Terence Tao

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.

There's no reason why they should unmix.

But in principle, because of all the collisions between them, there could be some sort of weird conspiracy.

Like maybe there's a microscopic demon called Maxwell's demon that will, every time an oxygen and nitrogen atom collide, they will bounce off in such a way that the oxygen sort of drifts onto one side and the nitrogen goes to the other.

And you could have an extremely improbable configuration emerge.

which we never see, and statistically it's extremely unlikely, but mathematically it's possible that this can happen, and we can't rule it out.

And this is a situation that shows up a lot in mathematics.

A basic example is the digits of pi, 3.14159 and so forth.