In science, as in other activities, there is a continuum of degrees of creativity, ranging from the solving of small problems to making major discoveries or conceptual breakthroughs which change the underpinnings of a field—such as three of the major developments in twentieth-century physics: special relativity, general relativity, and quantum mechanics. Each of these made striking changes to our view of the world.

A common aspect of all creativity is to give us some sense and meaning of the various observations, impressions, and emotions that fill our lives. For example, in a letter to his brother Theo, Vincent van Gogh wrote: "I see that nature has told me something, has spoken to me, and that I have put it down in shorthand . . . and it is not the tame or conventional language derived from a studied manner or system rather than from nature itself."

In physics we have a similar objective. We want to understand the various phenomena that we observe in the physical world. We try to find the fundamental principles that explain and relate these phenomena. We want to describe the world in a succinct and beautiful way—very much like a poet. Like a haiku, a set of equations describes and relates a complex assortment of phenomena with a great economy of symbols. Maxwell's equations, published in 1864, are a marvelous example of this. Four short related equations describe all of the manifestations of electricity and magnetism, at the macroscopic scale, in all conceivable situations. It is a great triumph.

There are similar satisfactions experienced by the scientist and artist in the creative process. As Arthur Koestler points out in The Act of Creation, the marvelous clarity that enraptures a scientist when he or she discovers a law is shared by a poet when the words of a poem fall into a pattern that seems to fit exactly—or when a felicitous image unfolds in the mind of the artist to express the inexpressible. He views the sense of oceanic wonder as the emotive aspect of both art and science. It is the most sublime expression of self-transcending emotion—an emotion that is the root of the scientist's quest for ultimate causes and the artist's quest for the ultimate realities of experience. Koestler asserts that intellectual illumination and the emotional catharsis that accompanies it form the essence of the aesthetic experience.

In physics, the description of nature must be limited to general concepts, and the language used is mathematics. Each physicist who reads the equations will understand them in the same way. Thus, scientific descriptions have a universal character. The laws of nature hold throughout the cosmos, and their articulation transcends personal and cultural boundaries.

What about art? An artist's interpretation of the world is always an individual interpretation. Van Gogh implies this in the previously cited quote, in which he speaks of his shorthand that "is not the tame or conventional language derived from a studied manner or system." However, a work of art must also have some universal aspect to make a connection with different individuals, enabling the artist to speak to them in some way. But even so, the viewer of a work of art may see it in a totally different way from the artist who created it. This reinterpretation makes the work of art accessible to the viewer and validates it in a personal way. Jacob Bronowski makes the same point in contrasting Pythagoras and Homer:

Pythagoras is deliberately trying to mean the same thing to everybody who listens to him, and Homer is not. Homer is content to say something universal—and yet mean different things to everybody who listens to him. A poem, unlike the theorem of Pythagoras, is not meant to make up your mind for you.

Another difference between art and science is that in art the manner of expression and content cannot be separated. In scientific creativity, these are separable. Only content is important scientifically; and although an insight into a law of nature can produce feelings and emotions, such as the joy of insight and a sense of awe, they are not part of the message.

What elements are necessary for creativity? I believe creativity requires a powerful imagination and a strong intuition. Imagination is always an experimental process. It is the ability to manipulate images and symbols in the mind to make combinations that are totally new. Reasoning is constructed with moveable images, just as poetry is. Very often analogies are the threshold to creativity. Creativity often results from combining images or ideas that appear to be quite dissimilar. Since the number of possible combinations of images in the imagination is exceedingly large, there must be some constraints that help select those which seem most promising.

One of the elements that help select possibilities for the imagination is intuition. I believe intuition consists of imprints of experience, knowledge, relationships, and taste just below our threshold of consciousness. The reason I think intuition exists in the unconscious is because, in general, we cannot justify it. The fact that a good deal of processing goes on below our conscious activity is suggested by a number of cases in the scientific literature of discoveries or crucial insights that appeared to occur spontaneously or took place in dreams.

