Motivations to learn mathematics

Think not just of climbing a mountain one way, reaching the summit is not the only thing of importance, but climbing the mountain in multiple ways. On one journey the views are just the best, on another journey greater climbing skill is needed, because on that particular climb few people have been that way.

You could also think of a mathematical quest not as a climb, but also as a trip into a deep sea looking for a wreck containing lost treasure! When you prepare for the dive you have much of the equipment you need, then you get to a point where you can just make out the shadow of the wreck. Suddenly you realise that you are going to need some new piece of equipment that you don't have with you, and you must return to the surface to get it.