Terence Tao

So if your number is even, we divide by two.

We make it smaller.

So 16 becomes eight.

But if it's odd...

you multiply by three and you add one.

So if you give me five, I multiply by five, it goes to 15, add one to 16.

So all the numbers become bigger, even numbers become smaller.

So now I just repeat this process.

So five becomes 16, but then 16 becomes eight, because it's even, eight becomes four, four becomes two, two becomes one, one is odd, you multiply by three and add one, it becomes four again, and you end up in a loop, one, four, two, one, four, two, one.

It always takes you back down to there.

Well, that's the conjecture.

So we've used computers.

If you take any number up to, say, a trillion, every single number that we tested ends up going down to 142, 142, 142.

But we don't know if all of them do.

So it's called the hailstone conjecture because there's this oversimplified model of hailstones.

Again, a spherical cow type model of hailstones where hail forms because a little ice crystal forms in the clouds.

Sometimes currents bring it up where it's colder and then more ice forms.

and then it goes down a little bit and maybe it melts.

And the, the, the hell stone bounces up and down in the cloud, but eventually it lands to earth.

All the hell stones eventually hit the ground.