Grigori Perelman

In dimension three, it's a little bit more complicated to state, but there is a complete classification of three-dimensional objects, and this is much more modern.

This is going from maybe '70s to 2000s work of Thurston and Perelman.

We totally...

Well, maybe I wanna be careful with the word totally, but I would say that we [laughs] totally understand three manifolds.

And in 25 years, exactly one has been solved.

Perelman with the Poincaré conjecture.

And he did it the old fashioned way and then turned down a million dollars for it.

So when you say AI is solving millennium problems, plural, present tense, which one? And solved or made real progress on a piece of it? because those get reported as the same headline and they're very much not the same claim.

These have not been solved yet.

Only one was solved by a Russian mathematician in 2004, Grigory Perelman.

And now he's a hermit in St. Petersburg, Russia.

So one got solved in 26 years.

So I think that there is the prize itself, which is fantastic, you know, we figured out, but then there's the route to the prize.

So Grigori Perelman, who, you know, solved the Poincaré conjecture, did some really interesting things.

These...

It was meant to be a topology problem, but he chose it as a physics problem, kind of carving out all of these tiny, like, instable elements, and it was some beautiful mathematics doing that.

But again, this is all about the initial datum showing in finite time a blowup because you have cancellation of the various elements, so the spaghetti string gets longer and longer of this vortex that goes out, and that's just a very delicate piece of mathematics.

Mm.

Just like, you know, Grigori Perelman's, um, Poincaré conjecture proof was incredibly delicate as a piece of mathematics as he cut out the various bits and pieces.

Again, like, it isn't the clearest paper [laughs] in the world.