Earlier today, I sat down with a student who had just begun calculus. She was desperate to get ahead of the next unit, which was the limit definition of derivatives. So we walked through the mechanics, but I warned her that the primary function of this unit was theoretical. She needed to understand what we were trying to accomplish with derivatives much more than she needed to know how to find derivatives using the limit definition. At one point, she asked the age-old question that so many math students have asked me: why do I even need to know this?
I love it when they ask this.
It’s one part existential scream and one part defiant challenge. It expresses a frustration succinctly, but it also throws the operation back in the face of the teacher, demanding something from the teacher, an answer, an explanation, a justification. They’re never ready for what I say next.
You don’t need to know this. We do not teach you math because you need to know how to do operations, how to manipulate algebra. You’ll never save a baby, dangling precariously from a tree branch, from being eaten by a bear simply because you remember trigonometry. You can ask your phone or Wolfram Alpha to do most math for you – and often it’s prone to fewer errors. There will never be a moment in your adult life when calculating the distance between two points on the coordinate grid will amount to more than a party trick. You do not need to know math.
But that isn’t why we’re teaching you math. We teach math because it is a highly organized, complex system. And I don’t care what you do in your life – whether you want to be the president, a plumber, or a porn star – you’re destined to find a place in your life where you MUST learn how to operate within a highly organized, complex system.
I’m a lawyer, and I recall – fondly – the day when Professor Sally Goldfarb told our 1L class that we were going to have to calculate some damages as a part of the day’s lecture. Lawyers are notoriously anti-math. Had they been good at math, they might have ended up elsewhere. The day’s work amounted to little more than adding and subtracting, occasionally multiplying by three for trebel damages. Everyone survived, but not without a significant amount of angst. What those law students failed to see, failed to internalize, during the many years that they were made to study math was NOT the proper application of simple operations but the direct connection between their pursuit of the law and math.
Lawyers are a classic case: an arcane system with millions of rules, some of which are entirely counterintuitive and others so opaque you’d need Black’s Law Dictionary or Wolfram Alpha to apply them correctly. The ability to learn those rules did not come from AP Gov. The ability to manage a complex set of rules came from years of remembering the Pythagorean Theorem, from dozens of tests with hundreds of tricky questions that demanded that we produce some magic formula or concept – or else we wouldn’t be able to proceed.
Math does not need to be useful to be important. Ask any tax attorney how useful knowing the Tax Code is to their general enjoyment of life. They’ll look at you like you’re a crazy person. Knowing the Tax Code is only useful insofar as a client may ask them a question about the Tax Code and it would be prudent to be able to answer them. Math does not need to be fun to be important. Ask those same attorneys how fascinated they are by the Tax Code.
Math is, to me, beautiful because of its underlying purpose: no matter what you want to do, you must be prepared to learn and apply a complex set of rules and learning math will help you do that. In this day and age, where it feels like the rules don’t exist and – if they do – they’re stacked against us, it is incredibly comforting to know that math – whether we want it to or not – creeps along aside us, reinforcing whatever it is we need to learn.