So much this. Through a series of unexpected events, I ended up studying math in undergrad with no clue why or what I was going to do with it. My senior year I took a class called "Applied Modelling". The first project was a simple, one sentence question: "What would happen if the Greenland ice cap melted?".
It reminded me a lot of Randal Munroe's "What If" blog on the XKCD site [1]. Easy to understand, open ended questions that encourage readers to learn a little about topics _outside_ of math to answer the question. The class gave me an appreciation for math that was lost during all those years of study before that, and it's basically my career now.