I like the story in the article, but I think it tries to create some drama where there isn't any.

I think it's great that a lot of work is done using proof assistants, because clearly it's working out for researchers; diversity of research and of methods is a great strength of science. I really can't see how you can "push it too far", pen-and-paper proofs are not going anywhere. And as more researchers write machine-checked proofs, new techniques for automating these proofs are invented (which is what my research is about hehe) which will only make it easier for more researchers to join in.

> Currently, mathematicians are hoping to formalize all of mathematics using a proof assistant called Lean.

_Some_ mathematicians are trying to formalize _some_ of mathematics using a proof assistant called Lean. It's not a new development, proof assistants have been used for decades. Lean 4 has definitely been gaining popularity recently compared to others, but other proof assistants are still very popular.

> a dedicated group of Lean users is responsible for determining which definitions should go into Lean’s library

The article makes it sound like there is a single, universal "The Lean Library" that everyone is restricted to. I assume it refers to mathlib? But at the end of the day it's just code and everyone is writing their own libraries, and they can make their own decisions.