Terence Tao

You stay up to speed on all the developments in this field.

You know all the history.

You have a very good understanding of exactly the strengths and weaknesses of each particular technique.

So yeah, I think you'd rely a lot more on sort of calculation than sort of trying to find narratives.

So yeah, I mean, I can do that too, but there are other people who are extremely good at that.

Let's step back and...

That's a good question.

When I came to graduate school in Princeton, so John Conway was there at the time.

He passed away a few years ago.

But I remember one of the very first research talks I went to was a talk by Conway on what he called extreme proof.

So Conway just had this amazing way of thinking about all kinds of things in a way that you wouldn't normally think of.

So

He thought of proofs themselves as occupying some sort of space.

If you want to prove something, let's say that there's infinitely many primes, there will be different proofs, but you could rank them in different axes.

Some proofs are elegant, some proofs are long, some proofs are elementary, and so forth.

The space of all proofs itself has some sort of shape.

He was interested in extreme points of this shape.

Out of all these proofs, what is the shortest at the expense of everything else, or the most elementary, or whatever?

He gave some examples of well-known theorems, and then he would give what he thought was the extreme proof.

in these different aspects.