As an undergraduate, I studied mathematics, with the single ambition of teaching it to high school students who, except for getting into college, would also have no other use for it. The major was not easy. I remember one night when, instead of watching the Super Bowl, I spent the evening trying to maximize the area of an industrial building. But schlepping a six-pound Calculus book makes you look smarter and improves muscle tone, which was good, because, as it turns out, I never actually taught mathematics to high school students. At least it wasn’t a total waste.
When designing our classical curriculums, we begin with the humanities, confident that literature and history grant us wisdom and make us more human, but we have no such assurances about math. Math is like the baking powder in the cake recipe. We don’t really know what it’s doing in there, but we know everything will fall apart if we leave it out. So we look for reasons post hoc, hoping to find a good justification for what we’ve already planned to do.
Of all the good reasons we find for studying math, two are the most common. The first is that math shows us the order and beauty of the created universe, which also tells us something about the Creator. The second is that math is a rigorous mental exercise that strengthens the intellect. Both are excellent reasons for studying mathematics, but I doubt that either justify the enormous amount of time and weight that we currently give to the subject in our curriculum. Math does reveal the orderliness of God’s creation, but so do many other studies, such as music, art, and science. A rigorous mathematical study does make your mind sharper, but perhaps no less than a rigorous study of Latin or even grammar.
It’s easy to conclude that math is nothing more than a utilitarian part of the curriculum, a necessary skill in a competitive technological age. But we can’t get away from the fact that the quadrivium, a major part of the classical curriculum, was essentially four different branches of mathematics. The ancients studied numbers when there were no SATs to pass and no industrial buildings to maximize.
The ancients studied math because it taught them to think about ideas. The Greek philosophers made explosive breakthroughs in philosophy because they learned to think in abstractions, and mathematics was the road that took them there. The Greeks wanted to move away from the temporal and get to the spiritual world where ideas were more real than material objects. David Hicks explains: “Mathematics, then, was meant to be a vehicle….carrying man from the lowest level-of-being toward the highest.”
For Plato, mathematics bridged the material world to the spiritual world of ideas. He said, “The knowledge at which geometry aims is knowledge of the eternal, and not of anything perishing and transient. Geometry will draw the soul towards truth, and create the spirit of philosophy.” Plato believed that a mind not weaned on mathematics was not capable of contemplating the important ideas of philosophy, which is why the sign at the gate of his famed Academy read: “Let none ignorant of geometry enter here.” In the Middle Ages, the Quadrivium had to be mastered before one could presume to study theology. Imagine if the first book on the required reading list of seminary was not Calvin’s Institutes, but Euclid’s Elements (Calvin certainly read it).
In Mathematics for the Liberal Arts, Morris Kline says that “mathematics is in fact ideally suited to prepare the mind for higher forms of thought” and that math “purifies the mind by drawing it away from the contemplation of the sensible and perishable and leading it to the eternal ideas.”
The goal of teaching mathematics, then, is to lead our students to truth. We want our students to see, know, and love the truth, and teaching math is precisely the way to take them there! That doesn’t mean that we can’t appreciate math’s astounding practical uses or rejoice in high test scores. As C.S. Lewis says, “Aim for heaven and you will get earth thrown in. Aim for earth and you get neither.” The modern world ignores, and even denies that transient world of eternal ideas, but if we want our students to engage in real thought and contemplate eternal ideas, we will begin learning how to teach mathematics, not in a utilitarian way, but in a way that will lead them to the truth.