It has been seen that in France prodigious scientific progress was made during the beginning and middle of the seventeenth century. The toleration which marked the reign of Henry IV. and Louis XIII. was accompanied by intense intellectual activity. Extraordinary confidence came to be placed in the power of the human mind. The bold intellectual conquests of Descartes, Fermat, and Pascal enriched mathematics with imperishable treasures. During the early part of the reign of Louis XIV. we behold the sunset splendour of this glorious period. Then followed a night of mental effeminacy. This lack of great scientific thinkers during the reign of Louis XIV. may be due to the simple fact that no great minds were born; but, according to Buckle, it was due to the paternalism, to the spirit of dependence and subordination, and to the lack of toleration, which marked the policy of Louis XIV.
In the absence of great French thinkers, Louis XIV. surrounded himself by eminent foreigners. Römer from Denmark,
Huygens from Holland, Dominic Cassini from Italy, were the mathematicians and astronomers adorning his court. They were in possession of a brilliant reputation before going to Paris. Simply because they performed scientific work in Paris, that work belongs no more to France than the discoveries of Descartes belong to Holland, or those of Lagrange to Germany, or those of Euler and Poncelet to Russia. We
must look to other countries than France for the great scientific men of the latter part of the seventeenth century.
About the time when Louis XIV. assumed the direction of the French government Charles II. became king of England. At this time England was extending her commerce and navigation, and advancing considerably in material prosperity. A strong intellectual movement took place, which was unwittingly supported by the king. The age of poetry was soon followed by an age of science and philosophy. In two successive centuries England produced Shakespeare and Newton!
Germany still continued in a state of national degradation. The Thirty Years' War had dismembered the empire and brutalised the people. Yet this darkest period of Germany's history produced Leibniz, one of the greatest geniuses of
modern times.
There are certain focal points in history toward which the lines of past progress converge, and from which radiate the advances of the future. Such was the age of Newton and Leibniz in the history of mathematics. During fifty years preceding this era several of the brightest and acutest mathematicians bent the force of their genius in a direction which finally led to the discovery of the infinitesimal calculus by Newton and Leibniz. Cavalieri, Roberval, Fermat, Descartes, Wallis, and others had each contributed to the new geometry. So great was the advance made, and so near was their approach toward the invention of the infinitesimal analysis, that both Lagrange and Laplace pronounced their countryman, Fermat, to be the true inventor of it. The differential