THE PRINCIPLES OF MATHEMATICAL PHYSICS 



BY JULES HENRI POINCARE 



(Translated from the French by George Bruce Hoisted, Kenyon College) 



[Jules Henri Poincare, Professor University of Paris, and the Polytechnic 

 School; Member of Bureau of Longitude, b. Nancy, April 29, 1854. D.Sc. 

 August 3, 1879; D.Sc. Cambridge and Oxford, 1879; Charge of the Course 

 of the Faculty of Sciences at Caen; Master of Conference of the Faculty of 

 Sciences of Paris, 1881; Professor of the same Faculty, 1886; Member of the 

 Institute of France, 1887; Corresponding Member of the National Academy 

 of Washington; Philosophical Society of Philadelphia; the Academies of 

 Berlin, London, St. Petersburg, Vienna, Rome, Munich, Gottingen, Bologna, 

 Turin, Naples, Venice, Amsterdam, Copenhagen, Stockholm, etc. Written 

 books and numerous articles for reviews and periodicals.] 



WHAT is the actual state of mathematical physics? What are the 

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

 on the point of modifying itself? 



Will the aim and the methods of this science appear in ten years 

 to our immediate successors in the same light as to ourselves; or, 

 on the contrary, are we about to witness a profound transformation? 

 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 feel ourselves tempted to risk a prognostication, we have, 

 to resist this temptation, only to think of all the stupidities the 

 most eminent savants of a hundred years ago would have uttered, 

 if one had asked them what the science of the nineteenth century 

 would be. They would have believed themselves bold in their pre- 

 dictions, yet after the event how very timid we should have found 

 them. 



Mathematical physics, we know, was born of celestial mechanics, 

 which engendered it at the end of the eighteenth century, at the 

 moment when the latter was attaining its complete development. 

 During its first years especially, the infant resembled in a striking 

 way its mother. 



The astronomic universe is formed of masses, very great without 

 doubt, but separated by intervals so immense that they appear to 

 us only as material points. These points attract each other in the 

 inverse ratio of the square of the distances, and this attraction is 

 the sole force which influences their movements. But if our senses 

 were sufficiently subtle to show us all the details of the bodies which 

 the physicist studies, the spectacle we should there discover would 

 scarcely differ from what the astronomer contemplates. There also 

 we should see material points, separated one from another by inter- 



