When I was nine years old, I came down with a somewhat rare disease that left me hospitalized for several weeks. (Don’t worry, I’m fine now.) One day, I noticed a sequence of numbers printed on the side of my IV drip:
That’s interesting, I thought. There are two twos and three threes, and five numbers altogether. And two and three add up to five. And if you add the twos together you get four, and the threes added together give you nine, and nine minus four is also five.
I told the nurse, who made a remark to the effect that I was an unusual child.
Maybe I was. But it seemed to me at the time that if there are a bunch of numbers lying around, the natural thing to do is to start playing with them.
Imagine giving a toddler a box of tissues. Without hesitation, she will pull them out one by one, try to stuff them back in, flip the box upside down and attempt to stand on it, or simply wear it like a hat. She does not need to know what tissues are, or what they are for. She just wants to see what they can do.
I believe that it’s a pretty small step from idly toying with physical objects, like tissues, to idly toying with abstract ones, like numbers.
And what makes numbers so fascinating is that although you can’t quite touch them, they still behave according to strict rules. They’re not physical, but they are very real.
Sixteen objects — whether they are paperclips or papayas — can always be arranged into a four-by-four square, because 16 is a square number. But no matter how you try, you can never do it with 17. In fact you can’t even make them into a rectangle, because 17 is prime. And 17 is just as prime in English as it is in Swahili, in base-10 as it is in binary. You can represent the number any way you like, but it’s still the same number.
The rules of language, words and grammar tend to be fuzzy: they can change over space and time. But the rules of numbers are timeless and universal. They may seem arbitrary, and they are. But we don’t create them; they have to be discovered. And while humanity has managed to discover quite a bit about math over the past few centuries, there is always plenty more out there to find.
So yeah, I like math. But when I tell people this, they immediately make two false assumptions about me.
The first is that because I like math, I am good at manipulating numbers in my head, which I am not. I am terrible at making change, I have great difficulty reading analog clocks, and if you ask me to calculate a good tip on a lunch bill of $26.95, I will panic and reach for a calculator.
But weirdly, if you ask the person earning that tip (who knows from experience that it ought to be between $4.00 and $5.50) whether they are good at math, they are likely to tell you that they are not.
This brings me to the second misconception, which my nurse also alluded to: people who like math are unusual, somehow different from the rest of us.
This has both its positive forms (“Wow, you must be really smart”) and its negative ones (“Guh, you’re such a nerd”) but either way, it’s just as false as the idea that loving numbers = being handy with figures.
And sadly, because we all want to be perceived as normal, this misconception leads a lot of people to downplay, brush off, or sabotage their own relationship with math.
For a couple of years in the mid-oughts, I was a high school math teacher. When I told people what I did for a living, they would usually wrinkle their noses, sigh deeply, and begin to describe the personality of the most disagreeable math teacher they had ever had.
This was odd to me. Most people don’t associate all the reading they ever do with their worst English teacher, or all the sports they have ever played with their most brutal Physical Education teacher.
But for whatever reason, many people seem to remember math only as an unavoidably unpleasant thing you are forced to do in a classroom between the ages of 4 and 18, and to retroactively amplify the worst aspects of that experience.
Even the people who had had a steady string of awesome math teachers would distance themselves from the idea that math could ever be viewed as an enjoyable pastime, rather than something you need to slog your way through in order to succeed at school or work. They would go to great lengths to assert that they always avoid doing math if at all possible.
This also seemed odd to me, as math is everywhere. And even if you use a calculator or a computer, it doesn’t mean you aren’t doing math. Rather, it means you are using a handy tool to do more math, more quickly than would be possible if you limited yourself to the confines of your own brain. It’s like saying “Oh, I never travel, I use cars, trains and airplanes instead.”
My math-nifesto, then, can be summed up as follows:
1. Math is not just working out sums or fractions quickly in your head. That is a handy skill, but that’s all it is. If you can do it, great, but you don’t need it to do math, and doing it is not quite the same as doing math.
2. Liking math doesn’t make you smart, or weird, or a nerd. In fact, it says absolutely nothing else about you. Liking math is no different from liking baseball, peanut butter or romantic comedies. It is what it is.
3. It is not unusual to want to play with numbers. Like the toddler with the tissues, it’s completely natural to want to explore the parts of the universe you can manipulate, including non-physical parts. What’s unnatural is pretending that it can never be fun, that it is something to be ashamed of, and that you have to stop doing this once you graduate from school.
You’ll find some version of the above sentiments in the hearts of anyone who loves math, which, if you have read this far, probably includes you. One of the good things about the internet is that it has made it easer than ever before for math-lovers to find each other, and to share the ideas that we find so mind-blowing. (We also live in an era where the rise of technology, social media and big data have demonstrated the money-earning power of being good at math, which has brought about a kind of grudging respect for math-lovers.)
But we’re not quite at universal acceptance yet, and there may be those of you who remain unconvinced that you also love math. If so, I would give you the same advice that I give my fellow math-lovers: don’t stop exploring.
There are plenty of ways to keep discovering new and exciting math without going back to school, and no matter what you have remembered or forgotten, I know you will find something that will surprise or amaze you. Here are some resources:
- Numberphile is aYouTube channel that has kinda changed my life. It’s hard-core math, but it’s not hard to follow, and it regularly introduces me to awesome ideas.
- Through Numberphile, I discovered Matt Parker, a self-described standup mathematician who has written some great books, including Things to Make and Do in the Fourth Dimension. Hannah Fry is also a frequent contributor and has written some great books too.
- Another great way to find new math to appreciate is to randomly google specific numbers. For example, when my grandfather turned 91, I checked to see if there was anything interesting about that number. Turns out it’s a square pyramidal number, as a result of being the sum of six consecutive squares: 91 = 12 + 22 + 32 + 42 + 52 + 62, which is just awesome. It’s also a triangular number, a hexagonal number, and a centred hexagonal number. There are many other kinds of numbers, including perfect numbers, amicable numbers and sociable numbers. Try your age, your house number, or your social insurance number and see what you stumble across.
- As a kid, I watched every single episode of a show called Square One TV, and I still think about some of the things I learned from it. For example, we throw around words like million, billion and trillion all the time. The fact that these words all rhyme masks just how different they are in terms of magnitude. Think about this: a million seconds is about a week and a half, but a billion seconds is nearly 32 years. A trillion seconds ago, woolly mammoths roamed the earth. The next level up is a quadrillion: think about what you might need a number as big as that for . . . there is probably something!
- Prime numbers are famously unpredictable, but did you know that if you take any prime number, square it and subtract one, the result is ALWAYS divisible by 24. (It doesn’t work for 2 and 3 because they are too small, but it works for every other prime number.) The proof of this is not particularly difficult to work out. Maybe you can do it on your own?
- There’s no reason why math has to be base-10. Lots of people think it would be better off with base-12. The Babylonians used base-60, which is why we have 60 seconds in a minute, and 360 degrees in a circle. Base-20 systems developed independently among cultures all over the world, including West Africa, Mesoamerica and the Pacific Northwest Coast of North America. Are there other examples? Which do you think is best? Why?
- Google the Mandelbrot set. You’ll be glad you did.