HENRI POINCARE AS AN INVESTIGATOR 223 



investigator should not include some course in design in his work, in 

 painting, architecture, music, poetry or sculpture. Courses in the 

 appreciation of art, rather than the criticism of art, might also be very 

 serviceable indirectly. The constructive philosophers, like Plato or 

 Bergson, might furnish valuable indirect training. Eeading that leads 

 to an appreciation of the beauty and sublimity of the universe is of 

 the same value. In any case whatever would intensify the esthetic 

 sensitiveness would be worth while. 



When the intuition does not favor us, the golden butterfly fails to 

 emerge from its chrysalis, what is to be done? Here is his answer for 

 whom time did not count, taken from one of his most recent papers. 11 

 There is a note of pathos in it as well as a hint of premonition. He 

 presents some incomplete results of a new and very important theorem 

 in geometrical transformation, which he is convinced is true, yet the 

 proof of it encounters great difficulties. Every particular case he has 

 been able to settle is favorable to the theorem. After explaining why 

 he is publishing an incomplete paper for the first time, he says : 



It would seem that in this situation I should abstain from all publication 

 bo long as I have not solved the problem, but after fruitless efforts for many 

 months it seems to me wisest to let the whole problem ripen during several years. 

 That would indeed be well, were I sure of some day being able to take it up 

 again, but at my age I can not go bail for this. On the other hand, the impor- 

 tance of the subject is great . . . and the totality of results so far obtained is 

 too considerable for me to resign myself to definitively allowing them to become 

 unfruitful. I may hope that the mathematicians who interest themselves in the 

 problem and who will be more fortunate than I without doubt will find some 

 means to resolve it. 



Again, Poincare points out that these flashes from below the horizon 

 of consciousness must be preceded by periods of prolonged attentive 

 work. It is like setting Pegasus to plowing corn, but this conscious 

 effort is necessary. This discouraging wandering over the hills and 

 rocks, examining the promising paths and the fragments that point to 

 a nearby mine, day after day, is indispensable to success. It is the 

 weary search over the face of the mountain and the driving of many 

 fruitless drifts that eventually lead the prospector to his mine of gold. 

 On this kind of drudgery Poincare spent two periods of two hours each 

 daily. The unconscious action of his mind did the rest of his work. 



Neither does the discovery of the mine develop it. After the 

 unconscious power has led us to our eldorado, it has done all it can. 

 The deductions, the demonstrations, the applications, must be carried 

 out at the expense of prolonged effort again. The intuition can not do 

 this kind of work. Its region is the nebulous part of thought where 

 the mental ions unite, dissolve, and whirl away, — or we may say that 



" Bend. Circ. Mat. Palermo, 33 (1912), p. 375. 



