THE FUTURE OF MATHEMATICS. 27 



cians are to confine ourselves to waiting for orders, 

 and, instead of cultivating our science for our own 

 pleasure, to have no other care but that of accom- 

 modating ourselves to our clients' tastes? If the only 

 object of mathematics is to come to the help of those 

 who make a study of nature, it is to them we must 

 look for the word of command. Is this the correct 

 view of the matter ? Certainly not ; for if we had not 

 cultivated the exact sciences for themselves, we should 

 never have created the mathematical instrument, and 

 when the word of command came from the physicist 

 we should have been found without arms. 



Similarly, physicists do not wait to study a phenom- 

 enon until some pressing need of material life makes 

 it an absolute necessity, and they are quite right. If 

 the scientists of the eighteenth century had dis- 

 regarded electricity, because it appeared to them 

 merely a curiosity having no practical interest, we 

 should not have, in the twentieth century, either 

 telegraphy or electro-chemistry or electro -traction. 

 Physicists forced to select are not guided in their 

 selection solely by utility. What method, then, do 

 they pursue in making a selection between the dif- 

 ferent natural facts? I have explained this in the 

 preceding chapter. The facts that interest them are 

 those that may lead to the discovery of a law, those 

 that have an analogy with many other facts and do 

 not appear to us as isolated, but as closely grouped 

 with others. The isolated fact attracts the attention 

 of all, of the layman as well as the scientist. But 

 what the true scientist alone can .see is the link that 

 unites several facts which have a deep but hidden 

 analogy. The anecdote of Newton's apple is probably 



