Intro to Mathology: 0

One of friends, Mistah Wong (as his kids address him), teaches maths at a high school, and a while back asked me if I wanted to give a guest-lecture/class to the kids. Luckily for his class(es), this didn't wind up happening. But it did make me think a bit about what mathematics is and how I can motivate some of the crazy stuff that maths people do.

So, here's an Intro to Mathology.

I have a tendency to start lectures with either a motivating problem (usually one that you can think about if you decide to tune out to my yapping) or a quote. And here's a quote by a pretty sweet dude:

"The mathematician's patterns, like the painter's or poet's, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: There is no permanent place in the world for ugly mathematics.”

-- G. H. Hardy

At the heart of it, mathematics is all about patterns. After all, one of the first pattern that each of us sees is:
\[
 1,2,3,\ldots
\]
and we're taught that the next number is \(4\) and the one after that is \(5\) and so on. Then, (prolly) at some point after we've learned to talk, we're taught a different way to continue that pattern:
\[
1,2,3,5,8,13,21,34,\ldots
\]
called the Fibonacci sequence. Which you can extend indefinitely by adding up the last two numbers (e.g.:\(5=2+3,\; 8=3+5\)). And you're probably also told that these numbers seem to pop up quite a bit in nature.

And maybe you're like...say whaaaaat?

But whatevs - the point is that there are two different ways that we could have landed at the Fibonacci sequence:
1. pattern-finding: observe what exists in nature and notice this pattern, and
2. pattern-making: make up this weird but funky rule of adding up the previous two digits...pretty much coz you can and it's easy.

Pattern-finding is basically what we do in physicsy-types of maths, and pattern-making is often what we do in recreational types of maths and in artsy-types of maths. And that's pretty much how mathematics works.

Of course, I've just lied to you.

But that's alright, because science is about telling lies - lies that get closer and closer to the Truth.

Let's just take a looking at pattern-finding: what happens is that after you've seen a lot of these patterns happen in nature, you can start to guess where-else you might expect similar patterns: pattern-predicting. On the other hand, sometimes the patterns are pretty complicated, and you'll just have to make do with something simple that looks reasonably close to it:  pattern-matching.

But then you start noticing that certain patterns are pretty similar, and you start wondering about other similar types of patterns - maybe ones that you haven't seen (yet) in nature. And so, starting from being a practical-minded pattern-finder, you've ended up at having a go at (motivated) pattern-making.

And then you start noticing patterns in the patterns, and patterns in the patterns in the patterns...
and all hell breaks loose.

So there you go: maths=stuff to do with patterns. 

Maybe I should do some actual maths next time. =P