Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.

Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.

Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.

Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.

Knots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?

A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.