One of the most surprising things about mathematics is its many unsolved mysteries. Mathematics is far from "done and dusted", and Steve Humble shows us how we can come up with some mathematical mysteries of our own.
Many things make a noise when you hit them, but not many are commonly used to play music — why is that? Jim Woodhouse looks at harmonic and not so harmonic frequencies and at how percussion instruments are tuned.
Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin.
The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square?
Insurance companies offer protection against rare but catastrophic events like hurricanes or earthquakes. But how do they work out the financial risks associated to these disasters? Shane Latchman investigates.