[kevinventullo]

Thanks for the reply. I am also a no-longer-practicing mathematician :)

I completely agree that a machine-generated formal proof is not the same thing as an illuminating human-generated plain-language proof (and in fact I suspect without further guidance they will be quite different, see my other stream of thought comment). However, I do think machine-generated formal proofs would be interesting for a few reasons:

1. Sometimes the obvious thing is not true!

2. I think the existence or non-existence of a machine-generated proof of a mathematical claim is interesting in its own right. E.g. what kinds of claims are easy versus hard for machines to prove?

3. In principle, I would hope they could at least give a starting point for a proper illuminating proof. E.g. the process of refinement and clarification, which is present today even for human proofs, could become more important, and could itself be machine-assisted.

[nicf]

Oh, I hope I didn't come off as talking down to you! As I said in another reply here, the intention behind this comment was pretty narrow --- there's a certain perspective on this stuff that I see pretty often on HN that I think is missing some insight into what makes mathematicians tick, and I may have been letting my reaction to those other people leak into my response to you. Sorry for math-splaining :).

Anyway, yeah, if this scenario does come to pass it will be interesting to see just how impenetrable the resulting formal proofs end up looking and how hard it is to turn them into something that humans can fit in their heads. I can imagine a continuum of possibilities here, with thousands of pages of inscrutable symbol-pushing on one end to beautiful explanations on the other.