Terence Tao

So this is what I said about cheating first.

It's like, to go back to the bridge building analogy, first assume you have an infinite budget and unlimited amounts of workforce and so forth.

Now can you build this bridge?

Okay.

Now have infinite budget but only finite workforce.

Now can you do that and so forth?

So, I mean, of course, no engineer can actually do this because they have fixed requirements.

Yes, there's this sort of jam sessions always at the beginning where you try all kinds of crazy things and you make all these assumptions that are unrealistic, but you plan to fix later.

And you try to see if there's even some

skeleton of an approach that might work.

And then hopefully that breaks up the problem into smaller subproblems, which you don't know how to do, but then you focus on the sub ones.

And sometimes different collaborators are better at working on certain things.

So one of my theorems I'm known for is a theorem, Ben Green, which is now called the Green-Tau theorem.

It's a statement that the primes contain arithmetic progressions of any length.

So it was a modification of this theorem as I'm already.

And the way we collaborated was that Ben had already proven a similar result for progressions of length 3.

He showed that sets like the primes contain lots and lots of progressions of length 3, and even subsets of the primes, certain subsets do.

But his techniques only worked for length 3 progressions, they didn't work for longer progressions.

But I had these techniques coming from ergodic theory, which is something that I had been playing with and I knew better than Ben at the time.

And so if I could justify certain randomness properties of some set relating to the primes, there's a certain technical condition which if I could