If mathematicians are in certain ways similar to developers, I'd expect them to hate fighting with the layout of their papers, and love fighting with a proof checker for the formulas.
[1] https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-e...
[2] https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-...
But to be clear: a community effort by 20+ people, after 6 months of work, managed to make progress toward proving a theorem, including proving some of the trickiest technical parts. As I said before, this is like 2 orders of magnitude more effort than the original plain-language (slightly sloppy/underspecified) proof.
Scholze:
> I cannot read the proofs at all — they are analogous to referring to theorems only via their LaTeX labels, together with a specification of the variables to which it gets applied; plus the names of some random proof finding routines.
At one point, I had to prove n / 15 + n / 4 + (2 * n / 3 + 1) <= n, for positive n. Seems simple right? But first you have to multiply by 60 so that you're working over actual naturals. But then you have to contend with the fact that n / 15 * 15 <= n itself needs proof (they're not just equal, since n / 15 actually represents the floor or that quotient). Automatic tactics that simplify things for you help some, but it still ends up being a good 8 lines of code for such a trivial statement. When things like this can be handled fully automatically, then it will be ready for mainstream use.
It is fun to fight the proof checker though! :)
In terms of lines of code, no. In terms of the learning curve, yes -- latex does a very good job of getting out of the way and letting a mathematician just write in English, where proof assistants require rigid structure that doesn't remotely resemble how (most) mathematicians think. In terms of runtime, oh my god, get out of town.
I think you're mixing two different things here. Runtime is large for proof assistants, e.g. programs that can actually generate pieces of proof for you. Specifically the generation part. Verification of a complete proof were all the steps are provided like you would do in a paper should not, AFAIU, take a long time.
But to get that more people would need to be involved into transcribing proofs into formal language. Ideally, everyone. This is a higher standard, and somebody needs to ask for it.