Terence Tao

So I mean, having a pedantic co-worker.

Right.

Yeah.

If that was the only aspect of it.

Okay.

But, um,

Okay, there's some cases where it's actually more pleasant to do things formally.

So there was a theorem I formalized, and there was a certain constant 12 that came out in the final statement.

And so this 12 had to be carried all through the proof, and everything had to be checked.

All these other numbers had to be consistent with this final number 12.

So we wrote a paper through this theorem with this number 12.

And then a few weeks later, someone said, oh, we can actually improve this 12 to an 11 by reworking some of these steps.

And when this happens with pen and paper, every time you change a parameter, you have to check line by line that every single line of your proof still works.

And there can be subtle things that you didn't quite realize.

Some properties on number 12 that you didn't even realize that you were taking advantage of.

So a proof can break down at a subtle place.

So we had formalized the proof with this constant 12.

And then when this new paper came out, we said, oh, so that took like three weeks to formalize, and like 20 people to formalize this original proof.

I said, oh, but now let's update the 12 to 11.

And what you can do with Lean is that you just, in your headline theorem, you change it 12 to 11, you run the compiler, and like of the thousands of lines of code you have,