130 SCIENCE AND METHOD. 



it does not tell us which is the road that leads to the 

 desired end. For this it is necessary to see the end 

 from afar, and the faculty which teaches us to see is 

 intuition. Without it, the geometrician would be like 

 a writer well up in grammar but destitute of ideas. 

 Now how is this faculty to develop, if, as soon as it 

 shows itself, it is hounded out and proscribed, if we 

 learn to distrust it before we know what good can be 

 got from it ? 



And here let me insert a parenthesis to insist on 

 the importance of written exercises. Compositions 

 in writing are perhaps not given sufficient prominence 

 in certain examinations. In the tLcole Polytec/migue, for 

 instance, I am told that insistence on such compositions 

 would close the door to very good pupils who know 

 their subject and understand it very well, and yet are 

 incapable of applying it in the smallest degree. I 

 said just above that the word understand has several 

 meanings. Such pupils only understand in the first 

 sense of the word, and we have just seen that this 

 is not sufficient to make either an engineer or a 

 geometrician. Well, since we have to make a choice, 

 I prefer to choose those who understand thoroughly. 



lO. But is not the art of exact reasoning also a 

 precious quality that the teacher of mathematics 

 should cultivate above all else? I am in no danger 

 of forgetting it : we must give it attention, and that 

 from the beginning. I should be distressed to see 

 geometry degenerate into some sort of low-grade 

 tachymctrics, and I do not by any means subscribe 

 to the extreme doctrines of certain German professors. 

 But we have sufficient opportunity of training pupils 



