20 
PRESIDENT’S ADDRESS — SECTION A. 
Of those things we know, our knowledge can only strictly he 
called exact if it is absolutely certain. But on reflection you will per- 
ceive that certainty is our possession in but a very small and apparently 
rather barren field. My certainty is limited absolutely to my own 
consciousness. I am certain that I feel warm or cold ; I am certain 
that I see — i.e have certain impressions called visual ; I am certain 
that I believe there are conscious beings like but other than myself. 
But I am not certain that I feel warm, because I am in an execrable 
climate, though 1 may think it highly probable. I am not certain that 
what I see before me arc really people’s faces, whatever people and face 
may mean. And although I am certain of the belief in the existence 
of other conscious beings, the belief itself is not a certainty. 
Enough of this, however. I merely wish to point out that no 
science is exact in the sense of dealing with certainties. But it is no 
violation of the English language to say that the distance between 
two milestones is exactly one mile. This may mean that the excess 
above or defect below one mile is so small as to be of no consequence 
in all the uses to which milestones are put, or it may mean that from 
a definite point on the one stone to some point unspecified on the 
other the distance is neither more nor less than a mile. 
I have said that in this second* sense all sciences are exact. And 
the reason is not far to seek. The whole object of science viewed from 
one point of view is to reduce knowledge to exactness. Just in so far 
as a branch of knowledge separates itself off from ordinary knowledge 
by reason of its becoming more and more exact does that branch 
justify its possession of the proud title — Science. Let me, in passing, 
however, protest against these words being caricatured. When I say 
that from one point of view the object of science is exactness, I only 
mean that this is the note of its method as distinguished from other 
methods of learning from our surroundings. The ultimate object of 
all science, as of all poetry, arts, and philosophies, is to bring us into 
closer harmony with the external universe. The scientist elects to 
adopt the humble and laborious task of going to Nature herself, 
asking questions, cross-questioning her, but, above all, cross- 
questioning himself in his deductions from her answers. 
It would take us too far afield to try to answer in general terms 
the question how the various sciences have been made more and more 
exact till one by one they have arrived at such a growth as to fill us 
with never-ceasing wonder at what men and generations in concert 
can intellectually accomplish. Suffice it that by one such process the 
science of mathematics has succeeded in an astonishingly great degree 
to distance all others in this pre-eminently scientific aim. 
Perhaps it is this feature more than anv other which has caused 
that curious phenomenon — that quite a multitude of semi-educated 
scientific men find a real difficulty in understanding that mathematics 
is a science. 
This prevalent notion seems to be connected with another one 
already hinted at — viz., that to become an expert mathematician the 
penalty must be paid of parting with half one’s humanity in order to 
become a calculating machine. This popular delusion constantly requires 
to be protested against. The mathematician is very rarely a calculator. 
Mathematical and calculating ability indeed seem to a large extent 
antagonistic. It is a well-known fact that when a mathematician is 
