Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.

If there's one bit of maths you remember from school it's probably Pythagoras' theorem. But what's a Pythagorean triple? How many triples are there and how do you find them? And what about quadruples, quintuples, sextuples....

In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?

In March 2011 a highly respected psychology journal published a paper claiming to provide evidence for extra-sensory perception (ESP). The claim was based largely on the results of a very common statistical procedure called significance testing. The experiments provide an excellent way into looking at how significance testing works and at what's problematic about it.

When NASA first decided to put a man on the Moon they had a problem: once the Apollo spacecraft was in flight, they would not be able to observe its exact location and neither would they be able to predict it using physics. How could they send astronauts to the Moon if they didn't know where they were? An ingenious mathematician came up with an answer.

String theory predicts there are more than the familiar four dimensions of space-time. But where do those extra dimensions come from? Eva Silverstein is looking for the answer.

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?

London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.