Occasionally, people tell me that calculus was when they really gave up on math. It’s a pity, because for me calculus was the first time math really started to become fun. After all, it’s when math introduces the Pokemon.

What Pokemon? Why, the special functions of course.

By special functions I mean things like $\sin x$, $\cos x$, $e^x$, and $\ln x$. Like Pokemon, these guys come in a bewildering variety. And in calculus, you learn that they, like Pokemon, can evolve.

$x$ integrates into $\frac{1}{2}x^2$!

$\frac{1}{x}$ integrates into $\ln x$!

$\sin x$ integrates into $-\cos x$, and $\cos x$ integrates into…$\sin x$.

Ok, the analogy isn’t perfect. Pokemon don’t evolve back into themselves. But the same things that make Pokemon so appealing are precisely why calculus was such a breath of fresh air. Suddenly, there was a grand diversity of new things, and those new things were related.

College gave me new Pokemon, in the form of the Bessel functions. Nowadays, I work with a group of functions called Polylogarithms, and they’re even more like Pokemon. Logarithms are like the baby Pokemon of the Polylogarithms, integrating into Dilogarithms. Dilogarithms integrate into Trilogarithms, and so on.

Polylogarithms, in turn, evolve into Poliwrath.

To this day, the talks I enjoy the most are those that show me new special functions, or new relations between old ones. If a talk shows me a new use of multiple zeta values, or new types of Polylogarithm, it’s not just teaching me new physics or mathematics: it’s expanding my Pokemon collection.

## 3 thoughts on “Calculus Is About Pokemon”

1. Wyrd Smythe

When I took (and loved) calc back in the late 80s, what really lit it up for me was writing little computer programs to graph the equations in my homework. Being able to see how derivative functions worked was a major “ah ha!”

I never had the chance to use much calc and have forgotten a lot of it, but the old saw about “I never using trig!” turned out to be false in my case. I’ve always been interested in image generation and electronics — both of which fields use a lot of trig (or at least sin, cos, and tan, functions).

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2. Vicki

When I took calculus back in the mid ’70s, what I loved was the way in which it used everything I had learned in math up to that point – suddenly all of those years made sense. It was all preparation for this class! And calculus provided new ways of understanding motion and dimensions, along with inter-relationships between terms that had previously not appeared to have any useful relationship to one another. What’s not to love?

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3. ohwilleke

At first blush, I wasn’t impressed with the Calculus is like Pokemon concept (in part, because I don’t know much about Pokemon). But, after reading your post, I think there is a lot of merit to it.

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