Terence Tao

So yeah, that is literally the million-dollar question.

So this is what distinguishes mathematicians from pretty much everybody else.

If something holds 99.99% of the time, that's good enough for most things.

But mathematicians are one of the few people who really care about whether 100%, really 100% of all

situations are covered by, yeah, so most fluid, most of the time, water does not blow up, but could you design a very special initial state that does this?

Yeah, so it has practical importance.

So this Clay-Price problem concerns what's called the incompressible Navier-Stokes, which governs things like water.

There's something called the compressible Navier-Stokes, which covers things like air.

And that's particularly important for weather prediction.

Weather prediction, it does a lot of computation of fluid dynamics.

A lot of it is actually just trying to solve the Navier-Stokes equations as best they can.

Also gathering a lot of data so that they can initialize the equation.

There's a lot of moving parts.

So it's a very important problem practically.

Why is it difficult to prove general things?

The short answer is Maxwell's demon.

So Maxwell's demon is a concept in thermodynamics.

Like if you have a box of two gases, oxygen and nitrogen, and maybe you start with all the oxygen on one side and nitrogen on the other side, but there's no barrier between them, right?

Then they will mix.

And they should stay mixed.