Why maths?
Don’t stop reading.
I hope you’re still with me. Whenever most people see the word ‘maths’ appear in anything, they tend to run away, muttering that they “were never any good at maths.” But please, I beseech you, do not run. I’m going to try and show you why maths is great; at the very least, I want you to understand why someone can think maths to be great.
I’m not going to spout off reams of superlatives and pretentious ‘hidden beauty’ claptrap. Maths certainly is beautiful, but that is a view exclusive to mathematicians. Instead, let me demonstrate why at the very least you can find maths to be interesting, by using an example.
We all learned the basic arithmetic operations in school: add, subtract, divide, multiply. We also all learned disguises for multiplication like squaring and cubing. I’m also certain that we all learned some elementary geometry; specifically, the little formulae for areas and circumferences of circles, πr2 and 2πr. This introduced us to that strange number π, approximately 3.14159, the ratio of a circle’s circumference to its diameter.
Now, let’s do a little basic arithmetic. Take the number 1. Square it. Then divide 1 by the reuslt. You get 1, right? Okay, now do it starting with 2; square it, divide 1 by the result. You should get a quarter. To put it simply, we’ve found 1/12 and 1/22. We can keep on going, finding 1/32, 1/42, and so-on, but that’s fairly boring.
Let’s do something bold, and try adding the results together as we go. The first number we worked out was 1, so we’ll start with that. The next one was a quarter, so we do 1 + (1/4), to give 5/4. Next is 1/9, so add that on to 5/4. And so on, and on, and on.
What’s the point of that? Well, it turns out that because each number we add on is getting smaller very fast, the sum we’ve got at each stage increases by smaller and smaller amounts every time. In fact, it increases slow enough such that it will never, ever go above a certain number.
Read that again. The sum we’re making at each stage will never, ever go above a certain threshold, nomatter how many more times we add on numbers. Ever. How do we know this? Because mathematicians have proven it to be true, through a sequence of logical, mathematical, infallible steps.
This begs the question: what is this threshold? Precisely what is the smallest number we can find which the sum will never reach?
This is where it gets interesting.
It turns out that this threshold, first identified by the mathematical giant Leonhard Euler, is π2/6.
That’s π squared, divided by six. Yes, π. The π we all know and love, 3.14159, crops up in something which has absolutely nothing to do with circles.
And that’s why maths is cool.
