This reminds me of a fairly common answer to "what good is a math major?" or "what good is a PhD in math if I don't want to be a professor?", namely that for most values of X, it's easier to teach a mathematician to do X than it is to teach an X-ist mathematics. I'm not sure what good this answer is, though, because it presupposes that having someone who can do both X and math is a Good Thing. That sounds plausible but I want a proof. Or at least some convincing numerical evidence.
According to Zeno, it was somewhat controversial that a two-year college degree in California was made to require more math than a high school diploma in the same state; this reminds me of what I noticed when I was studying for the GRE. The verbal section of the GRE seemed to me to be harder than the verbal section of the SAT -- it had more advanced vocabulary, more complicated reading passages, and so on. But the mathematics section seemed easier! It's as if the test-writers assume that people forgot math in college. (Since you're going to ask: I got a perfect score on the math section and would have been ashamed of anything less.) The average score in my department, depending on the sample, is somewhere between 789 and 794 out of a possible 800. But you'd expect a bunch of entering PhD students in math to be nearly perfect on math they should have learned by the ninth grade. I concluded, upon taking the test, that there was no score I could get on the math section that could possibly make my application look better -- that the test could only hurt me. (Fortunately, it didn't.)
Zeno also writes:
With enough sang froid, a math teacher could probably pose as an English teacher for a much longer time than an English teacher could do the same in a math class. Math doesn't have the wiggle room or the space for discourse that other subjects allow.
It's an interesting experiment. Sokal affair, anyone?
