VI PREFACE. 



touches to the last pages, in which I endeavour to secure 

 in advance the interest of my readers for the subsequent 

 portions of this work. To all these friends I wish to 

 express my sense of obligation and my sincere thanks. 

 I find it impossible to express how much this book owes 

 to my beloved wife, my constant helpmate on the long 

 course of this arduous enterprise. 



It is unnecessary for me to lighten the work of my 

 critics by pointing out the many defects of which I myself 

 am painfully conscious ; but, in the case of the last chapter 

 on "The Development of Mathematical Thought," I wish 

 to say that this is so far as I know the first attempt 

 to give to this abstract region of thought a place in a 

 general history of intellectual progress. I sincerely hope 

 that it will be followed by other and more successful 

 attempts to perform this very difficult task. It is now 

 abundantly clear that mathematical thought will play an 

 increasingly important part in the progress of science and 

 culture, and it is no longer permissible to consider it merely 

 an interesting specialty apart from the general course of 

 intellectual development. A due appreciation of its im- 

 portance and power will in future be expected, not only 

 from the practical thinker who applies science, but likewise 

 from the philosopher who assigns to science its place in 

 the comprehensive scheme of human culture. 



J. THEO. MERZ, 



THE QUARRIES, 

 NBWCASTLK-UPON-TYNB, October 1903. 



