When we finally meet the Martians, 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.

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.

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