Terence Tao

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.

But they can get closer over time.

The process of getting closer often means that you have to discard your initial intuitions.

Astronomy provides great examples.

An initial model of the world is flat because it looks flat, and it's big.

The rest of the universe, the sun, for example, looks really tiny.

And so you start off with a model, which is actually really far from reality, but it fits kind of the observations that you have.

So things look good, but over time, as you make more and more observations, bring it closer to reality, the model gets dragged along with it.