I 
6 MENDENHALL. 
versally agreed upon that in mathematics one can hardly 
go astray, at least not without the certainty of almost imme¬ 
diate detection and conviction at the hands of many skilled 
in the use of this wonderful intellectual device. When deal¬ 
ing with quantity in the abstract, or with matter under just 
such restrictions or possessed of just such properties as are 
prescribed, mathematics becomes a machine of certain per¬ 
formance, the output of which can only be in error through 
the conscious or unconscious mistakes of the operator. As 
such it challenges the admiration of all, and it must forever 
be regarded as among the first, if not, indeed, the very first, 
of the few really splendid creations of the human intellect. 
When Plato, in reply to a question as to the occupation of 
the Deity, answered, “ He geometrizes continually,” he em¬ 
phasized the dignity and the incontrovertibility of mathe¬ 
matical reasoning. 
It is no reflection, then, upon the importance and value of 
the science of mathematics to leave it upon the pedestal 
which it rightfully occupies, considering it as separate and 
apart from other sciences. In their development it ma}^ 
and does play a most important part, in which, however, it 
is identified rather with the investigator than with the sub¬ 
ject investigated; for, in studying the elementary principles 
of abstract dynamics, one may follow the now somewhat 
antiquated and cumbersome processes of Newton or the more 
simple and elegant methods of Clifford or Maxwell, but the 
results will in all cases be the same. 
Before finally dismissing the pure mathematics, however, 
especial attention must be invited to one or two principles 
involved in their application by way of contrast with the 
condition of things which exists in the domain of the other 
sciences. It is sometimes declared by way of a criticism of 
mathematics that “ what comes out of it is never better than 
what goes in.” In a certain narrow sense this is true, but 
in a broader and truer sense it is as false as it would be to 
say that grain and fruit are no better than the soil from 
which they spring. 
