Helen Joyce

Suppose you walk past a barber's shop one day, and see a sign that says "Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else." This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.

Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!

Suppose you have an infinitely large sheet of paper (mathematicians refer to this hypothetical object as the plane). You also have a number of different colours - pots of paint, perhaps. Your aim is to colour every point on the plane using the colours available. That is, each point must be assigned one colour.

Chomp is a simple two-dimensional game, played as follows. Cookies are set out on a rectangular grid. The bottom left cookie is poisoned. Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.

Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.

Scientists at the NEC Research Institute in Princeton have carried out an experiment in which a pulse of light appeared to emerge from a cloud of gas before it even entered.