MATHEMATICS 



BY ROBERT SIMPSON WOODWARD, 



Professor of Mechanics, Columbia University 



L'idee du progres, du developpement, me parait etre 1'idee fondamentale contenue 

 sous le mot de civilisation. GUIZOT. 



31 ON GST the causes which have made for 

 civilization during the past half-century, the 

 progress of science, it would seem, must be 

 given a very prominent, if not the first place. 

 Governmental, commercial, social, ethical, and 

 religious institutions and influences have each played an 

 important role in the general advance of humanity ; but the 

 pervading thought, the points of view, and the intellectual 

 activities have been predominantly scientific. To the world at 

 large the most striking results of this progress of science are 

 found in material benefits. The ease of intercommunication 

 by telegraph and telephone ; the facility of transportation 

 by railway and steamship ; the prevention of disease by ra- 

 tional sanitation, and the mitigation of pain by rational 

 surgery, along with a multitude of other benefits, appeal 

 directly and forcibly to the popular sense. To the student 

 of civilization, on the other hand, the most important results 

 of that progress are found in the development of a dis- 



