tjo SCIENCE AND METHOD. 



be afraid of forgetting one of the elements ; each of 

 them will place itself naturally in the position pre- 

 pared for it, without my having to make any effort 

 of memory. 



It seems to me, then, as I repeat an argument I 

 have learnt, that I could have discovered it. This 

 is often only an illusion ; but even then, even if I am 

 not clever enough to create for myself, I rediscover 

 it myself as I repeat it. 



We can understand that this feeling, this intuition 

 of mathematical order, which enables us to guess 

 hidden harmonies and relations, cannot belong to 

 every one. Some have neither this delicate feeling 

 that is difficult to define, nor a power of memory and 

 attention above the common, and so they are abso- 

 lutely incapable of understanding even the first steps 

 of higher mathematics. This applies to the majority 

 of people. Others have the feeling only in a slight 

 degree, but they are gifted with an uncommon 

 memory and a great capacity for attention. They 

 learn the details one after the other by heart, they 

 can understand mathemathics and sometimes apply 

 them, but they are not in a condition to create. 

 Lastly, others possess the special intuition I have 

 spoken of more or less highly developed, and they 

 can not only understand mathematics, even though 

 their memory is in no way extraordinary, but they 

 can become creators, and seek to make discovery 

 with more or less chance of success, according as their 

 intuition is more or less developed. 



What, in fact, is mathematical discovery? It does 

 not consist in making new combinations with mathe- 

 matical entities that are already known. That can 



