The great advances in science usually result from new tools rather than from new doctrines.

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.

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.

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.

Nothing is boring if you look at carefully.

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.