When we start by dividing a curriculum into sciences and humanities, we immediately run into the problem of what to do with math – no small problem given that it’s usually the thing most consistently studied. One response is to say that math is “the language of science”. Taken in the most straightforward sense, the description is unsatisfactory since this isn’t what mathematics is but only one limited way in which it is used. Math is only the language of, say, physics in the way that physics is in turn the language of engineering, but we don’t assume that the physics is a sort of pre-engineering. What we seem to mean by this “language of science” description is that it’s given that science has to be in a curriculum, and so one will need to know some math as a propaedeutic. But this description is also unsatisfactory since math is included in the curriculum even apart from this – we want to prepare students to understand compound interest, making change, using and converting various metrical systems, etc. This is before we say anything about what we want them to know about math simply as math. I suspect that if we took this “math as pre-physics” description seriously, we’d actually be able to make math much simpler. The math that a 12th grader has to know to find his way around a science is usually a lot less involved than the math we are asking them to learn in 12th grade math.
So maybe what we’re assuming is that the science-humanities binary describes different ways of knowing the world. On this account math only enters as a tool for knowing science and not the humanities. This description will probably work until we try to figure out what to do with logic. But it’s odd to assume that curricula are limited to knowledge of a world – even assuming this excludes math. Everyone assumes that we should teach composition, some course on persuasion (rhetoric, marketing, debate, public speaking, etc.) and some course on the fine arts. Are these supposed to be “the language of the humanities”? The description seems forced and clumsy, perhaps because we teach science with an eye to making students scientists, but we don’t teach classical authors or literature with an eye to making students authors. One learns algebra in order to do algebraic things in physics, but we don’t learn composition or grammar in order to compose or grammatically discuss things in literature or philosophy. Perhaps science is just something one must do and not just study (Think Feynmann’s quip about birds and ornithology). But then it sure seems like we should be doing more of it in the curriculum.