The Fall semester, as many of us know, is a popular semester for writing letters of recommendation and advising seniors on their future. As a math professor in a small liberal arts school, I am aware that many (most?) of our majors are not going to go on to graduate school. Certainly, it is not true that math majors can only have careers in academia. There are many options for them and this fact has led to higher enrollments in the mathematical sciences (I think). But this doesn’t mean that we should discourage students from pursuing academic careers, and in this post I will share some of my thoughts on when and how to advise students to pursue higher degrees in mathematics.