Majority of mathematics isn't at all concerned with calculation techniques, this is a fundamental misunderstanding many people get from school, mathematics is t

Majority of mathematics isn't at all concerned with calculation techniques, this is a fundamental misunderstanding many people get from school, mathematics is the study of concepts and relationships between them. If you do not understand the proofs, you do not understand the concepts and you will not be able to apply them. People who learn mathematics as calculation are the ones that most often claim that have no use for mathematics, where in fact they did not really learn any. Proofs are also crucial in Computer Science, for example you do not really understand recursion until you see how it is related to an inductive proof. The widest areas of fruitful application of mathematics do not arise simply from "calculation techniques", whatever that would mean.