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Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?

Can we always find order in systems that are disordered? If so, just how large does a system have to be to contain a certain amount of order?

A Gömböc is a strange thing. It wriggles and rolls around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all.

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.