Terence Tao

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.

And in mathematics, there's definitely both hedgehogs and foxes.

And then there's people who can play both roles.

And I think ideal collaboration between mathematicians involves... You need some diversity.

A fox working with many hedgehogs or vice versa.

But I identify mostly as a fox, certainly.

I like...

arbitrage somehow, like learning how one field works, learning the tricks of that wheel, and then going to another field, which people don't think is related, but I can adapt the tricks.