24 
PRESIDENT S ADDRESS — SECTION A. 
been mentioned more than once, that mathematics possesses more 
exclusively than any other science what are regarded by all scientists 
as the essential characteristics of science. 
The results in applied mathematics are in a sense not precise. 
They are exact only in proportion to the exactness of the data sup- 
plied. The mathematical part of the work is as precise as ever, but 
the part for which the mathematician is not responsible is not so. 
The fundamental data that the astronomer hands over to the 
mathematician, from which he is to deduce far-reaching consequences, 
are confessedly but approximations — wonderfully close, it is true — and 
tbe deduced consequences are approximations of the same order. The 
approximations provided by the engineer are much less close, and the 
results deduced by tbe mathematician for the business of the engineer 
are corresponding. 
But it is in this region of applied mathematics that mathema- 
ticians have rightly tried to impress the popular mind with the 
wondrous power of the science. Many books have been, are being, 
and will continue to be, written on this subject. And as the wealth 
of materials fully warrants this it -would be but futile to do more here 
thau make a passing allusion. 
In conclusion, we may sum up the peculiar characteristics of the 
science of mathematics. It is unique in the cosmic nature aud the 
universality of the questions it deals with, in the stability of the data 
on which it rests, in the reliableness of the assistance it renders to 
every other science which has become sufficiently highly generalised 
or sufficiently piecise. It has been disputed whether mathematics is 
a branch of logic or logic a branch of mathematics. If we group them 
together for the moment wc may say that they are further unique in 
the almost inconceivable exactness of their methods, and in their being 
exclusively an intellectual product as opposed to a combined intellec- 
tual and observational one. I am not prepared to defend the strict 
accuracy of this last distinction, but when you reflect on what is meant 
by observation and experiment in all the other sciences you will see 
that there is here a substantial difference. 
It may be added that, notwithstanding this purely intellectual 
nature of the subject, notwithstanding the highly general nature of 
most of its results, the mere volume of these results, as in so many 
other sciences, is so great that it is imjmssiblo now for a single man to 
be really conversant with any but a small portion of the whole. 'The 
prospects opened up to the merely acquisitive mathematician, however 
great his powers in that direction, are far more than sufficient for his 
lifetime, whereas the inducements offered to him who would walk 
where no man walked before are only rendered the more numerous in 
that mathematics from its very extension provides more points of 
contact of the known and unknown than in any former age. 
