Terence Tao

I can't pick a sequence of stacks that goes up and down.

Your aim is to lose as little money as possible.

My aim is to get as much money from you as possible.

So you want to arrange your stacks to sort of bounce up and down in such a way that it's hard for me to find a sequence of coins that go up or a sequence of coins that go down.

Right, yeah.

So for example, if you're only allowed to divide your coins into three piles, I can always pick the two biggest ones because the two biggest ones will either be an increasing or decreasing sequence.

So I can always grab at least two thirds of your coins.

But the more columns, the more stacks that you're allowed to make, the less and less I can win from you.

And the question was exactly how much, what is the maximum loss you can have from this game?

So what is the fair price to charge from me to play this game?

Yeah, yeah, yeah, yeah.

So it comes actually from this, this, this theme of Erdős and another mathematician, Sekeresh, yeah, that given any sequence of numbers that goes up and down, you can find within it some sequence that goes up for a long time or some sequence that goes down for a long time.

Yeah, there is order and chaos, actually.

That's almost exactly how it's described.

Yeah, I know this happens all the time.

Eugene Wigner, a physicist, once called this the unreasonable effectiveness of mathematics in the physical sciences.

That there are lots of concepts that mathematicians played with for their own sake.

And only later did, often decades later, did scientists realize they were valuable for other things.

The most famous example is that non-Euclidean geometries.

There you go.