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THE NATURE OF MATHEMATICS 



INTRODUCTION 

AN eminent mathematician once remarked that he was never 
satisfied with his knowledge of a mathematical theory until he 
could explain it to the next man he met in the street. That 
is hardly exaggerated; however, we must remember that a 
satisfactory explanation entails duties on both sides. Any one 
of us has the right to ask of a mathematician, " What is the 
use of mathematics ? " Any one may, I think and will try to 
show, rightly suppose that a satisfactory answer, if such an 
answer is anyhow possible, can be given in quite simple terms. 
Even men of a most abstract science, such as mathematics or 
philosophy, are chiefly adapted for the ends of ordinary life ; 
when they think, they think, at the bottom, like other men. 
They are often more highly trained, and have a technical facility 
for thinking that comes partly from practice and partly from 
the use of the contrivances for correct and rapid thought given 
by the signs and rules for dealing with them that mathematics 
and modern logic provide. But there is no real reason why, 
with patience, an ordinary person should not understand, 
speaking broadly, what mathematicians do, why they do it, 
and what, so far as we know at present, mathematics is. 

Patience, then, is what may rightly be demanded of the 
inquirer. And this really implies that the question is not 
merely a rhetorical one an expression of irritation or scepti- 
cism put in the form of a question for the sake of some fancied 
effect. If Mr. A. dislikes the higher mathematics because he 
rightly perceives that they will not help him in the grocery 
business, he asks disgustedly, " What's the use of mathematics ? " 
and does not wait for an answer, but turns his attention to 

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