100 years after the birth of Paul Dirac, mathematicians and physicists gather to celebrate his beautiful work.

Can mathematics help defend against another attack?

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?

If your team scores first in a football match, how likely is it to win? And when is it worth committing a professional foul? John Haigh shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.