In this lecture we shall see how natural philosophy—or what we traditionally call applied mathematics—is continually changing. I hope to show that the subject is far livelier and more adventurous than we sometimes suppose, and that each advance opens ever wider vistas of further progress. We are concerned with the relation between mind and experience of the physical world. Our minds are such as to be most strongly persuaded that there is a significant relationship by their being able to predict experience that no one has ever had before.