> It's unintuitive, uninformative, excessively complicated jargon which exists only to gatekeep and save paper.

As a mathematician, notation exists because it's easier to read things with good notation than without. I have some advanced mathematics books in my table and in most of the pages you'll find far more text than notation. Notation is usually explained when it starts being used, usually in the definition. For example, the problem with understanding the notation "Aut(L|k)" is not the notation, because if the author wrote "group of field automorphisms of L fixing k elementwise" I'd be equally lost if I don't understand those words. And once I understand those words, the notation makes it easier to read and understand things whenever the author is talking about that group, because your brain automatically identifies the concept associated with the notation instead of having to read the words and linking them with the concept.

People who don't understand math have this phantasy that they would understand everything only if mathematicians decided to use normal language instead of math symbols. This is just a phantasy, there is no simplification if you stop using math symbols, in fact it is just the opposite. Try to describe some intricate math without symbols and you'll see this.

I do complex math without using greek letters and other untypable characters all the time. It's called programming. The order of operations is explicit, the operations themselves are explicit, and there is very little room for ambiguity. The notation is only for saving space, not because it's the be-all end-all absolute best solution for representing mathematics.

Sorry to tell you, but most programming is just elementary school math and boolean operations. In many cases it doesn't even require high school math. I'm not saying it is easy, but it certainly doesn't require any sophisticated math.

> I do complex math without using greek letters and other untypable characters all the time. It's called programming.

This is simple math.

Start writing formal proofs for your programs. You will then be in the realm of something more complex (and still far lower than the level in a research paper).

Even a proof of the complexity of your algorithm (let alone the correctness) will get ugly without this notation.

My first step to trying to understand an unfamiliar equation or proof is, if I am to have any hope of figuring it out, always breaking it down by term and operation and figuring out WTF each one means in context. Usually on paper. In normal words. Typically I end up turning it into something more "algorithmic" (OK, what happens as the value "passes through" this operation, and then on to this next one...). I'm 1000% useless at understanding equationally- or identity-focused writing, and have to both painstakingly decipher every term and translate it to something more algorithm-like before I can do anything more than stare at the page and drool.

So... yes, I do think it would help if at least some of that were already done for me. As it is it takes so damn long that I don't bother unless I have a good reason.