Our aim has been to illustrate the power and elegance of mathematical reasoning in science with some examples ranging from the work of Archimedes to that of Einstein. We started with problems of the lever, the mirror, went on to the growth of populations and ended up with problems of space travel and atomic energy. The early chapters dealt with subject matter of common experience for which we all have a feeling. We all have carried ladders; we all have the comforting assurance of bone borne intuition. In contrast, the latter chapters dealt with subjects beyond our everyday experience, such as intergalactic travel at nearly the speed of light. Here our intuition has to be brain borne; and therein lies the real difficulty—and novelty—of our later chapters. As science and engineering move into “unaccustomed magnitudes”, that is, into the subatomic world of the very small and into the world of galaxies of the very large, our intuition fails and our only guide is that sixth sense, mathematics.

Many illustrations in this book dealt with questions of 20th Century science; yet the only mathematics we have used is algebra and calculus. Is it not surprising that calculus, developed nearly three centuries ago, has the power to deal with subjects so modem? The philosopher Philipp Frank has compared the relation between mathematics and science to that between the sewing machine and the fashion industry: Fashions change fast, but the sewing machine serves them all.