In mathematics, a certain surprising thing happens again and again. Someone poses a simple question, a question so simple that it seems no useful result can come from answering it. And yet it turns out that the answer opens the door to all kinds of interesting developments, and gives great power to the person who understands it.

Calculus is an example of this. Calculus begins with an apparently simple and harmless question, “What is speed and how can we calculate it?” This question arose very naturally round about the year 1600 a.d., when all kinds of moving objects—from planets to pendulums—were being studied. Men were then just starting to study the material world intensively. From that study the modern world has developed, with the knowledge of stars and atoms, of machines and genes, that we have today, for good and for ill. One might have expected the study of speed to have very limited applications—to machinery, to falling objects, to the movements of the heavenly bodies. But it has not been so. Practically every development in science and mathematics, from 1600 to 1900 a.d., was connected with calculus. From this single root, in a most unexpected way, knowledge grew out in all directions. You find calculus applied to the theory of gravitation, heat, light, sound, electricity, magnetism; to the flow of water and the design of airplanes.