Terence Tao

And you could create what's called a blow-up, where these waves, their amplitude becomes so great that the laws of physics that they're governed by are no longer wave equations, but something more complicated and nonlinear.

In mathematical physics, we care a lot about whether certain equations in wave equations are stable or not, whether they can create these singularities.

There's a famous unsolved problem called the Navier-Stokes regularity problem.

The Navier-Stokes equations are equations that govern the fluid flow for incompressible fluids like water.

The question asks, if you start with a smooth velocity field of water, can it ever concentrate so much that the velocity becomes infinite at some point?

That's called a singularity.

We don't see that in real life.

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.