Terence Tao

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

habit if ben could supply me that this fact i could give i could conclude the theorem but i what i asked was a really difficult question in number theory which um he said there's no way we can prove this can so he said can you prove your part of the theorem using a weaker hypothesis that i have a chance to prove it and he proposed something which he could prove but it was too weak for me uh i can't use this um so there's this there's this conversation going back and forth um

Different cheats too.

Yeah, yeah.

I want to cheat more, he wants to cheat less.

But eventually we found a property which A, he could prove, and B, I could use, and then we could prove our view.

So there's all kinds of dynamics.

Every collaboration has some story.