Utility and Futility of Mathematics
by Daniel Lee
Abstract
Usefulness of math rarely comes into question. No educational curriculum is built without it; no scientific discipline is free from its principles and notations. But utility of math is not free from criticisms, and the assertions like “math is a game played with meaningless symbols on paper” maintains silent subscribers. Is math really “useful”? In this essay, I question the “usefulness” of mathematics and conclude that mathematics, at its core, is not “useful” - and that its futility is perfectly okay.
I think my calculus teacher in highschool enjoyed being asked the ominous question, “When will I ever use Calculus in my life?” She would grin lightly, taking pleasure in the opportunity to imbue a significant knowledge onto the dull, unsharpened mind who had mustered enough courage (and ignorance) to ask that infamous question, and gently quip back at him with plethora of reasons why he should care to learn calculus; that calculus, in fact, was employed to predict the trajectory of a football, used to describe the planetary motions, that civil engineers use calculus to build beautiful and durable skyscrapers. All reasons culminates to a single potent argument: that calculus, and more broadly mathematics, is indispensable for scientists and engineers.
No scientifically literate person denies the utility of mathematics in science. Mathematics plays a central role in science: Open any scientific literature and you cannot get very far without encountering a mathematical notations or two and no respectable university curriculum is science or engineering discipline is without a calculus sequence. A sensible response and the universal consensus for utility of mathematics is a definite YES.
But I can also certainly sense an equally strong and wildly contradictory motion against the utility of mathematics. For one, I am in constant pressure to justify my studying mathematics in college- the immediate reaction when I disclose my major is not of approval but of amusement or puzzlement. Another- generally, mathematics is appreciated by only when its application is revealed. All those abstract theorems that require an ideal agent who can draw perfectly straight line on an infinitely long blackboard infinitely many times is less appreciated. Very few people tries understands the abstruse mathematical concepts. Even less does it with joy.
Why the discrepancy?
I think that child who had dared to question the usefulness of mathematics has only gotten a partially satisfactory answer.. The question itself has a sacrilegious tone. It cries heresy: “HOW DARE YOU, BENEFICIARY OF ALL THE MODERN SCIENTIFIC ADVANCES, ASK THAT QUESTION?” I think that child has simply learned to keep his mouth shut. Enough people had commented on his ignorance, he had seen few examples of math being useful, and accepted the usefulness of math as a fact.
And that child is still within me, and I think within many others as well. Even my math professor, upon showing us the proof that the identity element of addition, 0, is less than the identity element of multiplication, 1, joking remarked, “Don’t forget to call your parents tonight; tell them how you learned 1>0 in school today and that their tuition money is being very well spent.” And maybe, that child is not wrong at all. Maybe, mathematics is not that useful.
