Terence Tao

If you want to study, for example, Zermatt's theorem, you want to study all possible subsets of numbers 1 to 1,000.

There's only 1,000 numbers.

How bad could it be?

It turns out the number of different subsets of 1 to 1,000 is 2 to the power of 1,000.

which is way bigger than any computer can currently enumerate.

In fact, any computer ever will ever enumerate.

There are certain math problems that very quickly become just intractable to attack by direct brute force computation.

Chess is another famous example.

The number of chess positions, we can't get a computer to fully explore.

But now we have AI.

We have tools to explore this space, not with 100% guarantees of success, but with experiment.

We can empirically solve chess now.

For example, we have very, very good AIs that don't explore every single position in the game tree, but they have found some very good approximation.

And people are using actually these chess engines to do experimental chess.

They're revisiting old chess theories about, oh, this type of opening, this is a good type of move, this is not.

And they can use these chess engines to actually refine, in some cases overturn, conventional wisdom about chess.

And I do hope that mathematics will have a larger experimental component in the future, perhaps powered by AI.

Well, there are these three ontological things.

There's actual reality, there's observations, and our models.

And technically they are distinct, and I think they will always be distinct.