As someone that also doesn't like the status quo - I would love for there to be a better mathematical notation. If we could get some kind of functional programming-like syntax it would be nice and consistent.
Also what's up with the acceptance of single letter variables in math?
Single-variable letters and suggestive notation make it easier to recognise patterns, and give a good level of abstraction at which thinking about the problem rather than muddling through notation can happen. For example one can rather easily check
a(b + c) + (b - d - a)(b + c) = (b - d)(b + c)
But it will be hard to simplify
add(mul(amins, add(boo, cold)), mul(…
You are not expected to understand what the notation means without further context, in the same way a programmer is not meant to see a function call to main(foo) and understand what will happen.
Find yourself a copy of The Structural Interpretation of Classical Mechanics. The primary author of this textbook on mechanics was the inventor of Scheme. It uses two notations throughout. The first will be very familiar to mathematicians, but with some changes to disambiguate things like derivatives, while the other notation is Scheme.
The Mechanics package for MIT-Scheme adds a whole computer algebra system so that it can compute the derivatives of ordinary Scheme functions, symbolically evaluate them, etc.
Interesting bit of history that's relatively unknown: APL was originally an attempt by Iverson to create a uniform and systematic mathematical notation. It was only after he'd designed the notation that it was turned into a programming language. This helps explain APLs quirks, and perhaps the limit of popularity it hit.
I think maybe you mean what's up with the dearth of multi letter variables, and if so IMO the answer is, satisfying or not, that juxtaposition as an operator is too hard to give up.
Edit: juxtaposition without some sort of brackets, of course
Also what's up with the acceptance of single letter variables in math?