Bill Carey states that mathematics most certainly has a grammar, just as language does. For instance, we know how letters, words, and sentences work. They have a concrete system or pattern. In this same way, something like long division also has a “grammar”. Long division has “presumed prescriptive notions about correct use”. So, could mathematics — knowing it has a grammar — also be considered a form of rhetoric?
Interestingly enough, Carey goes on to discuss math as an artform. When writers work, they end up with a book. When painters work, they end up with a painting. When mathematicians work, what do they end up with? Carey’s response is, writing. Mathematicians work through problems to discover new methods or theories about mathematics, but they must then divulge their findings via written papers. These papers are then published in journals if they are not only correct in their math, but also, if the paper is elegant, interesting, witty, a “good read”, etc. Now, this doesn’t necessarily mean mathematics is a form of rhetoric, but it does bring us one step closer by allowing mathematics to be a subject tied directly to or even nested in the humanities.
Something else I find quite interesting about mathematics (when looking at it through a humanities lens), is that math doesn’t have to be translated. Languages, to be read/understood, must be translated in languages we are familiar with. For instance, I speak no Russian at all, so, to be able to read and grapple with ideas from Mikhail Bahktin (for example), I will have to read an English translation. Now, the issue this presents is one of thought patterns. Because we think in words and symbols, our language(s) determine our perception of reality; it determines our thinking. With that being the case, the issue that arises with translation is that you muddy the water that is the original text. You put a different frame of thinking upon the text and, essentially, alter the meaning — whether done so with effort or through innocuous translation. So, when we read Bahktin and begin grappling with heteroglossia, for example, we see how this can be made doubly true via multiple lenses. If we understand heteroglossia as a form of code-switching, or perhaps we understand that a word in any language can have multiple connotations (depending on the author/speaker), this would certainly be magnified when placing the same word through a filter of various other languages. Meaning would change. The thought would change. Here lies the problem with language, thought, meaning, and ambiguity. However, mathematics seems immune.
Another very interesting observation (regarding mathematics as a subject of humanities) is the notion of the “writing process” (e.g., brainstorming, drafting, editing, redrafting, finalizing, etc.). In many ways, mathematics follows this same principle, but because we don’t look at math as language, we are unable to see the merit in this.
When (in math classes), students mull over simple or difficult problems, abstract or concrete problems, they are rarely given the opportunity to go through the writing process.
Students — in traditional math classes — are given problems and a timer, and the more problems the student solves correctly the “better they are” at math. Imagine if this was the same for a traditional English class. Students were given prompts and a timer, and the more “well written” stories the student came up with in that time measured the student’s literacy or ability to perform well in an English course. This method seems to be effective only in one regard: giving students a distaste for mathematics. Instead, math could be viewed through the lens of the writing process. A student might attempt a problem, work through it, edit it (to see where issues arise), redraft the work, obtain a different solution, conference with peers over their attempts and solutions, and perhaps come to a somewhat final draft (all of this done with the teacher acting as a guide, not a lecturer).
Granted, this tangent is moving far from the argument that mathematics is a form of rhetoric, but I do believe it is important to first argue math as a language. That will be the most difficult aspect. Once others can see this connection (between math and humanities), the idea of math and rhetoric will surely fall into place. That said, what we (as educators and creators of curricula must look to), it a mathematics appreciation course (to be continued…).