Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem.

Remember how hard it was to fold maps? Mathematicians have struggled with map folding problems for ages but a recent insight suggests there might be another way to approach them, making an unlikely connection between combinatorics, origami and engineering.

Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.