Terence Tao

If you splash around water on a bathtub, it won't explode on you.

Or have water leaving at the speed of light.

But potentially, it is possible.

In fact, in recent years, the consensus has drifted towards the

The belief that, in fact, for certain very special initial configurations of, say, water, that singularities can form.

But people have not yet been able to actually establish this.

The Clay Foundation has these seven millennium prize problems, has a million dollar prize for solving one of these problems.

This is one of them.

Of these seven, only one of them has been solved.

At that point, great conjecture, my parliament.

So the Kakeya conjecture is not directly, directly related to the Navier-Stokes problem, but understanding it would help us understand some aspects of things like wave concentration, which would indirectly probably help us understand the Navier-Stokes problem better.

Can you speak to the Navier-Stokes?

Right, yeah.

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.