I have taken ten years of math in school and then calculus, discrete math, linear algebra. That's all useless if I want to follow math in a simple research paper because they're using notation common in THAT field and it has nothing to do with the notation in another math field.
And it's all V hat superscript pi subscript h. It's not like code, where I get descriptive variable names. And you thought pi meant pi? No, it means policy in THIS context.
Reading a "simple" research paper requires a different approach compared to reading a newspaper or a blog. I hope the following explanation helps.
The notation actually helps to keep things simple. I think of it as a kind of metalinguistic programming [1] where a notation is introduced which then makes the important parts easier to understand.
I am not mathematically inclined but I have to read papers containing maths quite a lot of the time. I tend to read them 3 times.
The first time, I tend to skip the equations altogether and just get a feeling for the paper - what is it about, is it useful for me to read?
The second time I have a pen and a highlighter where I actually label the mathematical symbols with arrows and words (using the textual descriptions). I also highlight important sentences. I think of this stage as trying to make the paper as clear as possible for later reading.
In the third stage I am trying to understand the paper as a whole - something it seems you try to do on the first read, I am familiar with the frustration because this is what I used to do.
I quite enjoy reading papers now and I have more respect for the notation.
> The second time I have a pen and a highlighter where I actually label the mathematical symbols with arrows and words (using the textual descriptions).
Gee, it's almost as if we should be writing the words out instead of writing one letter variable names.
Funny how programmers found this to be good practice and mathematicians still write with a notation that's purposefully unreadable.
I've taken years of English Studies in school, then German, Greek, Russian. That's all useless if I want to read a French book, because they are using a language common in THAT country, and it has nothing to do with the language in another country.
That's not a direct equivalent, but it is close; somewhat equivalent but distinct notations arise in Math and Physics because authors weren't working together (much like natural languages). But otherwise it is "turtles all the way down" - it can only be "simple" or "needlessly complicated" if you assume something about the reader's knowledge.
All of
integrate(f(x)dx,dx)
sum f(x_i) for i=1..n
f(x_1) + f(x_2) + .... + f(x_3)
Are essentially equivalent to a mathematician, often with a preference for the first, whereas someone unfamiliar may claim that only the 3rd is clear and the others are unreadable. A friend of mine was in a classroom where the lecturer started with the first form, when to the 2nd and 3rd over class objections, and finally switching to something like "our function result at the first data point, added to our function result at the second data point, ....". This was an OR class for students pursuing an MBA.
And it's all V hat superscript pi subscript h. It's not like code, where I get descriptive variable names. And you thought pi meant pi? No, it means policy in THIS context.