THE VALUE OF SCIENCE 175 



THE VALUE OF SCIENCE 



By m. h. poincare 



MEMBER OF THE INSTITUTE OF FRANCE 



Chapter V. Analysis and Physics 



~V7~ IT have doubtless often been asked of what good are mathematics 

 -"- and whether these delicate constructions entirely mind-made 

 are not artificial and born of our caprice. 



Among those who put this question I should make a distinction; 

 practical people ask of us only the means of money-making. These 

 merit no reply; rather would it be proper to ask of them what is the 

 good of accumulating so much wealth and whether, to get time to 

 acquire it, art and science are to be neglected, which alone should 

 make us capable of enjoying it, ' and for life's sake to sacrifice all reasons 

 for living/ 



Besides, a science made solely in view of applications is impossible ; 

 truths are fecund only if bound together. If we devote ourselves solely 

 to those truths whence we expect an immediate result, the intermediary 

 links are wanting and there will no longer be a chain. 



The men most disdainful of theory get from it, without suspecting 

 it, their daily bread; deprived of this food, progress would quickly 

 cease, and we should soon congeal into the immobility of China. 



But enough of uncompromising practicians ! Besides these, there 

 are those who are only interested in nature and who ask us if we can 

 enable them to know it better. 



To answer these, we have only to show them the two monuments 

 already rough-hewn, Celestial Mechanics and Mathematical Physics. 



They would doubtless concede that these structures are well worth 

 the trouble they have cost us. But this is not enough. Mathematics 

 have a triple aim. They must furnish an instrument for the study of 

 nature. But that is not all : they have a philosophic aim and, I dare 

 maintain, an esthetic aim. They must aid the philosopher to fathom 

 the notions of number, of space, of time. And above all their adepts 

 find therein delights analogous to those given by painting and music. 

 They admire the delicate harmony of numbers and forms ; they marvel 

 when a new discovery opens to them an unexpected perspective; and 

 has not the joy they thus feel the esthetic character, even though the 

 senses take no part therein? Only a privileged few are called to enjoy 

 it fully, it is true, but is not this the case for all the noblest arts ? 



