As much as it hurts me to repost a Mankiw post, this one was too good not to repost. I know that by doing so, I will only fall further behind in my quest to jump ahead of Mankiw in the list of Google search results. However, there comes a time when we must put aside our petty individual goals and, in the words of Grindelwald, we must do something for the greater good.
While some of the points apply only to economists, there are two points that are applicable to all people:
"3. Math is good training for the mind. It makes you a more rigorous thinker."
"4. Your math courses are one long IQ test. We use math courses to figure out who is really smart."
Beginning with the second point, when people see that I have taken all sorts of math classes, they automatically assume that I am very smart; it is only much later, after they have gotten to know me, that they come to realize what an idiot I really am. People tend to avoid voluntarily taking math classes. While liberal arts students may pick up an extra literature class to study Shakespeare or a history of video games class because they find the topics interesting, rarely does a sane person think to himself: "I ought to sign up for a Modern Algebra class as an elective." One could think of math classes like a form of advertising. It like the pick-up truck commercial that show ridiculous feats of strength. It shows people what you are capable of difficult, abstract tasks.
The first point that Mankiw makes about math being more rigorous is somewhat debatable. Math can be rigorous. It is hard for higher level math classes to not be rigorous. However, from the perspective of a prospective secondary educator, math class has the potential to be about rote memorization of math facts or a rigorous examination of how things work. We just have to focus on making it more of the latter and less of the former. In that way, math class can be less about the fancy course name on the transcript and more about helping students development the necessary quantitative reasoning skills for when they move beyond the classroom.
Mankiw closes with his best line, "The fact is, if you are thinking about a PhD program in economics, you are advised to take math courses until it hurts." Taking more math is classes is good for employment prospects, not just PhD applications. According to BLS.gov: Fastest growing jobs, the jobs that are growing most quickly tend to be either in medicine (most of which will require passing algebra classes as part of the program) or construction (which requires an understanding of geometry to be successful). So, it might just be easier to say that aspiring [your profession] need math, too.