HENRI POINCABE XORDMAiSTX. 749 



"Should \vc be surprised if a lion d(jes not run with the steps of a 

 mouse?" 



Upon the very structure of his thoughts, upon the mechanism of 

 his maiTelous cerebral workshop, Poincaire has left us strange and 

 suggestive confidences. Since what we know of the universe comes 

 only from its image as reflected to us through our brain, that knowl- 

 edge is affected by all the properties and deformations of that mner 

 mirror, and psychology will without doubt one day be tlie master 

 science. Accordmgly the psychological aspects of a brain like that 

 of Pomcare, which he has shown us naked with such touching sin- 

 cerity, are of unequaled interest. In studying the genesis of mathe- 

 matical invention, ''which mthoub doubt is the purest and most 

 exclusively rational process of our brain because it seems the least 

 conditioned by the exterior world," we find the most essential char- 

 acteristics of the human mind which we may ever hope to get. La- 

 place has said, ''A knowledge of the methods of a man of science are no 

 less useful to the progi-ess of science or toward his o^vn glory than the 

 discoveries themselves." 



Contrary to our expectations, conscious work, voluntary and logical, 

 did not with Poincare play the most important part. Nothing is 

 more amusing m that respect than the manner in which he has told 

 us of liis discovery of the Fuchsian function. This idea which strug- 

 gled vaguely m his brain one evening after he had taken, contrary to 

 habit, a cup of coffee so that he could not sleep, took shape little by 

 little under the strangest of ckcumstances. Everyone has read the 

 pages where he has told how he saw in due proportion all the chief 

 difficulties but did not consider them further, and then how, long 

 afterwards, in a flash, the solutions he wished appeared to him when 

 lie was putting his foot on the step of an omnibus; at another time 

 when crossing a street, and yet again on a geological stroll in the midst 

 of a triflmg conversation. 



The ''subconscious self," or, as some have put it, ''the subliminal 

 self," plays in mathematical invention a supreme part. There whore 

 we believe reason and will ruled alone we find something appearing 

 analogous to the mspiration which custom attributes to poets and 

 composers. And it is a troublesome ckcumstance that this subcon- 

 scious self succeeds in solving problems and overcoming difficulties 

 which the conscious self could not. Is then the subconscious not 

 superior to the conscious self ? Have we not here somethmg withm, 

 which is greater than ourselves, a sort of divine essence superior to 

 our will and reason whichmakos us capable of tasks greater than our- 

 selves ? We can understand the importance of such a question and 

 the spiritual significance of a positive relpy. The positive mind of 

 Poincare, however, would not admit supernatural explanations unless 

 absolutely necessary and in a penetratmg and accurate investigation 



