Infinity is a concept that fascinates everyone from a seven-year-old child to a maths professor. So remarkable and strange is it that contemplating it has driven at least two great mathematicians over the edge into insanity. Where did the concept of infinity come from? Who were the people who originally defined and later refined this paradoxical quantity? Why is infinity, a concept we can never experience or truly grasp, at the heart of science? How can some infinities be bigger than others?