I recently came across this diagram by Peter Salamon, a US mathematician. He calls it his map of maths. Here it is:
I like it because it’s a mathematician admitting to getting stuck – and it expresses so well what goes on when you’re doing maths. You’re endlessly trying to push that white line over, so that you can have more orange and less blue, more of the universe that’s obvious and less that’s utterly incomprehensible.
That’s true if you can count, and are struggling with fractions… or if you get fractions, but really don’t see what this x thing is all about… or if you’re a world-class mathematician trying to break through the frontier of human knowledge.
So when you’re struggling to figure out whatever you find hard in maths, and trying lots of methods (doodling, waiting for an idea, asking friends, ranting and raving, reading again how to do it) you can remember that famous mathematicians through history have felt just as you do, and that the real thing about getting somewhere with maths isn’t getting it right first time – it’s learning to break through those barriers, learning to move that white line just a little further towards the blue.