Humans struggle at a lot of intellectual endeavours. But for some reason, of all of them, maths seems to have an unreasonable level of arcane-ness (arcanity?). People who haven't spent much time thinking about maths are not only unable to appreciate mathematical arguments, but seem to be unwilling to. The same isn't true of other disciplines.
Why is this?
Here's a metaphor: Imagine that the only person who was able to hear a piece of music is the person playing it. So someone is playing a piece of music on the piano. You're watching, and you can only watch their hands move over the keys. If you're observant you may start to get an idea of which keys they press at the same time, and which ones tend to follow each other.
But then they give you the score, and you sit down at the piano and start to play through it yourself. Now you can hear it, and you begin to understand how it fits together and what makes it beautiful.
That's what maths seems to be like. You can't understand or appreciate the complexity or beauty of a piece of maths unless you're creating it yourself. And you can't create it yourself without having learnt a bit about it. And you probably won't want to learn anything about it until you've had a small experience of hearing it.
Why is this?
Here's a metaphor: Imagine that the only person who was able to hear a piece of music is the person playing it. So someone is playing a piece of music on the piano. You're watching, and you can only watch their hands move over the keys. If you're observant you may start to get an idea of which keys they press at the same time, and which ones tend to follow each other.
But then they give you the score, and you sit down at the piano and start to play through it yourself. Now you can hear it, and you begin to understand how it fits together and what makes it beautiful.
That's what maths seems to be like. You can't understand or appreciate the complexity or beauty of a piece of maths unless you're creating it yourself. And you can't create it yourself without having learnt a bit about it. And you probably won't want to learn anything about it until you've had a small experience of hearing it.
