Herbert Butterfield on History of mathematics

“[T]he whole Newtonian synthesis would never have been achieved—without, first, the analytical geometry of René Descartes and, secondly, the infinitesimal calculus of Newton and Leibnitz. Not only, then, did the science of mathematics make a remarkable development in the seventeenth century, but in dynamics and in physics the sciences give the impression that they were pressing upon the frontiers of the mathematics all the time. Without the achievements of the mathematicians the scientific revolution as we know it, would not have been possible.”

“[T]he intellectual changes of Louis XIV's reign touch the history of science—especially as they represent the extension of the scientific method into other realms of thought. ...we meet the beginnings of the criticism of the French monarchy... acute criticism from... the French intelligentsia who could claim to understand the... state better than the king himself. ...The funeral orations of Fontenelle call attention to an aspect of this movement... [i.e.,] the initial effect of the new scientific movement on political thought. ...The first result ...as Fontenelle makes clear, was the insistence that politics requires the inductive method, the collection of information, the accumulation of concrete data and statistics. ...He describes ...how Vauban... travelled over France, accumulating data, seeing the condition[s]... for himself, studying commerce and the possibilities of commerce... gaining a knowledge of local conditions. Vauban, says Fontenelle, did more than anybody else to call mathematics out of the skies... [he] put statistics to the service of modern political economy and first applied the rational and experimental method in matters of finance. ...Fontenelle tells us that ...Sir William Petty, the author of Political Arithmetic, showed how much of the knowledge requisite for government reduces itself to mathematical calculation.”