III. 



MATHEMATICAL DISCOVERY. 



The genesis of mathematical discovery is a problem 

 which must inspire the psychologist with the keenest 

 interest. For this is the process in which the human 

 mind seems to borrow least from the exterior world, 

 in which it acts, or appears to act, only by itself and 

 on itself, so that by studying the process of geometric 

 thought we may hope to arrive at what is most 

 essential in the human mind. 



This has long been understood, and a few months 

 ago a review called V Enseigneinent MatJieuiatiqiie, 

 edited by MM. Laisant and Fehr, instituted an en- 

 quiry into the habits of mind and methods of work 

 of different mathematicians. I had outlined the 

 principal features of this article when the results of 

 the enquiry were published, so that I have hardly been 

 able to make any use of them, and I will content 

 myself with saying that the majority of the evidence 

 confirms my conclusions. I do not say there is 

 unanimity, for on an appeal to universal suffrage we 

 cannot hope to obtain unanimity. 



One first fact must astonish us, or rather would 

 astonish us if we were not too much accustomed to 

 it. How docs it happen that there arc people who 



