What do people who studied theoretical math (or some other theoretical subject) think about whether their work had applications in the real world? I study the subject since I really enjoy it, but I can't think of a good reason about why my work could be "useful" and how I can use it to help other people/make a difference in their lives. Of course there are the usual arguments about how long-term impact isn't something we can predict at all with various historical examples, but I can't help but feel that I'm avoiding the original question. What are your thoughts? (hopefully this is appropriate for the forum - feel free to move somewhere else if this post doesn't belong in this section of the forum) EDIT: All comments about this are welcome (didn't intend to limit to people studying such fields).