Mathematics as of 1700

At the opening of the seventeenth century Galileo still found it necessary to argue with the past. By the end of the century, mathematics had undergone such extensive and radical changes that no one could fail to recognize the arrival of a new era. The European mathematicians produced far more between about 1550 and 1700 than the Greeks had in roughly ten centuries. This is readily explained by the fact that, whereas mathematics in Greece was pursued by only a handful of men, in Europe the spread of education, though by no means universal, promoted the development of mathematicians in England, France, Germany, Holland, and Italy. The invention of printing gave wide access not only to the Greek works but to the results of the Europeans themselves, which, now readily available, served to stimulate new thoughts. But the genius of the century is not evidenced solely by the expansion of activity. The variety of new fields opened up in this brief period is impressive. The rise of algebra as a science (because the use of literal coefficients permitted a measure of proof) as well as the vast expansion of its methods and theory, the beginnings of projective geometry and the theory of probability, analytic geometry, the function concept, and above all the calculus were major innovations, each destined to dwarf the one extensive accomplishment of the Greeks-Euclidean geometry.

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