Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? This article explores modern visualisation techniques and finds that the right picture really can be worth a thousand words.

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.

What do butterflies, ketchup, microcellular structures, and plastics have in common? It's a curious minimal surface called the gyroid.

Paraconsistent mathematics is a type of mathematics in which contradictions may be true. In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean?