Terence Tao

Yeah, it's a really interaction between all these things.

So over time, the observations and the theory and the modeling should both get better.

closer to reality.

But initially, and this is always the case, they're always far apart to begin with.

But you need one to figure out where to push the other.

So if your model is predicting anomalies that are not predicted by an experiment, that tells experimenters where to look to find more data to refine the models.

So it goes back and forth.

Within mathematics itself, there's also a theory and experimental component.

It's just that until very recently, theory has dominated almost completely.

99% of mathematics is theoretical mathematics, and there's a very tiny amount of experimental mathematics.

I mean, people do do it, you know, like if they want to study prime numbers or whatever, they can just generate large data sets.

So once we had the computers, we began to do it a little bit.

Although even before, well, like Gauss, for example, he discovered, he conjectured the most basic theorem in number theory, which is called the prime number theorem.

which predicts how many primes, up to a million, up to a trillion.

It's not an obvious question.

And basically what he did was that he computed, I mean, mostly by himself, but also hired human computers, people whose professional job it was to do arithmetic, to compute the first 100,000 primes or something, and made tables and made a prediction.

That was an early example of experimental mathematics.

Theoretical mathematics was just much more successful because doing complicated mathematical computations was just not feasible until very recently.

Even though we have powerful computers, only some mathematical things can be explored numerically.

There's something called the combinatorial explosion.