Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medicine asked me whether it is necessary to write a thesis to get a Ph.D. in math, and then added, "After all, isn't it all already known?". Literate people generally know that physics and biology are fields in which new discoveries are constantly being made. Why should it be any more difficult to let people know that about mathematics than about physics? After all, it's not as if most people who know that about physics have any idea what those new discoveries are.

Liberal arts students are often required to take *one* math course. Often that course consists of a bunch of useless clerical skills. How to do partial fractions decompositions and the like is what students are told "mathematical thinking" is about. In some cases professors feel the one math course that the philosophy major takes is not worth attention because students who didn't learn that material in high school the way they were supposed to aren't any good.

When a university has a course intended to acquaint those who take only one math course with the fact that mathematics is an intellectual field, there are still nonetheless numerous students who take only the algebra course whose content is taught only because it's prerequisite material for other subjects that the student will never take.

So what should we teach to liberal arts students who will take only one math course?

needanything beyond high-school math). – Ilya Grigoriev Jun 19 '10 at 0:21