THE VALUE OF SCIENCE 437 



THE VALUE OF SCIENCE 



Chapter IX. The Future of Mathematical Physics 



By m. h. poincare 



MEMBER OF THE INSTITUTE OF FRANCE 



The Principles and Experiment. — In the midst of so much ruin, 

 what remains standing? The principle of least action is hitherto 

 intact, and Larmor appears to believe that it will long survive the 

 others; in reality, it is still more vague and more general. 



In presence of this general collapse of the principles, what attitude 

 will mathematical physics take? And first, before too much excite- 

 ment, it is proper to ask if all that is really true. All these deroga- 

 tions to the principles are encountered only among infinitesimals; 

 the microscope is necessary to see the Brownian movement; electrons 

 are very light; radium is very rare, and one never has more than some 

 milligrams of it at a time. And, then, it may be asked whether, besides 

 the infinitesimal seen, there was not another infinitesimal unseen 

 counterpoise to the first. 



So there is an interlocutory question, and, as it seems, only experi- 

 ment can solve it. We shall, therefore, only have to hand over the 

 matter to the experimenters, and, while waiting for them to finally 

 decide the debate, not to preoccupy ourselves with these disquieting 

 problems, and to tranquilly continue our work as if the principles were 

 still uncontested. Certes, we have much to do without leaving the 

 domain where they may be applied in all security; we have enough 

 to employ our activity during this period of doubts. 



The Bole of the Analyst. — And as to these doubts, is it indeed true 

 that we can do nothing to disembarrass science of them? It must 

 indeed be said, it is not alone experimental physics that has given birth 

 to them; mathematical physics has well contributed. It is the experi- 

 menters who have seen radium throw out energy, but it is the theorists 

 who have put in evidence all the difficulties raised by the propagation 

 of light across a medium in motion; but for these it is probable we 

 should not have become conscious of them. Well, then, if they have 

 done their best to put us into this embarrassment, it is proper also 

 that they help us to get out of it. 



They must subject to critical examination all these new views I 

 have just outlined before you, and abandon the principles only after 

 having made a loyal effort to save them. What can they do in this 

 sense ? That is what I will try to explain. 



