TENDENCIES IN MATHEMATICAL SCIENCE 335 



employed about the speculative part of geometry, and the cultivation 

 of the specious Algebra I had been taught very young, a good part 

 of that time and industry that I had spent about surveying and forti- 

 fication (of which I remember I once wrote an entire treatise) and 

 other parts of practick mathematicks. 



Mathematicks may help the naturalists, both to frame hypotheses, 

 and to judge of those that are proposed to them, especially such as 

 relate to mathematical subjects in conjunction with others. 



Even in natural science Stephen Hales says in 1727 : 



And since we are assured that the all-wise Creator has observed 

 the most exact proportions, of number, weight and measure, in the 

 make of all things ; the most likely way therefore to get any insight 

 into the nature of these parts of the creation, must in all reason be 

 to number, weigh and measure. And we have much encourage- 

 ment to pursue this method, of searching into the nature of things, 

 from the great success that has attended any attempts of this 

 kind. 



Summing up these tendencies, a recent writer remarks : -. 



In the eighteenth century mathematics was regarded by many 

 scholars as the ideal, the completeness and exactness of whose methods 

 should be arrived at by other less highly developed branches. So 

 Laplace's popularized version of his celestial mechanics met an eager 

 need, and even Voltaire undertook the championship of the Newtonian 

 philosophy. Logic and even ethics were drawn into the mathematical 

 retinue. For Maupertuis the good is a positive quantity, the bad a 

 negative. Joys and griefs make up human life according to the laws 

 of algebraic addition, and it is the business of statesmen to see that the 

 positive balance is as large as possible. The great Buffon adds to his 

 natural history a supplement on moral arithmetic. Mathematics 

 aims at the leadership both in natural science and in human affairs. 



In spite of this perhaps exaggerated predilection in learned 

 and polite society, educational curricula remained weak and 

 conservative. Powerful progressive tendencies growing out of 

 the French Revolution found expression in the founding of the 

 Ecole polytechnique, under the leadership of Monge, which 

 has ever since been an important centre of mathematical activity. 



