A story from geometry shows how developments in mathematics have fundamentally changed the way we think about the world around us.
We can't visualise it, but we can still think about it! And there are clever ways of glimpsing what it might look like.
In normal life higher dimensions smack of science fiction, but in mathematics they are nothing out of the ordinary.
How will the Universe end? In a big crunch? Or a big freeze? It all depends on its shape...
Keats complained that a mathematical explanation of rainbows robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.
