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The human brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost" — the sum of the length of all the connections — because communication over distance takes a lot of energy. It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.

It is thought that the next great advances in biology and medicine will be discovered with mathematics. As biology stands on the brink of becoming a theoretical science, Thomas Fink asks if there is more to this collaboration than maths acting as biology's newest microscope. Will theoretical biology lead to new and exciting maths, just as theoretical physics did in the last two centuries? And is there a mathematically elegant story behind life?

A new mathematical analysis of team tactics predicts a Spanish win in Sunday's FIFA World Cup final and also sheds some light on why England were trashed by Germany.

Road colouring problem solved

Graph theory helps answer Sudoku questions

Why do the rich and popular get richer and more popular?

A computer program that can learn languages

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.

We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.