“Euclid alone has looked on Beauty bare.”
This line, written by American poet Edna St. Vincent Millay, expresses a sentiment contrary to what many Hillsdale students may think. The popular belief that mathematics is pure calculation ignores the beauty of logic to which Millay alludes. This logic, critical to our liberal arts education, pervades all of mathematics. Yet misconceptions of mathematics still abound on this campus. How, then, do we view math in relation to the good, the true, and the beautiful?
In actuality, the mathematics department dedicates itself to the pursuit of truth. It does not allow itself to be engrossed and overtaken by symbols, theorems, and proofs, though these are certainly a part of its work. Here, we put aside the calculator to understand the rigor, genius, and clarity of math and its language.
Each mathematics professor not only seeks excellence and mastery within his discipline, but also understands the importance of interdisciplinary thought among his students. Sure, I have talked with my professors about the “practical” things of math — derivatives, integrals, graphs, matrices, proofs — in an earnest attempt to further my knowledge of them.
But the conversations don’t always begin and end with math. Professor of Mathematics David Murphy’s History and Philosophy of Mathematics course explores the intriguing ideas of math and asks thought-provoking Socratic questions, such as “What is quantity?” Through this course, we discover the relationships between math and other disciplines, math and nature, and man and the universe. These relationships belong among the other phenomena we study in the humanities: the relationships between man and his nature, man and other men, and man and God.
Students of math are not thrown into a classroom, lectured to, forced to memorize formulas, and told to regurgitate information on a test. Instead, we explore both the theoretical and computational aspects of mathematics. We learn math for its own sake, yet we understand the usefulness of it in our everyday lives. We need not choose between math’s beauty and utility. We can, and should, have both.
In math, we make arguments. These arguments come in the form of proofs, theses, and conversations with others. When we argue in math, we take great care to adhere to logic strictly, otherwise the argument fails horrendously and loses its worth. No discipline cultivates this logic to the same extent that mathematics does. All disciplines require arguments to discern what is good, true, and beautiful. Math’s strong logic helps students strengthen their argumentative skills elsewhere on campus. For example, logic has aided me in reasoning conclusions from given principles within my politics major. These conclusions cannot simply appear. Well-formulated proofs are necessary to express ideas effectively.
Additionally, math allows us to explore both subjective and objective elements of our world. For example: Geometry poses problems which help us understand our tangible world, yet force us to discern what is true. Euclid proved the Pythagorean theorem in a straightforward, beautiful way. His logic is compelling and allows students to see an example of sublime argumentation. But if we discard his axioms, where does that leave us? We can then try to comprehend parallel lines that intersect and triangles with more than 180 degrees. These ideas, though unintelligible to reality, carry their own logic in the realm of Non-Euclidean geometry. By partaking in this thinking, we develop a richer view of the world around us as we make sense of what is real.
In the broader sense, mathematics facilitates our desire to ponder eternal, unchanging principles while also analyzing, using, and appreciating practical, tangible applications in our world. In fact, mathematics without these applications clouds our view of reality. The English mathematician Alfred North Whitehead warns of studying pure mathematical abstractions in his address “Mathematics and Liberal Education”: “Vague generalities are worse than useless, and if we attempt to embody abstractions in short, precise formulӕ, the pupils will simply learn them by heart as empty sounds.” Hillsdale’s math department rejects a view of mathematics as simply “empty sounds.” Instead, it gives meaning, purpose, and reason to that which we study.
To borrow the words of Petrus Paulus Vergerius, a liberal education is one “which calls forth, trains, and develops those highest gifts of body and of mind which ennoble men.” Hillsdale’s math department relentlessly seeks to develop students’ intellects. Thus, mathematics is an intrinsic element of any genuine liberal arts education. It cultivates our reason and elevates the importance of sound logic.
So, what does mathematics have to do with the good, true, and beautiful? Much more than most people think. Indeed, math strives toward that which is true, applies that which is good, and revels in that which is beautiful.
