Terence Tao

And they're a good source of conjectures for mathematicians to work out.

Yeah, well, mathematicians are in some ways exploring other universes, but just very abstract numerical universes, not as interesting as the sci-fi alternate universes.

Yeah, so Vladimir Arnold, who is a famous mathematician, he once wrote that mathematics is the part of science where experiments are cheap.

Oh, I like that.

Before you invest billions of dollars in a new telescope or a collider or something, you do the math and you see what is theoretically possible, maybe assuming spherical cows and things like that.

But it tells you in theory what you can and what you can't do, and it sets good targets.

And then it allows you to allocate the more expensive resources more intelligently.

Yeah, so this is a dangerous conjecture.

It has trapped many mathematicians and amateurs because it feels like something so simple that we should be able to solve it.

But it's been around for at least 100 years and we haven't solved it.

Well, maybe if you try it a little harder.

If you try, I've worked on this too.

I could describe it.

I'm just worried, as I said, it could trap some audience members to work on it obsessively.

That's good.

So the glass conjecture, it's also called the hailstorm conjecture for a reason I'll explain later.

So it sets a fine.

So you give me a number, your favorite number, 37 or 69 or whatever.

Okay.

And then we do the following.