Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that proceed them.

Research is industrial prospecting. The oil prospectors use every scientific means to find new paying wells. Oil is found by each one of a number of methods. My own group of men are prospecting in a different field, using every possible scientific means. We believe there are still things left to be discovered. We have only stumbled upon a few barrels of physical laws from the great pool of knowledge. Some day we are going to hit a gusher.