> I initially try to accomplish X in the simplest way possible by breaking it down into trivial steps. I know there is a famous programming quote that pertains to this process, but I can't find it right now
Maybe this is it?
A program should be light and agile, its subroutines connected like a strings of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little nor too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity. -- The Tao of Programming
That's kind of the way mathematics expands its knowledge base. Not always, of course. But it's a fine approach. It's an application of the KISS principle.
Maybe this is it?
A program should be light and agile, its subroutines connected like a strings of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little nor too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity. -- The Tao of Programming