To date, what have we done? First we discussed measurement, especially in astronomy; then simple but pervasive topics culled from the history of statics, and finally, great discoveries from the history of dynamics—so many of which hark back to the stars. We have seen something of the role played by mathematics in the development of science; that the aim of physics is to condense its knowledge into mathematical formulae; that, as Galileo so delightfully expressed it, the book of Nature is written in mathematical characters.

Yet this view, although undeniable, is one-sided—or should I say unidirectional? Of course mathematics helps physics. But you must not suppose that help always flows downstream from mathematics to physics; the river of thought is tidal. My object in this chapter is to navigate an incoming tide, to show how help flows also from physics to mathematics.

My lecture-room navigation will not be reproduced here as my upstream voyage is already carefully charted in my Mathematics and Plausible Reasoning, Vol. 1, pp. 142–167, to which the interested mariner is directed.