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12 THE NATURE OF MATHEMATICS 

and so, in a way, it is. But whereas the aims of a business 
are not, at least directly, concerned with the satisfaction of 
intellectual needs, science including natural science, logic, 
and mathematics uses business methods consciously for such 
ends. The methods are far wider in range, more reasonably 
thought out, and more intelligently applied than ordinary 
business methods, but the principle is the same. And this 
may strike some people as strange, but it is nevertheless true : 
there appears more and more as time goes on a great and 
compelling beauty in these business methods of science. 

The economical function appears most plainly in very ancient 
and modern science. In the beginning-, all economy had in 
immediate view the satisfaction simply of bodily wants. 
With the artisan, and still more so with the investigator, 
the most concise and simplest possible knowledge of a given 
province of natural phenomena a knowledge that is attained 
with the least intellectual expenditure naturally becomes in 
itself an aim ; but though knowledge was at first a means to 
an end, yet, when the mental motives connected therewith are 
once developed and demand their satisfaction, all thought of 
its original purpose disappears. It is one great object of science 
to replace, or save the trouble of making experiments, by the 
reproduction and anticipation of facts in thought. Memory is 
handier than experience, and often answers the same purpose. 
Science is communicated by instruction, in order that one man 
may profit by the experience of another and be spared the 
trouble of accumulating it for himself; and thus, to spare the 
efforts of posterity, the experiences of whole generations are 
stored up in libraries. And further, yet another function of 
this economy is the preparation for fresh investigation. 1 

The economical character of ancient Greek geometry is not 
so apparent as that of the modern algebraical sciences. We 
shall be able to appreciate this fact when we have gained 
some ideas on the historical development of ancient and 
modern mathematical studies. 

The generally accepted account of the origin and early 
development of geometry is that the ancient Egyptians were 
obliged to invent it in order to restore the landmarks which 
had been destroyed by the periodical inundations of the Nile. 

1 Cf. pp. 7, 16, 20, E3, 89.