It's us that's really amazing. As far as I can see, our concentration of different abilities in one species - there's nothing I can see that in this Darwinian evolution that could've done that. So it seems to be a miracle of some sort.

If you go to London now, not everything is beautiful, but it's amazingly better than it was. And the Thames is certainly a lot better: There are fish in the Thames.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too. And that, by some miracle, the language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

There is a great satisfaction in building good tools for other people to use.

I grew up in England at a time when England was winning Nobel Prizes right and left. I mean it was amazing how many Nobel Prizes England was winning in chemistry and physics and biology and all the sciences and at that time the teaching of science in the schools was really lousy.

Almost everything about the universe is astounding. I think the most amazing thing is how gifted we are - we are only monkeys who came down from the trees just recently. We have these amazing gifts of music and mathematics and painting and Olympic running.

To me, mathematics is like playing the violin. Some people can do it - others can't. If you don't have it, then there's no point in pretending.