The next advance was due to Newton, the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics. As a physicist, he was of course an ardent adherent of the empirical method, but his greatest title to fame lies in another direction. Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases.[1] But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought just as in the mechanical domain the lever multiplied our physical action. It is this application of mathematics to the solution of physical problems, this combination of two separate fields of investigation, which constitutes the essential characteristic of the Newtonian method. Thus problems of physics were metamorphosed into problems of mathematics. But in Newton’s day the mathematical instrument was still in a very backward state of development. In this field again Newton showed the mark of genius, by inventing the integral calculus. As a result of this remarkable discovery, problems which would have baffled Archimedes were solved with ease. We know that in Newton’s hands this new departure in scientific method led to the discovery of the law of gravitation. But here again the real significance of Newton’s achievement lay not so much in the exact quantitative formulation of the law of attraction, as in his having established the presence of law and order at least in one important realm of nature, namely, in the motions of heavenly bodies. Nature thus exhibited rationality and was not mere blind chaos [Pg xi] and uncertainty. To be sure, Newton’s investigations had been concerned with but a small group of natural phenomena (planetary motions and falling bodies), but it appeared unlikely that this mathematical law and order should turn out to be restricted to certain special phenomena; and the feeling was general that all the physical processes of nature would prove to be unfolding themselves according to rigorous mathematical laws. It would be impossible to exaggerate the importance of Newton’s discoveries and the influence they exerted on the thinkers of the eighteenth century. The proud boast of Archimedes was heard again—“Give me a lever and a resting place, and I will lift the earth.”—But the boast of Newton’s successors was far greater—“Give us a knowledge of the laws of nature, and both future and past will reveal their secrets.”