PRESIDENT’S ADDRESS — SECTION A. 
23 
this I mean that we know that the properties of our space so closely 
approximate to those of Euclidean space that from a scientific point 
of view the question for or against Euclidean space is not a practical 
one. When not only all the living things on the earth live under one 
federal government, but when also all the living things in the solar 
system have united, and when we can, after due deliberation, guide for 
the good of the whole the solar system itself whither we will through 
space, when our commands of nature are such as these, we may expect 
the question possibly to become a practical one. 
But let me not be misunderstood. I only say that, measured by 
the meaning of belief and knowledge in any other science, we know 
that our space is Euclidean. 1 may go further, and say that we are 
far more certain of this than of such well-established laws as those 
of gravitation and the conservation of matter. Only in this sense do 
I say that the question is not a practical scientific one. But looked 
at more generally by the inclusion of mathematics among the sciences, 
it becomes a most practical one. It is only because mathematics is so 
much more scientific than any other science that questions are raised 
in it of such transcendent interest. No other science has ever 
clearly stated and grasped the conditions of so far-reaching a question. 
Compared with this the question of the mode of evolution of worlds 
ts a paltry problem. 
Of the processes of mathematics the precision has grown to be a 
proverb. And were it not that perhaps for this very reason its signi- 
ficance is overlooked it need not even be mentioned here. To realise 
the vast importance of this precision, from a scientific point of view, 
we need only try to imagine the blessings that geologists would bestow 
ou an apostle among them who should be able to render their own 
methods a tenth as precise. Not alone do scientists value this useful 
feature of mathematics. Even the scornful “ practician,” as Dr. 
Heavenside clubs him, recognises it, and is only too glad in the lower 
walks of mathematics to avail himself of it. The main reason why all 
sciences as soon as they arc sufficiently developed look for aid to 
mathematics, is this valuable feature. 
Turning now to the results of mathematic 4 — I have said that 
these are also precise. But this must be interpreted with caution. 
So long as we deal with mathematics proper — i.e., pure mathematics, 
the statement passes without any qualification. To other than mathe- 
maticians pure mathematics is so much an unknown region that I 
believe for the most part it is the applications of mathematics that are 
confounded with mathematics itself. This confounding of applied 
mathematics with mathematics proper is very analogous to the popular 
confounding of the applications of science to such purposes as electric 
traction and sanitation with science itself. There is an important dis- 
tinction, however, which divests the confusion in mathematics of much 
of the liarmfulness of the confusion in the other eases. Eor no 
scientific man holds that the application of science to sanitation is in 
itself science, however much a scientific training may be useful to 
those responsible for good sanitation. In tins case, then, there is a 
popular misapprehension of what science really is. The applications 
of mathematics which we are now considering are on the other hand 
quite rightly regarded as a part of science rather than a part of the 
useful arts. This is owing, at any rate in part, to what has already 
