A post at Language Log explores the use of mathematics in linguistics. It closes with
Anyhow, my conclusion is that anyone interested in the rational investigation of language ought to learn at least a certain minimum amount of mathematics.
Unfortunately, the current mathematical curriculum (at least in American colleges and universities) is not very helpful in accomplishing this — and in this respect everyone else is just as badly served as linguists are — because it mostly teaches thing that people don’t really need to know, like calculus, while leaving out almost all of the things that they will really be able to use. (In this respect, the role of college calculus seems to me rather like the role of Latin and Greek in 19th-century education: it’s almost entirely useless to most of the students who are forced to learn it, and its main function is as a social and intellectual gatekeeper, passing through just those students who are willing and able to learn to perform a prescribed set of complex and meaningless rituals.)
Before getting into economics and after getting out of physics, I took calculus and found it very useful and interesting for its own sake. I do see that the way calculus is taught in the US is geared toward engineers and physicists, but I have a hard time thinking of what mathematics would substitute for calculus in the undergraduate curriculum if the goal was to teach students something useful. It can’t be analysis or topology. I took abstract algebra as an undergraduate and found it esoteric and boring. Discrete mathematics? OK maybe statistics, but don’t you need integration for that? Help me out here, if you had the choice, what would you replace calculus with? And remember the goal is to teach something useful.