I love the analogy in David Bessis's wonderful book Mathematica (nothing to do with Wolfram). We all know how to tie our shoes. Now, write in words and symbols to teach someone how you tie your shoes. This is what a proof is.
Often even people with STEM degrees confuse what mathematicians do with the visible product of it - symbols and words on a page. While the formalism of mathematics has immense value for precision, and provides a "serialization language" (to borrow a CS analogy), it would be akin to confusing a Toaster with the Toaster manual, or shoelaces with the instructions.
I started having a much easier time with mathematics when I realized and got comfortable with this idea. In hindsight it should've been obvious to me as a programmer - when I'm building something, I don't ideate in terms of individual lines of code, after all
I love the analogy in David Bessis's wonderful book Mathematica (nothing to do with Wolfram). We all know how to tie our shoes. Now, write in words and symbols to teach someone how you tie your shoes. This is what a proof is.
Often even people with STEM degrees confuse what mathematicians do with the visible product of it - symbols and words on a page. While the formalism of mathematics has immense value for precision, and provides a "serialization language" (to borrow a CS analogy), it would be akin to confusing a Toaster with the Toaster manual, or shoelaces with the instructions.