The climate is not the end of the planet. So the planet is going to be fine - Bill Gates

The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.

Personal computing today is a rich ecosystem encompassing massive PC-based data centers, notebook and Tablet PCs, handheld devices, and smart cell phones. It has expanded from the desktop and the data center to wherever people need it — at their desks, in a meeting, on the road or even in the air.

Sometimes we do get taken by surprise. For example, when the Internet came along, we had it as a fifth or sixth priority. It wasn't like somebody told me about it and I said, "I don't know how to spell that." I said, "Yeah, I've got that on my list, so I'm okay." But there came a point when we realized it was happening faster and was a much deeper phenomenon than had been recognized in our strategy.