I am looking to gain a deeper understanding of, and increase my own skill in "Mathematical Simplification". But I've been finding the concept overly vague and haven't been able to find any good resources myself.
Here are some of the questions/ideas I am attempting to clarify: -When exactly is a number or expression considered "Simpler" than another? -What are common and useful techniques for Simplification? -How much of Simplification is Objective and how much is Subjective? -Is there a generalization of Simplification that covers much more of Mathematics then basic Arithmetic and Algebra? (Say from the perspective of Set Theory, Category Theory, Abstract Algebra etc.)
My question can best be summed up by asking if there are any detailed, formal and rigorous explanations of Simplification? If there isn't, why is that so? Is this concept of "Simplification" that textbooks seem to assign such paramount importance simply an artifact of "school-math" that proper mathematicians don't concern themselves with?
Suggestions of external resources and/or personal insight are both appreciated.