But the teachers are right, you know. Professional mathematicians doing research will practically jump at the chance to tell you that their work is meant to be beautiful, not practical. I think that's the message we should be imparting to students: math doesn't have to be useful for you to study it, just as poetry doesn't have to be useful for you to read it.
I remember my year-12 math teacher being the first true teacher I had for the subject in a very long time who actually cared, A student who came up with a varied or creative solution to a normal problem was praised with an overwhelmingly happy and teary exclamation.
I tried harder that year than ever before, Not just because of the importance of my results, But because I wanted to understand her euphoria at really giving yourself over to the problem.
Unfortunately Teachers who inspire such enthusiasm are a desperately rare breed.
It should delight them that writing proofs help you think about thinking logically, monads help you write abstract code, prime numbers (and the difficulty of factoring them) helps you think about encryption; it's just that explaining that "doing this proof is like doing stretches before you work out" leaves some unfulfilled.
