The mysteries of 4 dimensions Abstract of talk by Sir Michael Atiyah 3.30PM, Thursday, 24 September, Royal Observatory Edinburgh In recent years there has been a remarkable interchange of new ideas between mathematics and theoretical physics. Perhaps the most spectacular was the discovery of totally new and unexpected facts about geometry in 4 dimensions by Simon Donaldson and its subsequent physical interpretation by Witten.  I will try to explain this story in non-technical terms and put it into a larger context.