Terence Tao

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.

No two are the same.

Yeah, so it makes everything compatible and trustable.

Yeah, so currently, only a few mathematical projects can be cut up in this way.

At the current state of the art, most of the lean activity is on formalizing proofs that have already been proven by humans.

Math paper basically is...

a blueprint, in a sense.

It is taking a difficult statement, like a big theorem, and breaking it up into maybe a hundred little numbers, but often not all written with enough detail that each one can be sort of directly formalized.

A blueprint is like a really pedantically written version of a paper where every step is explained to as much detail as possible, and you're trying to make each step kind of self-contained, depending on only a very specific number of previous statements that have been proven.

so that each node of this blueprint graph that gets generated can be tackled independently of the others.

And you don't even need to know how the whole thing works.

So it's like a modern supply chain.

If you want to create an iPhone or some other complicated object, no one person can build a single object.

But you can have specialists who just, if they're given some widgets from some other company, they can combine them together to form a slightly bigger widget.