80 MATHEMATICS 



Napier, the tercentenary of the publication of 

 which was the occasion of a gathering of Mathema- 

 ticians of all nations a few days before the essential 

 unity of the co-operative work of men of Science 

 was obscured for the immediate future by the 

 outbreak of the European war. The Engineer 

 when he makes the necessary graphical calculations 

 of the stresses in the bridge he is building ; or the 

 Statistician who constructs his graphs, has to 

 employ methods and conceptions belonging to a 

 relatively advanced state of mathematical thought. 

 The Philosopher, in his reflections on spatial and 

 temporal relations, on number and quantity, on 

 matter and motion, is in a region in which the 

 boundary between his own domain and that of 

 the Mathematician is scarcely discernible. By the 

 Epistemologist mathematical knowledge has always 

 been taken as a kind of touchstone on which to 

 test his general theories of the nature of knowledge. 

 The origins of Mathematical thinking, and the 

 reason of its ubiquity in all departments of Science 

 that have reached a certain maturity, and even 

 in practical life, are not far to seek. The physical 

 world which forms our environment appears to 

 us as a manifold of objects extended in space, the 

 spatial relations of the various objects exhibiting 

 at any one time an endless variety, and varying 

 at different times. The primary mathematical 

 operations of counting and measuring, which give 

 rise in the reflecting mind to the concepts of number 