The great mathematician Karl Frederick Gauss described in a letter to a friend how he finally proved a theorem on which he had worked unsuccessfully for four years. He wrote, "As a sudden flash of light, the enigma was solved. . . . For my part I am unable to name the nature of the thread which connected what I previously knew with that which made my success possible." Similarly, George Polya, a twentieth-century mathematician, remarked: "When you have satisfied yourself that the theorem is true, you start proving it." There are a number of other similar examples in the literature.

With regard to discoveries made in dreams, there is the case of Frederick August von Kekule, a professor of chemistry who, one afternoon in 1865, fell asleep and had a dream that revolutionized organic chemistry. He dreamed of the benzene molecule as a snake biting its tail while in a whirling motion. From that vision his concept of the six-carbon benzene ring was born, which in turn led to the idea of a closed structure for certain organic molecules. In another example, Otto Loewi had a dream that led to his discovery in 1920 of the chemical transmission of nerve impulses.

While the use of imagination is an exploratory process, a sometimes overriding constraint to flights of the imagination is knowledge or logic in the conscious mind—including principles that are considered too important to be violated. But these constraints should not be too strong. Very often they arise from the intellectual orthodoxy of the time. Still, there are some constraints which must be there because they embody extensive, well-established experimental evidence, such as the conservation of energy. But one of the most important constraints is aesthetics. There is an implicit assumption that the laws of nature are elegant and beautiful. If there is a choice between two theories—one ugly and one beautiful—the beautiful theory wins out.

In 1957, I attended a conference at which Murray Gell-Mann was describing a new theory of the weak interactions, one that he had just developed with Richard Feynman, to explain some recent astonishing experimental results. However, there were three experiments in the literature that contradicted this new theory. Gell-Mann boldly asserted that these three experiments must be faulty, because his new theory was too beautiful to be wrong. And future experiments decisively proved that Gell-Mann was correct.

Dirac, the father of relativistic quantum mechanics, clearly stated the importance of beauty in discovering the laws of nature. He remarked "I think . . . it is more important to have beauty in one's equations than to have them fit experiments." He went on to explain that some discrepancies with experiment may be due to minor features that are not properly taken into account in a theory and which will be cleared up with further developments. As previously noted, these discrepancies can also be due to faulty experiments. A similar point of view exists in mathematics. In his classic book, A Mathematician's Apology, G.H. Hardy wrote "Beauty is the first test; there is no permanent place in the world for ugly mathematics."

Thus, in the creative process in science, beauty can be the compass to finding one's way. In the turmoil of the creative process, the scientist is in no better position than is the artist, because at the scientific frontier, truth is as uncertain and subjective a guide as beauty.

But what is beauty in this context? Defining beauty in physics and mathematics presents difficulties as daunting as those in defining beauty in the arts. However, since I have already shown my audacity in discussing creativity, I will briefly discuss this issue and make an attempt to suggest some characteristics.

Numerous scientists and philosophers have wrestled with this question. From the writings of Werner Heisenberg, Jacob Bronowski, S. Chandrasekhar, and others, I would list three criteria that I find compelling for beauty in physics:

1. A beautiful theory has an unexpected simplicity;
2. Every part of the theory fits in harmoniously (it has no ad hoc elements);
3. It has strangeness to a degree that excites wonderment and surprise.

Still, in the long run, a theory—no matter how beautiful or self-consistent—must provide predictions that conform to nature, or it will be discarded. Are there any such restrictions in art? In the theory of aesthetics there has been a good deal of discussion about what role truth plays in the validity of art. In this context, truth certainly has a different meaning than in the sciences. However, it seems to me that a work of art must have a certain compatibility with the experiences and culture of the observer to produce what Arthur Koestler calls a re-creative echo: the work is validated by providing a confirmation of certain inner truths, but also by moving the observer beyond them.

Let me sum up by stating that creativity in science combines rationality and non-rational processes, recklessness and constraint, and imagination reigned in—but not too tightly. I think the same description would aptly apply to the arts and humanities.