Mathematics is really an art, not a science. You could say science also is an art. So I would say the difference is something you can't really describe - you can only recognize. You hear somebody playing the violin, and it was Fritz Kreisler or it was somebody else, and you can tell the difference. It is so in almost every art. We just don't understand why it is that there are just a few people who are just completely off the scale and the rest of them are just mediocre. And we don't know why. But I say it's certainly true of mathematics.

Technology is a gift of God. After the gift of life it is perhaps the greatest of God's gifts. It is the mother of civilizations, of arts and of sciences.

When the great innovation appears, it will almost certainly be in muddled, incomplete and confusing form. ... For any speculation which does not at first glance look crazy, there is no hope.

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.

I don't know, but I think it's quite possible that the more science you teach kids in school the more it turns them off, so I don't know. I mean you never can tell which way it will go.

The Ph.D. system was designed for a job in academics. And it works really well if you really want to be an academic, and the system actually works quite well. So for people who have the gift and like to go spend their lives as scholars, it's fine. But the trouble is that it's become a kind of a meal ticket - you can't get a job if you don't have a Ph.D.

The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily over time. Also, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily over time.