I learned RPN as a college freshman studying engineering in the late 1980's. Almost all of my fellow students had HP RPN calculators. Once we where doing more advanced math RPN -- with the accompanying stack -- became so much easier to enter. We all quickly learned it and I think most of us came to hate standard calculators.
> Could there have been different notations used for things like factoring out a quadratic equation?
well, you're talking about high school algebra, but just adjacent to that is the lisp programming language which uses polish notation. It also uses parentheses because parsing the parentheses-less polish notation requires that the operators have a fixed number of operands
Sussman, co author of SICP and co creator of lisp-like Scheme, has a current idea/book/project he's advocating which is to teach physics using scheme instead of algebraic-calculus because the notation is more precise: rather than differential equations which you need to be skilled at reading, you use polish notation computer programs that can be executed and studied.
I was just thinking of notation, but making math parsable, or teaching a regular math notation, that should be a thing.
I remember hearing generalizations like "chess is pattern matching", and "math is just symbol manipulation", but latter really comes to life if we make math notation regular enough to be funamentally machine readable.
I wonder if teaching it early on, instead of parenthesis, would have made math lessons different?
Could there have been different notations used for things like factoring out a quadratic equation?