INTRODUCTION. 



In this work I have collected various studies which are 

 more or less directly concerned with scientific metho- 

 dology. The scientific method consists in observation 

 and experiment. If the scientist had an infinity of 

 time at his disposal, it would be sufficient to say to 

 him, " Look, and look carefully." But, since he has 

 not time to look at everything, and above all to look 

 carefully, and since it is better not to look at all than 

 to look carelessly, he is forced to make a selection. 

 The first question, then, is to know how to make this 

 selection. This question confronts the physicist as 

 well as the historian ; it also confronts the mathema- 

 tician, and the principles which should guide them all 

 are not very dissimilar. The scientist conforms to 

 them instinctively, and by reflecting on these principles 

 one can foresee the possible future of mathematics. 



We shall understand this still better if we observe 

 the scientist at work ; and, to begin with, we must have 

 some acquaintance with the psychological mechanism 

 of discovery, more especially that of mathematical dis-' 

 covery. Observation of the mathematician's method 

 of working is specially instructive for the psychologist. 



In all sciences depending on observation, we must 



