Your unstated major premise here is that their intent was to make a universal statement about how proofs work and not just talking to humans about how they teach humans.

That premise seems unlikely to be correct.

Why? The entire subject of conversation is triggered by things which are not humans producing proofs.

If it's possible for a machine to produce a proof without intuition then clearly a human could also do it too. (And in fact I'd argue I've seen many people like that, simply very good at pattern matching over memorised items).

Because regardless of the point TFA is making, that interpretation makes less sense for the specific comment. It doesn’t fit with the immediate context, which was a response to a thoughtful comment about how humans do math. And it requires assuming a math professor doesn’t understand a very basic and obvious thing about their area of expertise.

That doesn’t really read as good faith engagement in the discussion. At best, it reads as being so AI pilled that you can’t even fathom that others might want to have a little side discussion about something other than AI.

You realize the commenter has now confirmed my interpretation was right?

What is up with this whole sub thread of obvious hole digging?

That math prof was talking about his stance in discussion between mathematicians long before AI.

Plus, I studied math, I am from that environment. His description matches how math is done by people.

People who are good at pattern matching and memorize are, frankly, shit mathematicians. They are find in fun culture around math, but rarely in actual math. They cant really do it as science.