Mathochism: Real math

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Under the compass of Damocles We’ve moved into antiderivatives, which remind me, perversely, of logarithms.

Before I get piled on by indignant mathematicians, let me explain. When we first learned about exponential equations and logarithms, there was a very specific relationship between the two. To put it crudely, you dismantle the exponential, then put it together sort of backwards, and get a logarithm. For someone used to doing things a certain way, it’s a bit mind-bending. I got it eventually, but it took a while.

With an antiderivative, you take a derivative and return it to the original function. Well, almost the original — in most cases, you also add a C, for constant.

I understand how it works, but it really is a lot like learning a dance routine, then having to learn it again with the steps reversed. Yes, there’s a formula, and that makes it better. But my brain is still addled from sinus and other issues from last week. Therefore, my coordination is off, and I found myself lurking at the back of the class, admiring the more adept hoofers as they twirled around the variables with ease.

When we started this week’s lectures, the professor wrapped up chapter 4, focusing on Newton’s Method. As she explained it, she also told us that we were finally getting into “real math.” I was curious about this statement, and thought about a link a kind reader left a few weeks ago that said much the same thing.

I was also a bit dismayed. Did she mean everything I have learned so far is not real? I went home and did some research, and realized she was talking about pure math (she is not a native English speaker, and this was one of those times when things got lost in translation). And apparently people have been discussing the difference between pure math and applied math for millennia. And some of the pure math fans have always been ever-so-slightly snooty about applied math. (Not that this sort of thing doesn’t happen in the humanities. Fiction versus literature, anyone?)

Wanting to be precise (precision has always been a big deal for me, even before I started math again), I asked her after our next class if by real math she meant pure math, as in the sort of math that reaches levels of abstraction that often place it in the same realm as philosophy.

It was like I gave her an early Christmas present. Her face lit up, and she said yes, that was it, and that, as a fan of pure math, she is also interested in philosophy, and enjoys reading philosophy books in her spare time, calling philosophy “very logical”.

Sadly, we couldn’t have a longer discussion on the topic. I would have loved to hear more. I would also have loved to hear her thoughts on the relationship between math and theology, since theology and philosophy so often go hand in hand.

History is full of mathematicians looking for deities in numbers, from Pythagoras, who turned math into a cult, to Blaise Pascal, who all but abandoned a promising math career for religion, to Newton himself, who held views many called heretical.

I can understand the allure of pure math. Whether I could truly understand pure math is another question. Maybe I could, with time, and plenty of practice and support. It’s definitely interesting.

All text copyrighted by A.K. Whitney, and cannot be used without permission.


  • Not all pure mathematicians look down on applied math… I certainly don’t, and my work is about as “pure” as you can get. But it’s always exciting to introduce students to their first bit of pure mathematics, since you don’t really see that until at least your second semester of calculus (and sometimes, not even then.)

    If you ever have the time, you might consider reading a bit about the history of the philosophy of mathematics. I’m actually reading through a book about it right now, and anyone even vaguely interested in ontology would probably find the whole thing fascinating. Here’s a link to the book I’m reading if you want to check it out (it stays away from anything a calculus student might not understand):

  • Heh. I was being cheeky. My pure math-loving prof, like you, seems to appreciate applied math also, calling the formulas “elegant.” All literature lovers don’t look down on fiction, either (though as a writer, I couldn’t get through the “Twilight” books, even on morphine and Percocet).
    Thanks so much for the link! I will put it on my list. I should have time soon, since I am alternating with doses of Tess Gerritsen and Tana French.

  • I have always been intrigued by the idea of “pure math”. Maybe it’s because I also enjoy philosophy, and it’s interesting to think that, once you master so many different mind-twisting proofs and theorems, you can get to other ways to conceptualize reality.

  • I love your reference to the link between math and philosophy. It seems you have to have a different way of thinking when approaching some of the pure math. This is coming from someone on the applied math/engineering side.

  • While everything you’ve said about pure vs. applied math is true (including, I will admit as a pure mathematician, that there is a fair amount of snobbery), I’m not sure that is the only way to interpret the “real mathematics” comment.

    Basic algebra and trigonometry are building blocks of mathematics, but they are not the buildings of mathematics, regardless of whether it is pure or applied. They are absolutely essentially and certainly a part of mathematics, but it’s only when you understand them well that you can start putting them together and building something deep. Both applied and pure mathematics depend essentially on them, but they are tools that are used to describe the more complicated mathematics that is the goal of these.

  • Also, if you want to see true pure math snobbery at it’s finest, you should consider reading G.H. Hardy’s A Mathematician’s Apology. The context to this essay is that Hardy realized that as he aged his career was diminishing and it is partially his sadness at this which motivated the writing.

  • I was thinking of Hardy when I wrote this. And of Plato. But not of you, or Antonia, or any of my lovely pure mathematician readers, I swear!! (;

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