By Brian Simanek
When it comes time to sign up for classes, I always wonder if I should continue to focus on taking classes most relevant to my research or if I should take some time and learn some advanced math not related to my research.
On one hand, one could make the case that it is always fun and helpful to learn as much math as possible and being in a class that is not related to my research would certainly force me to learn quite a lot. On the other hand, I have learned that most advanced mathematics requires more than three hours a week to be thoroughly learned and understood, so being enrolled in such a class would require a significant commitment. I chose my research field because it is the one I like to spend most of my time thinking about. Does it make sense to devote a non-trivial amount of time to a field in which I am less motivated? I think the answer is yes… sometimes. It does make sense to think critically about as many different mathematical ideas as possible, but one must also choose a specialty and focus most of one’s time learning in that field. That being said, whenever I have taken the time to learn new math in any field, I have always been glad I did so.