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Kissing the curve
Curves bring great beauty to our world. But how curvy is a curve?
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Problems of gravity
Why (some) physicists want to modify Einstein's general theory of relativity.
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Play to win with Nim
In the game of Nim one player always has a winning strategy — it depends on an unusual way of adding numbers.
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The power of good questions
Asking good questions is an important part of doing maths. But what makes a good question?
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The art gallery problem
Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem.
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Blink and you'll miss it: The free kick in football (part II)
In the first part of this article we let maths set the scene for a free kick. Now we continue the drama, tracing the trajectory of the ball throughout the milliseconds it takes it to reach the goal line.
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Blink and you'll miss it: The free kick in football (part I)
Free kicks will deliver much of the drama in the football world cup this summer. But how should strikers approach them and how does the design on the ball impact on its behaviour in flight? Maths can give us answers...
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Dividing the indivisible
Disputes over property are all too common. It's quite easy to share a cake, but how do you share out indivisible goods, such as houses or cars, without causing resentment? Here are two easy methods.
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Patterns and structures
Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?
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From dancing alone, to dancing together
Many materials around us are oxides – such as rocks, window glass and some of the materials used in your computer. These materials may seem hard and rigid, but mathematics reveals a hidden flexibility that can explain many of their properties.
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Playing billiards on doughnuts
The paths of billiard balls on a table can be long and complicated. To understand them mathematicians use a beautiful trick, turning tables into surfaces.