MATHET^IATICAL DISCOVERY. 57 



is to show that the unconscious ego, or, as it is called, 

 the subliminal ego, plays a most important part 

 in mathematical discovery. But the subliminal ego 

 is generally thought of as purely automatic. Now we 

 have seen that mathematical work is not a simple 

 mechanical work, and that it could not be entrusted 

 to any machine, whatever the degree of perfection we 

 suppose it to have been brought to. It is not merely 

 a question of applying certain rules, of manufacturing 

 as many combinations as possible according to certain 

 fixed laws. The combinations so obtained would 

 be extremely numerous, useless, and encumbering. 

 The real work of the discoverer consists in choosing 

 between these combinations with a view to eliminating 

 those that are useless, or rather not giving himself 

 the trouble of making them at all. The rules which 

 must guide this choice are extremely subtle and 

 delicate, and it is practically impossible to state them 

 in precise language ; they must be felt rather than for- 

 mulated. Under these conditions, how can we imagine 

 a sieve capable of applying them mechanically ? 



The following, then, presents itself as a first hypoth- 

 esis. The subliminal ego is in no way inferior to the 

 conscious ego ; it is not purely automatic ; it is capable 

 of discernment ; it has tact and lightness of touch ; 

 it can select, and it can divine. More than that, 

 it can divine better than the conscious ego, since 

 it succeeds where the latter fails. In a word, is not 

 the subliminal ego superior to the conscious ego? 

 The importance of this question will be rcadiU- 

 understood. In a recent lecture, M. Boutroux showed 

 how it had arisen on entirely different occasions, and 

 what consequences would be involved by an answer 



