunk, right?

And you get depressed about everything you do, right?

So the two buts kind of cancel out.

But the reason I mention this is that because of the fact that these two buts cancel each other out, these two negatives cancel each other out, this idea of using

Computers to check proofs, or to computer-aided proofs, really goes back to the 1950s.

So despite the, you know, the what Goethe and Church and Turin have proved, which is foundational, even back in 1956, Noah, Simon and Shaw devised this logical theory machine.

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