A bizarre set of of 8-dimensional numbers could explain how to handle string-theory's extra dimensions, why elementary particles come in families of three... and maybe even how spacetime emerges in four dimensions.

Space is three-dimensional... or is it? In fact, we are all used to living in a curved, multidimensional universe. And a mathematical argument might just explain how those higher dimensions are hidden from view.

String theory has one very unique consequence that no other theory of physics before has had: it predicts the number of dimensions of space-time. But where are these other dimensions hiding and will we ever observe them?

Learning mathematics involves a progression to higher and higher concepts, building on the foundations of what we have already learnt. But Andrew Irving and Ebrahim Patel explain that no matter how high your mathematical knowledge reaches you must never lose sight of your foundations, no matter how basic they may seem.

Andy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?

In the previous article we introduced Schrödinger's equation and its solution, the wave function, which contains all the information there is to know about a quantum system. Now it's time to see the equation in action, using a very simple physical system as an example. We'll also look at another weird phenomenon called quantum tunneling.