In the era bounded by Galileo's Dialogo of 1632 and Newton's Principia of 1687, science changed. Observation, even when performed with enough care to be called experimentation, gave way to rigorous mathematical analysis as the primary approach to physical phenomena. Whereas Galileo aimed to instruct laymen about his view of the world order by means of plausible arguments and analogies, only an experienced mathematician could hope to understand the world picture envisioned by the Principia. This mathematization of physics was a defining element of that intellectual upheaval we call the Scientific Revolution, and the requirement, still imposed today, that a theoretical physicist be an able mathematician stems from a tradition that flowered in the seventeenth century.

Such sweeping change cannot be attributed to one particular moment or person. Yet the development of this interrelationship between mathematics and physics has remained too long in the realm of vague generalizations, whose validity has yet to be substantiated by a careful comparison with actual events. A new difficulty arises, however, because the particulars against which any generalization must be tested are not well documented. It is the latter deficiency that this book addresses by focusing on a specific person and event in the development of mathematical physics during the seventeenth century. This is a modest endeavor, designed not to explain the greater phenomenon but to provide a case study that any general account must encompass. The person is Christiaan Huygens; the event is his creation of the theory of evolutes.

Preeminent mathematician, physicist, and astronomer, Christiaan Huygens (1629–95) was one of the major figures of the Scientific Revolution.