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.

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.

Florence Nightingale died a hundred years ago, in August 1910. She survives in our imaginations as an inspired nurse, who cared passionately for injured and dying soldiers during the Crimean war, and then radically reformed professional nursing as a result of the horrors she witnessed. But the "lady with the lamp" was also a pioneering and passionate statistician. She understood the influential role of statistics and used them to support her convictions. So to commemorate her on the centenary of her death, we'll have a look at her life and work as a statistician.

When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.

Mr and Mrs Magnus are a happy gnome couple. Unfortunately, foreseeing that they will be unable to keep up with their rising mortgage repayments, they've been forced to move into my back garden, where they've acquired a plot to build a house on. Gnome by-laws state that the total number of bricks used in any construction project must be 177 or planning permission will not be granted. How can they manage to stick to the rules?