*this*." Like nails on a chalkboard! I find the question especially difficult to answer as a pure mathematician. I enjoy mathematics particularly because it is not something that can be used -- the abstractness is exciting. But students don't want to hear this. Increasingly, students go to college for the purpose of getting a higher paying job, and have little patience for anything they will not need to know in the workforce.

To be clear, there are two very different questions of this type. One is an honest question: "What can this mathematics be used for?" This question deserves an honest and careful answer. The other: "Why do I need to know this if I won't ever use it in my particular job?" It is this latter question I want to answer here. Of course, I realize that often students pose the question as rhetorical, as an exhibition of their frustration. In that case, the following can be used to motivate them to get back to work.

A few years back I was watching a baseball game, and the commentators got to talking about a particular player and how dedicated he was. They said that he spent even more time lifting weights than his teammates did. The whole idea of baseball players weightlifting was perplexing to me: why not spend that time at batting practice, or running sprints? Baseballs are not that heavy, and it's not like once reaching second base the runner must bench-press his bodyweight. But of course upon further reflection, it became clear that while the players do not need to use the particular weightlifting skills they work so many hours on, doing so makes them stronger over all. It makes them better athletes. Similarly, doing mathematics makes (future) scientists better thinkers.

Baseball players are not the only people who lift weights. Most everyone can benefit from weightlifting as it is a great way to stay fit and healthy. Similarly, mathematics is a great way to stay mentally fit and healthy. Like weightlifting, it can be difficult when you first start out, especially if you are not doing it correctly. But once you get the hang of it, not only can you lift more and more weight, but it will become enjoyable. In fact, there are people who enjoy weightlifting so much, they do it professionally.