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SCIENCE 



[N. S. Vol. XXXVI. No. 927 



one of them was greatly aided by the work 

 along the other lines. 



The breadth of scholarship exhibited by 

 Poincare in his early writings and his great 

 ability to observe relations between appar- 

 ently widely different subjects became still 

 more pronounced as he grew older, but we ob- 

 serve even at this early date a mind of very 

 broad sympathies and of extraordinary abil- 

 ity to generalize. His principal writings 

 may be classed under the following four 

 headings: pure mathematics, analytic and 

 celestial mechanics, mathematical physics, 

 and the philosophy of science. 



In 1909 Emile Borel published, in the 

 journal called La Revue du Mots, an article 

 on the method of Poincare. Parts of this 

 were translated for the first article in the 

 Bulletin of the Calcutta Mathematical So- 

 ciety. In view of the great importance of the 

 method of work, we quote parts of this trans- 

 lation. 



The method of Poincarfi is essentially active 

 and constructive. He approaches a question, ac- 

 quaints himself with its present condition without 

 being much concerned about its history, finds out 

 immediately the new analytical formulas by which 

 the question can be advanced, deduces hastily the 

 essential results, and then passes to another ques- 

 tion. After having finished the writing of a 

 memoir, he is sure to pause for a while, and to 

 think out how the exposition could be improved; 

 but he would not, for a single instance, indulge 

 in the idea of devoting several days to didactic 

 work. Those days could be better utilized in ex- 

 ploring new regions. 



AH this is not specially applicable to mathe- 

 matics. Let us examine more closely the mech- 

 anism made use of for discovery. The essential 

 feature of that mechanism is, as we have already 

 pointed out, the construction of new formulas. 

 It is not useless that some stress is laid on this 

 point, for this constructive power is the essential 

 trait of the genius of Poincarg. The non-mathe- 

 matical readers can be made to understand all 

 this by means of a comparison. They know what 

 arithmetical calculation is, and are often led to 

 believe that mathematicians are in the habit of 

 making interminable additions, multiplications, 

 etc., and also extractions of cube roots. 



In reality, arithmetical operations are iinique 



combinations of integral numbers formed of units 

 which are all equal to one another. These opera- 

 tions can be compared to the construction of 

 regular walls by means of bricks of uniform sizes. 

 The work requires only some patience and a little 

 care. On the contrary, analytical operations make 

 use of extremely numerous materials and their 

 variety is comparable to those of structures, where 

 stone, marble, wood, iron, etc., are used. These 

 operations are as different from each other as 

 cuirassS is from a Gothic church. They have also 

 with the architectural constructions this in com- 

 mon, that an impression of beauty is produced by 

 the simplicity and elegance of the essential lines, 

 without exhibitrag any of the effort by means of 

 which the result has been obtained. 



Poincare was a great pioneer, boldly enter- 

 ing into unexplored regions and noting some 

 of the most important objective points and 

 then leaving to others the details of organi- 

 zation. In the words of Borel he was more 

 of a conqueror than a colonizer, and he at- 

 tached little importance to conceptions which 

 can not be realized in a concrete form. In 

 this respect he may be compared with men of 

 action; his method of work was too active to 

 leave much room for such reflections as do 

 not lead to concrete results. 



On January 28, 1909, Poincare was re- 

 ceived as member of I'Aeademie Frangaise, 

 and on this occasion M. Masson, Directeur de 

 I'Aeademie, delivered an address in which he 

 entered into many details in Poincare's career. 

 A translation of a part of this address ap- 

 peared in the Popular Science Monthly, Sep- 

 tember, 1909, page 267. A sketch of Poin- 

 care's career may also be found in the Inde- 

 pendent, October 5, 1911, under the general 

 title of " Twelve Major Prophets of To-day." 

 An elementary article by Poincare on the 

 foundations of geometry appeared in the 

 Monist, October, 1898, and a number of his 

 other articles have been translated into Eng- 

 lish from foreign journals. 



In 1909 Ernest Lebon published, in his 

 series entitled " Savants du Jour," a little 

 volume on Henri Poincare. This volume 

 contains a list of his 436 different publica- 

 tions. The largest number of articles classed 

 under one heading is 98, under the general 



