Well, to quote the article, you can see things like "p is absolutely continuous with respect to the Lebesque measure on En" and hundreds of variable names and sub/superscripts, none of which are intuitively named. It's really hard to argue that anyone who is not in academia would understand this without passing through it multiple times.

That being said, I think mathematicians should be perfectly permitted to do this, seeing as most people who read their papers are themselves, mathematicians. Thus spelling out every dumb detail would probably just be a waste of their time for the one case that the brave soul who is a programmer tries to decipher it.

Like another comment above alluded to, mathematicians tend to have parallel gripes about code. While technically we're speaking the same language, the dialect is often quite different.

Yes, which is why I mentioned that it makes sense for mathematicians to use the language they do.