The big question in cosmology in the early 1960s was did the universe have a beginning? Many scientists were instinctively opposed to the idea, because they felt that a point of creation would be a place where science broke down. One would have to appeal to religion and the hand of God to determine how the universe would start off. This was clearly a fundamental question, and it was just what I needed to complete my PhD thesis. Roger Penrose had shown that once a dying star had contracted to a certain radius, there would inevitably be a singularity, that is a point where space and time came to an end. Surely, I thought, we already knew that nothing could prevent a massive cold star from collapsing under its own gravity until it reached a singularity of infinite density. I realised that similar arguments could be applied to the expansion of the universe. In this case, I could prove there were singularities where space-time had a beginning. A eureka moment came in 1970, a few days after the birth of my daughter, Lucy. While getting into bed one evening, which my disability made a slow process, I realised that I could apply to black holes the casual structure theory I had developed for singularity theorems. If general relativity is correct and the energy density is positive, the surface area of the event horizon--the boundary of a black hole--has the property that it always increases when additional matter or radiation falls into it. Moreover, if two black holes collide and merge to form a single black hole, the area of the event horizon around the resulting black hole is greater than the sum of the areas of the event horizons around the original black holes.