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By Thomas HulseIn the McConnell Center, with political science to your left and to your right, you stand out when you say that your major is physics, and I have yet to hear a single positive thing said in response to that. Invariably, I’m given some sound of disgust followed by something about how they hated physics and pity me for going through it. And if that’s a poor reception, then the mathematics minor triggers a memory even more tragic for them to recollect. On the receiving side of this, I find it unencouraging to ceaselessly hear my passions dragged through the dirt every time it’s mentioned.
And so, perhaps mathematics is in need of a defense:
The knowledge of which geometry aims is the knowledge of the eternal. – Plato
For all the time spent on the ponderings of the ancient Greeks, one preoccupation of theirs seems to pass under our modern radar: mathematics. Curious to us today, every classical philosopher was a classical mathematician too: Thales, Pythagoras, Aristotle, Archimedes. But to the Greeks, the study of the true nature of the world was equivalent to the study of mathematics, particularly geometry. Nowhere is this more explicit than in a reading of Plato’s Republic where he writes that mathematics is essential to the philosophical mind, opening it to abstract thinking about the forms themselves rather than about their physical manifestations. Deeper truth is found through the application of pure reason, casting away reliance on sensory stimuli. These beliefs have been lost almost entirely since then. Consider Euclid’s Elements, the world’s most successful textbook for more than two millennia, where Euclid proved all of classical geometry in a fantastical show of human brilliance. Newton is said to have only laughed at two things in his life, the first being when asked why one should study Euclid. Yet, what was once a rite of passage for the learned has been largely wiped from public memory.
The pure mathematician, like the musician, is a free creator of his world of ordered beauty. – Bertrand Russell
Mathematics is an art; it is the art of human reason. In the same way that painting is the art of human vision; that music is the art of human hearing; that drama is the art of human emotion; mathematics is the unadulterated art of human reasoning. The unanticipated corollary that the universe we live in is a mathematical one is of little consequence to this effect. Through the power of our minds, we can discover statements that are true in a world not quite like the one we live in. We can think about the infinite, though no infinity exists; and we can create imaginary numbers, though nowhere in nature are these found. Is this an expression of imagination any less than Shakespeare? The art form is a constrained one but does it lack any more creativity than painting does, constrained to its canvas? Mathematics is not a subject in which to be trapped; it is a field in which to run free with imagination.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
– David Hilbert
And just like an art, mathematics is accessible to the minds of all. Mathematics is as ubiquitous as music, and even purer than it because it is pervasive for all humanity rather than any one culture. Anyone who holds the power of reason—which is us all—can hold the pleasure of the beauty of mathematics. There is nothing particularly special about mathematicians that give them specialized delight to the richness of their study, other than being exposed in the right way to that medium. The hatred for mathematics comes from multiplication-times tables, from memorizing the quadratic formula, and from the repetitive mundane of algebra homework. Rote memorization is useful, but they do not capture the beauty of mathematics which all of us can understand in our mind, but which for the most part lies hidden. These exercises do not awaken our reason in the way mathematics should, by thinking. If one’s reason can be wakened, then beauty is there for all who care to think.
Have the courage to use your own reason. – Immanuel Kant
Even beyond the age of Athenian democracy, mathematics retained its link to philosophy. Only relatively recently, the term “science” has distinguished itself from what it had always been called: “natural philosophy.” Newton himself never viewed his work as that of science, but as of the philosophy that governs the natural world. It has only been in relatively recent times that mathematics has gained a status as unique from philosophy—in fact, almost something alien to it entirely. Mathematicians today seem to gain very little from delving into metaphysics and ethicists seem to gain very little from learning differential equations. I am willing to accept that and would not foist either upon the other. What I am not willing to accept, however, is that individual persons have very little to gain from mathematics, for I would just as soon accept they have very little to gain from ethics.
If a man’s wit be wandering, let him study the mathematics. – Francis Bacon
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Thomas Hulse is a member of the McConnell Scholar Class of 2023. The Lexington, Ky., native studies physics and political science at the University of Louisville.