[davidgrenier]

I think his argument was restricted to a human-produced mathematical result being ported to a Lean program where one would be just as likely to commit a mistake. However I disagree as well, I recall the difficulty of expressing what I wanted to Coq being a barrier to expressing it incorrectly.

[SkiFire13]

The thing about proof checkers is that they won't accept invalid proofs (assuming their internal axioms are consistents...), so if you make a mistake there it will simply reject your proof. The only place where it won't catch some mistakes is in proposition you want to prove, because the only way for it to know what you want to prove if for you to tell it, but that's much easier to humanly verify.

[robinzfc]

Having worked with a proof assistant is what separates you from Granville (the interviewee in the article). If he had formalized at least a couple of proofs he would not have written things like "people who convert the proof into inputs for Lean". One does not "convert the proof into inputs for Lean" for a simple reason that a proof written in a formal proof language usually contains much more information than the informal prototype. At best one can try to express similar ideas, but it is far from converting a proof from one form to another. If he had formalized a couple of hundred he would have gained a different opinion on the quality of informal proofs as well. A nice list of typical mistakes can be found in this [answer](https://mathoverflow.net/a/291351/163434) to a MathOverflow question.

[calf]

It would be interesting to see some computer-aided proof expert write a possible counter-response to the article.

[Tainnor]

Yeah it's likely he hasn't worked much with Lean and may have some misconceptions around it.