Terence Tao

It's a combinatorial explosion.

So the thing with large language models is that they make mistakes.

And so if a proof has got 20 steps and your large language model has a 10% failure rate at each step of going in the wrong direction, it's just extremely unlikely to actually reach the end.

Oh, yeah, it's extremely hard, actually.

Natural language, you know, it's very fault tolerant.

Like, you can make a few minor grammatical errors and a speaker in the second language can get some idea of what you're saying.

But formal language, if you get one little thing wrong, the whole thing is nonsense.

Even formal to formal is very hard.

There are different incompatible prefaces and languages.

There's Lean, but also Koch and Isabel and so forth.

Even converting from a formal language to a formal language is an unsolved problem.

Yeah.

we talked earlier about things that are amazing over time become kind of normalized.

So now somehow it's, of course, geometry is a silver bullet problem.

Right.

That's true.

That's true.

I mean, it's still beautiful.

Yeah.

It's a great work that shows what's possible.