Thanks for this discussion. I like it. 

Maybe I would like to argue with this point:

On 28/05/2019 10:50, Michael Shulman wrote:

> I think it's fairly hopeless to convince a classical mathematician

> that they should put in a lot of work to convince a computer of the

> truth of *something they already knew*.

I am not sure why the person who started this thread, a mathematician,

Kevin Buzzard, decided to put in such a lot of work, but did and he

has (in Lean), with his students.

But having interacted with a lot of students (from my institution, and

from everywhere in the world, from maths, logic, computer science and

philosophy departments (and once even a high school student in the

UniMath School)), what I can say is that they are not trying to

convince the computer. 

They are trying to convince themselves, using the computer to both 

check their understanding and record their understanding when 

the proof is complete.

If I am allowed to speak for myself, I created a univalent library in

Agda for the purpose of *doing something else*. However, it is nice to

stare at the library and see everything developed from first

principles. When presented with the mathematical literature, both as

students and experienced mathematicians, we are never sure how far

back one has to read until everything begins in a precise way. How

much have we created, and how do all the different fields of

mathematics interact with each other? When one records mathematics in

the computer, this begins to become clear, or at least the asnwers to such

questions become possible.

We don't need to *convince* anybody. This will *happen*. And it is

already happening. The students like it. This is my experience.

M.