Thanks to the discoveries of astronomers in the twentieth century, we now know that the heat death is a myth. The heat death can never happen, and there is no paradox.

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.

There is no way to find the best design except to try out as many designs as possible and discard the failures.

I think that the artificial-intelligence people are making a lot of noise recently, claiming that artificial intelligence is making huge progress and we're going to be outstripped by the machines. But, in my view, this whole field is based on a misconception. I think the brain is analog, whereas the machines are digital. They really are different. So I think that what the machines can do, of course, is wonderful, but it's not the same as what the brain can do.

The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole. A reductionist philosophy, arbitrarily proclaiming that the growth of understanding must go only in one direction, makes no scientific sense. Indeed, dogmatic philosophical beliefs of any kind have no place in science.

The more I examine the universe and study the details of its architecture, the more evidence I find that the universe in some sense must have known that we were coming.

The biggest breakthrough in the next 50 years will be the discovery of extraterrestrial life. We have been searching for it for 50 years and found nothing. That proves life is rarer than we hoped, but does not prove that the universe is lifeless. We are only now developing the tools to make our searches efficient and far-reaching, as optical and radio detection and data processing move forward.