Math researcher here. I agree with the basic idea of this article, but not the specifics.
So: notation is a wonderful thing. If someone can improve on it, then great, but modern math notation is what makes math doable. It's true that there is poor notation and poorly used notation; these things need to be fixed.
Regardless, I agree that math is hard to read. I read a lot of math. It's hard. Part of this is because it involves abstract, complicated stuff that often must be understood exactly. But part is because we are not very good at writing it. Or perhaps we don't put as much effort into making it readable as we should.
Being someone who knows a fair amount about programming (or so I like to think) and also writes math research papers, I've found that some of the concepts used to manage complexity in software are also applicable to math.
In particular, I must agree about scope. I've made an effort in my recent writing to be careful about this issue. Another helpful idea involves how to write good comments in code. Too many mathematical proofs perform some operation without telling the reader why or giving any kind of overview. There is nothing wrong with saying, "Here's what we're going to do," and then doing it, and then saying, "Here's what we just did."
So: notation is a wonderful thing. If someone can improve on it, then great, but modern math notation is what makes math doable. It's true that there is poor notation and poorly used notation; these things need to be fixed.
Regardless, I agree that math is hard to read. I read a lot of math. It's hard. Part of this is because it involves abstract, complicated stuff that often must be understood exactly. But part is because we are not very good at writing it. Or perhaps we don't put as much effort into making it readable as we should.
Being someone who knows a fair amount about programming (or so I like to think) and also writes math research papers, I've found that some of the concepts used to manage complexity in software are also applicable to math.
In particular, I must agree about scope. I've made an effort in my recent writing to be careful about this issue. Another helpful idea involves how to write good comments in code. Too many mathematical proofs perform some operation without telling the reader why or giving any kind of overview. There is nothing wrong with saying, "Here's what we're going to do," and then doing it, and then saying, "Here's what we just did."