Mathematicians are chronically lost and confused

I'd love to read alternate viewpoints, but this is an excellent read.

Absolutely.

However, the rabbit hole is very deep. Many papers make leaps from one sentence to the next that, if you're not familiar with the field, can take a couple days to figure out. Even then, real world proofs are informal and therefore not air-tight. They're close enough, almost always, but there's a reason why a mathematical proof isn't considered valid unless it's lived for two years under peer scrutiny.

One could drill down to formal proof in the Godelian sense, in which proofs are mere typography and can be checked mechanically, but that's not how most of real mathematics is done and, practically speaking, most of it can't be done that way and remain useful to humans (like assembly language, it's too low-level for most applications).

It's more about finding good conjectures, and realizing which theorems and lemmas are actually worth proving, because they say something interesting about the topic.

By analogy, it's certainly important to understand complex grammar, have a large vocabulary, etc in order to be a writer, and develop a good sense of word choice, but that's not really what writing is about; writing is fundamentally about the process by which we tell a story using these tools.