The courses in Mathematics during a student’s career at the School are especially focused upon training in the liberal arts of mathematics, as well as beginning the student’s deeper understanding of mathematics as a theoretical or philosophical discipline. Mathematics is both an art and a science in this way, for the art of producing proofs, geometric constructions, or arithmetic calculations is learned so that the student can see the truth for its own sake. To learn mathematics as a liberal art and a science requires going beyond a method that focuses solely upon the inculcation of formal rules. Paul Lockhart expresses well what the School’s curriculum aims to avoid, namely,
the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, [which] creates its own culture and its own set of values. Those who have become adept at it derive a great deal of self-esteem from their success. The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions.
from Paul Lockhart, “A Mathematician’s Lament,” available online here.
The order of the School’s mathematics curriculum, while externally very similar to a typical order, must be animated by the “liberal” spirit that Lockhart describes. The ancient Greek mathematicians recognized a distinction between arithmētikē, or the theory of number pursued for its own sake, and logistikē, the art of calculation that is good because it is useful. The true form of mathematics was not for the sake of problem solving, but for the sake of seeing and contemplating mathematical truths. The challenge, then, is to raise student’s minds from mathematics as rote application of rules for solving problems to mathematics as revealing the existence of a whole realm of universal truths, which are worthy of exploration in their own right. Indeed, it is precisely for this reason that mathematics is a prerequisite to higher philosophical studies.
The students will study geometry (in particular, Euclid’s Elements), followed by more advanced geometry (trigonometry, astronomy, and conic sections) alongside the study of astronomy, then one year of algebra, and conclude with a one-year study of Calculus. A cross-curricular aspect of the mathematics courses will be their reference to and coordination with the courses in the natural sciences, especially physics.