> However, consider that for people who are already used to the notation those "unnecessary" equations are actually more compact and precise than reading the accompanying text. What seems difficult to you may be easy for someone else, and vice versa.
A struggle for me over the years has been that there does not really seem to be any way of learning the notation, separate from the standard university education process. I'm not about to drop out of my career and go back to school just to learn to read mathematical notation, and it's basically impossible to look up the definitions for obscure symbols with unguessable names, so I simply remain ignorant.
Can you give an example of a place you've seen notation you can't understand? Typically, papers include a brief notation section where they define notation you can then google. In other cases, I've normally been able to google things like "what does the bar over <entity> mean?" successfully.
The last paper I remember trying to crack was Damas & Milner, on type systems, since I was working on a problem which appeared to be analogous to type inference. I asked a friend for help, and he very kindly translated it for me - he's actually written a long series of blog posts now, based on those emails:
As with virtually every other CS paper using math notation, I found the Damas & Milner paper utterly incomprehensible at first, but once I'd seen the formulas translated into a notation I can actually read, I was able to go back and learn something useful from it.
Unfortunately, it appears to be the case that there really is no one such thing as "math notation", not in the sense that there is one programming notation called "Python" and another called "Haskell" and yet another called "C++", such that one can go read a tutorial for some specific language and thereby come to understand how its notation works. Instead, it appears that "math notation" is a huge collection of little micro-notations, all mixed up together in a more or less ad-hoc fashion by the author of each paper.
A struggle for me over the years has been that there does not really seem to be any way of learning the notation, separate from the standard university education process. I'm not about to drop out of my career and go back to school just to learn to read mathematical notation, and it's basically impossible to look up the definitions for obscure symbols with unguessable names, so I simply remain ignorant.