120 SCIENCE AND METHOD. 



2. What different tendencies we have here ! Are 

 we to oppose them, or are we to make use of them ? 

 And if we wish to oppose them, which are we to 

 favour? Are we to show those who content them- 

 selves with the pure logic that they have only seen 

 one side of the matter, or must we tell those who are 

 not so easily satisfied that what they demand is not 

 necessary ? 



In other words, should we constrain young people 

 to change the nature of their minds? Such an 

 attempt would be useless ; we do not possess the 

 philosopher's stone that would enable us to transmute 

 the metals entrusted to us one into the other. All 

 that we can do is to work them, accommodating our- 

 selves to their properties. 



Many children are incapable of becoming mathe- 

 maticians who must none the less be taught 

 mathematics ; and mathematicians themselves are 

 not all cast in the same mould. We have only to 

 read their works to distinguish among them two kinds 

 of minds — logicians like Weierstrass, for instance, and 

 intuitionists like Riemann. There is the same 

 difference among our students. Some prefer to treat 

 their problems " by analysis," as they say, others " by 

 geometry." 



It is quite useless to seek to change anything in 

 this, and besides, it would not be desirable. It is 

 well that there should be logicians and that there 

 should be intuitionists. Who would venture to 

 say whether he would prefer that Weierstrass had 

 never written or that there had never been a Rie- 

 mann ? And so we must resign ourselves to the 

 diversity of minds, or rather we must be glad of it. 



