"Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination."

"What philosophical conclusions should we draw from the abstract style of the superstring theory? We might conclude, as Sir James Jeans concluded long ago, that the Great Architect of the Universe now begins to appear as a Pure Mathematician, and that if we work hard enough at mathematics we shall be able to read his mind. Or we might conclude that our pursuit of abstractions is leading us far away from those parts of the creation which are most interesting from a human point of view. It is too early yet to come to conclusions."

"Imagine, if you can, four things that have very different sizes. First, the entire universe. Second, the planet Earth. Third, the nucleus of an atom. Fourth, a superstring. The step in size from each of these things to the next is roughly the same... twenty powers of ten...."

"Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry? ...It cannot be answered by a definition."

"Scientifically speaking, a butterfly is at least as mysterious as a superstring. When something ceases to be mysterious it ceases to be of absorbing interest to scientists. Almost all things scientists think and dream about are mysterious."

"There is no easy solution to the conflict between fundamentalist Christian dogma and the facts of biological evolution. I am not saying that the conflict could have been altogether avoided. I am saying only that the conflict was made more bitter and more damaging, both to religion and to science, by the dogmatic and self-righteousness of scientists. What was needed was a little more human charity, a little more willingness to listen rather than to lay down the law, a little more humility. Scientists stand in need of these Christian virtues just as much as preachers do."

"Science is not a monolithic body of doctrine. Science is a culture, constantly growing and changing. The science of today has broken out of the molds of classical nineteenth-century science, just as the paintings of Pablo Picasso and Jackson Pollock broke out of the molds of nineteenth century art. Science has as many competing styles as painting or poetry. The diversity of science also finds a parallel in the diversity of religion."

"An awareness of our smallness may help to redeem us from the arrogance which is the besetting sin of the scientists."

"Science and religion are two human enterprises sharing many features. They share these features also with other enterprises such as art, literature and music. The most salient features of all these enterprises are discipline and diversity. Discipline to submerge the individual fantasy in a greater whole. Diversity to give scope to the infinite variety of human souls and temperaments. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual — these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion."

"A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering."

"The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design."

"A good cause can become bad if we fight for it with means that are indiscriminately murderous. A bad cause can become good if enough people fight for it in a spirit of comradeship and self-sacrifice. In the end it is how you fight, as much as why you fight, that makes your cause good or bad."

"It is characteristic of all deep human problems that they are not to be approached without some humor and some bewilderment."

"If we had a reliable way to label our toys good and bad, it would be easy to regulate technology wisely. But we can rarely see far enough ahead to know which road leads to damnation. Whoever concerns himself with big technology, either to push it forward or to stop it, is gambling in human lives."

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

"... the most important questions and insights and goals are unpredictable."

"The public has a distorted view of science, because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries. (New York Review of Books, 2011)"

"It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex."

"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."

"Thirty-one years ago [1948], Dick Feynman told me about his "sum over histories" version of quantum mechanics. "The electron does anything it likes," he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function." I said to him, "You're crazy." But he wasn't."

"I have felt it myself. The glitter of nuclear weapons. It is irresistible if you come to them as a scientist. To feel it's there in your hands, to release this energy that fuels the stars, to let it do your bidding. To perform these miracles, to lift a million tons of rock into the sky. It is something that gives people an illusion of illimitable power, and it is, in some ways, responsible for all our troubles — this, what you might call technical arrogance, that overcomes people when they see what they can do with their minds."

"As we look out into the Universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must in some sense have known that we were coming."

"The whole point of science is that most of it is uncertain. That's why science is exciting--because we don't know. Science is all about things we don't understand. The public, of course, imagines science is just a set of facts. But it's not. Science is a process of exploring, which is always partial. We explore, and we find out things that we understand. We find out things we thought we understood were wrong. That's how it makes progress. (2014 interview)"