Every teacher knows this question. Douglas Corey from Brigham Young University answers this question in a great essay: “When Will I Ever Use This? An Essay for Students Who Have Ever Asked This Question in Math Class.” It’s on math, but still can be used for anyone asking this question.
When will you use what you are learning in your classes? I don’t know. No one does. Is it worth learning even if we don’t see an immediate application to something you are interested in? Probably, because most knowledge gets applied to situations we never anticipated or to situations in which we don’t even realize what knowledge we are using. This is a situation in which we ask that you have a little faith in those who have gone before you and are teaching you. The ideas in this essay do not get your teachers off the hook for doing the best they can at helping you understand how the applied fields of mathematics are used. They still have a great responsibility to do that. But if they are doing their best and you are not completely satisfied, then you can use the ideas in this essay to better understand why.
It pays to learn all you can about all you can. Of course, you can’t learn everything, but the more you learn, the better judge you can be of what is worth learning. Exactly how you benefit from what you learn will best be seen by connecting the dots backwards.