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If I'm flying to China, I can sit and think about a problem. Other scientists have to go to the lab. I'm always thinking about maths, even when I'm doing other things. A lot of the time you're going up blind alleys and it's very frustrating, but then you have a sudden rush of ideas. You can live off that for quite some time.
As a kid, I was growing up in an era of celebration of the Civil War centennial, with a lot of 'Lost Cause' emphasis on the Confederacy. I used to play Civil War soldiers with my brothers as a child, and my older brother always insisted that he got to be Lee, and I got be Grant. I never knew that Grant won until quite some time had passed.