I have been thinking for several days about how to answer your question.
I have no particularly good examples, but I think your question misses the point.
I suspect you are saying to yourself: "Well, if there is no 'real world' example, then why should I bother (or more likely, be required to) learn it?"
In fact, you need to understand a great deal more about mathematics in order to answer your question.
However, I will try to give you a short but meaningful answer.
First, mathematics is not directly concerned with "real world" problems. Mathematics is a discipline which starts with a set of assumptions (axioms, postulates) and generates conclusions based on those assumptions. For intellectual completeness, mathematicians pursue those conclusions irrespective of practical utility.
Secondly, sometimes mathematical theory generates solutions for (or at least better understanding of) physical problems and sometimes physical problems generate new mathematics. However, whether or not mathematics has "real world" applications is not an appropriate yardstick by which to measure mathematical concepts.
