## Articles

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?

**John Conway**believes they are going to want to talk mathematics. He talks to

*Plus*about his

*Life*game, artificial life and what we will have in common with extraterrestrials.

**John Haigh**shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.

**Herbert Huppert**tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.

**Tom Körner**speculates on the historical reasons why computers were invented when they were.

**Paulus Gerdes**takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.

**C. J. Sangwin**shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.