338 POPULAR SCIENCE MONTHLY 



THE VALUE OF SCIENCE 



By M. H. POINCARE 



MEMBER OF THE INSTITUTE OF FRANCE 



Chaptee VII. The History of Mathematical Physics 

 The Past and the Future of Physics 

 TT7 HAT is the present state of mathematical physics ? What are 

 » » the problems it is led to set itself ? What is its future ? Is 

 its orientation about to be modified ? 



Ten years hence will the aim and the methods of this science ap- 

 pear to our immediate successors in the same light as to ourselves; 

 or, on the contrary, are we about to witness a profound transforma- 

 tion? Such are the questions we are forced to raise in entering to-day 

 upon our investigation. 



If it is easy to propound them: to answer is difficult. If we felt 

 tempted to risk a prediction, we should easily resist this temptation, 

 by thinking of all the stupidities the most eminent savants of a hun- 

 dred years ago would have uttered, if some one had asked them what 

 the science of the nineteenth century would be. They would have 

 thought themselves bold in their predictions, and after the event, how 

 very timid we should have found them. Do not, therefore, expect of 

 me any prophecy. 



But if, like all prudent physicians, I shun giving a prognosis, yet 

 I can not dispense with a little diagnostic; well, yes, there are indica- 

 tions of a serious crisis, as if we might expect an approaching trans- 

 formation. Still, be not too anxious : we are sure the patient will not 

 die of it, and we may even hope that this crisis will be salutary, for 

 the history of the past seems to guarantee us this. This crisis, in fact, 

 is not the first, and to understand it, it is important to recall those 

 which have preceded. Pardon then a brief historical sketch. 



The Physics of Central Forces 



Mathematical physics, as we know, was born of celestial mechan- 

 ics, which gave birth to it at the end of the eighteenth century, at the 

 moment when it itself attained its complete development. During its 

 first years especially the infant strikingly resembled its mother. 



The astronomic universe is formed of masses, very great, no doubt, 

 but separated by intervals so immense that they appear to us only as 

 material points. These points attract each other inversely as the 



