Mm-hmm

... results from other paper.

We want to have-- Essentially, you can read the whole paper from beginning to the end.

It's completely self-contained.

So that's one thing.

And also, we, we try to put all the calculations.

I mean, again, many papers, people don't really put the calculations, right.

Right.

And that's the process of proving something, right? So you have the process of discovery, but then the process of justification.

The process of justification.

So mathematics, at the end of the day, it looks like a chain of logical sequences that the computer can also, I mean, once you have the chain, the computer can go very fast to it and maybe even check.

So there are yet no computers that can check large, I mean, they can check small proofs, but not large.

In any case, it's sort of a very good example, I think, that illustrates very well relations between math and physics.

Take geometry.

So the geometry was the first really theory of the physical world, right? I mean, it's what it describes.

And then lo and behold, it's absolutely crucial for doing quantum mechanics, which is our most fundamental physical theory, or one of them.