This a thousand times. I boycott math notation. My most memorable math moments are:
- giving a talk on notation in high school (I was not tasked to do this, I decided to do it on my own) because I was FREAKED OUT by how we were using tons of symbols nobody had ever explained or defined
- converting all Math I encountered in University to Common Lisp programs to get rid of the shit notation
- bursting into crazy laughter when after five algebra lectures the prof notices that the students parse his notation differently than he does
I had the similar experience when I started to learn math, even the Common Lisp part. I knew how to program from young age and I thought math syntactically. From that mindset it was obviously painful.
But once you really start to understand math, you realize that mathematical notation is not very formal or rigorous. It's shorthand visual help to keep track actual mathematical objects behind the notation. S-expressions are perfect for formal definitions and programming. They are not so good for actually thinking mathematics. Mathematical notation can be dense and contain lots of information.
Notation is problematic for students because underlying concepts or notation is almost never explained well. For example, I don't remember anyone explaining what functional or implicit functions are before using them heavily. I had to figure them out myself.
Out of interest, what subject did you study at University? I studied maths, and everything was defined rigorously at the start of every pure course; and you could always stop the lecturer and ask them what a given piece of notation meant.
Mathematical notation was designed to calculate by hand. If you actually tried to calculate anything by hand, you'd dread long variable names and not being able to use infix symbols with sensible precedence rules. But, of course, a programmer would rather die than calculate anything by hand.
- giving a talk on notation in high school (I was not tasked to do this, I decided to do it on my own) because I was FREAKED OUT by how we were using tons of symbols nobody had ever explained or defined
- converting all Math I encountered in University to Common Lisp programs to get rid of the shit notation
- bursting into crazy laughter when after five algebra lectures the prof notices that the students parse his notation differently than he does
Give it names, use S-Expressions.