Terence Tao

An ancient example is geometry and number theory.

So in the times of the ancient Greeks, these were considered different subjects.

I mean, mathematicians worked on both.

Euclid

worked both on geometry, most famously, but also on numbers.

But they were not really considered related.

I mean, a little bit, like, you know, you could say that this length was five times this length because you could take five copies of this length and so forth.

But it wasn't until Descartes, who really realized that, who developed what we now call analytic geometry, that you can parameterize the plane, a geometric object, by two real numbers.

Every point can be...

So, geometric problems can be turned into problems about numbers.

Today, this feels almost trivial.

There's no content to this.

Of course, a plane is xx and y, because that's what we teach, and it's internalized.

But it was an important development that these two fields were unified.

And this process has just gone on throughout mathematics over and over again.

Algebra and geometry were separated, and now we have algebraic geometry that connects them over and over again.

And that's certainly the type of mathematics that I enjoy the most.

So I think there's sort of different styles to being a mathematician.

I think hedgehogs and foxes.

A fox knows many things a little bit, but a hedgehog knows one thing very, very well.