SEPTEMBER 18, 1913] 
NATURE 69 
: Section L—Education. 
Prof. J. J. Findlay, mental 
and physical factors ee 215) Melee) 
Dr. G. A. Auden, influence 
of school books on eye- 
sight ... Seo Pie oa 
Sir H. Miers, Number, &c., 
of scholarships, &c., held 
by university students ... 5 0 0 
Myers, Dr. S., binocular 
combination of kinemato- 
eraph pictures 3 ae LOM OO 
Prof. J. A. Green,  char- 
acter and maintenance of 
museums nee 10 0 0 
Ne 
Corresponding Societies Committee. 
W. Whitaker, for preparation 
of report oA ; 25 0 0 
Total ... ares) IL 
SECTION A. 
MATHEMATICS AND PHYSICS. 
Openinc Appress By H. F. Baker, Sc.D., F.R.S., 
PRESIDENT OF THE SECTION. 
The Place of Pure Mathematics. 
Ir is not a very usual thing for the opening address 
of this section to be entrusted to one whose main 
energies have been devoted to what is called pure 
mathematics; but I value the opportunity in order to 
try to explain what, as I conceive it, the justification 
of the pure mathematician is. You will understand 
that in saying this I am putting myself in a position 
which belongs to me as little by vocation as by 
achievement, since it was my duty through many years 
to give instruction in all the subjects usually regarded 
as mathematical physics, and it is still my duty to be 
concerned with students in these subjects. But my 
experience is that the pure mathematician is apt to be 
regarded by his friends as a trifler and a visionary, 
and the consciousness of this becomes in time a 
paralysing dead-weight. I think that view is founded 
on want of knowledge. 
Of course, it must be admitted that the mathe- 
matician, as such, has no part in those public en- 
deavours that arise from the position of our Empire 
in the world, nor in the efforts that must constantly 
be made for social adjustment at home. I wish to 
make this obvious remark. For surely the scientific 
man must give his time and his work in the faith of 
at least an intellectual harmony in things; and he 
must wish to know what to think of all that seems out 
of gear in the working of human relations. His own 
cup of contemplation is often golden; he marks that 
around him there is fierce fighting for cups that are 
earthen, and largely broken; and many there are that 
go thirsting. And, again, the mathematician is as 
sensitive as others to the marvel of each recurring 
springtime, when, year by year, our common mother 
seems to call us so loudly to consider how wonderful 
she is, and how dependent we are, and he is as curious 
as to the mysteries of the development of living things. 
He can draw inspiration for his own work, as he 
views the spectacle of a starry night, and sees 
How the floor of heaven 
Ts thick inlaid with patines of bright gold. 
Each orb, the smallest, in his motion, sings, 
but the song, once so full of dread, how much it owes 
to the highest refinements of his craft, from at least 
the time of the Greek devotion to the theory of conic 
NO. 2290, VOL. 92] 
sections; how much, that is, to the harmony that is 
in the human soul. Yet the mathematician bears to 
the natural observer something of the relation which 
the laboratory botanist has come to bear to the field 
naturalist. Moreover, he is shut off from inquiries 
which stir the public imagination; when he looks back 
the ages over the history of his own subject, the 
confidence of his friends who study heredity and teach 
eugenics arouses odd feelings in his mind; if he feels 
the fascination which comes of the importance of such 
inquiries, he is also prepared to hear that the subtlety 
of Nature grows with our knowledge of her. Doubt- 
less, too, he wishes he had some participation in the 
discovery of the laws of wireless telegraphy, or had 
something to say in regard to the improvement of 
internal-combustion engines or the stability of aéro- 
planes; it is little compensation to remember, though 
the mathematical physicist is his most tormenting 
critic, what those of his friends who have the physical 
instinct used to say on the probable development of 
these things, however well he may recall it. 
But it is not logical to believe that they who are 
called visionary because of their devotion to creatures 
of the imagination can be unmoved by these things. 
Nor is it at all just to assume that they are less 
conscious than others of the practical importance of 
them, or less anxious that they should be vigorously 
prosecuted. 
Why is it, then, that their systematic study is given 
to other things, and not of necessity, and in the first 
instance, to the theory of any of these concrete pheno- 
mena? This is the question I try to answer. I can 
only give my own impression, and doubtless the 
validity of an answer varies as the accumulation of 
data, made by experimenters and observers, which 
remains unutilised at any time. 
The reason, then, is very much the same as that 
which may lead a man to abstain from piecemeal 
indiscriminate charity in order to devote his attention 
and money to some well-thought-out scheme of reform 
which seems to have promise of real amelioration. 
One turns away from details and examples, because 
one thinks that there is promise of fundamental im- 
provement of methods and principles. This is the 
argumentum ad hominem. But there is more than 
that. The improvement of general principles is 
arduous, and if undertaken only with a view to results 
may be ill-timed and disappointing. But as soon as 
we consciously give ourselves to the study of universal 
methods for their own sake another phenomenon 
appears. The mind responds, the whole outlook is 
enlarged, infinite possibilities of intellectual compre- 
hension, of mastery of the relations of things, hitherto 
unsuspected, begin to appear on the mental horizon. 
I am well enough aware of the retort to which such a 
statement is open. But, I say, interpret the fact as 
you will, our intellectual pleasure in life cometh not 
by might nor by power—arises, that is, most com- 
monly, not of set purpose—but lies at the mercy of the 
response which the mind may make to the oppor- 
tunities of its experience. When the response proves 
to be of permanent interest—and for how many 
centuries have mathematical questions been a fascina- 
tion?—we do well to regard it. Let us compare 
another case which is, I think, essentially the same. 
It may be that early forms of what now is specifically 
called art arose with a view to applications; I do not 
know. But no one will deny that art, when once it 
has been conceived by us, is a worthy object of 
pursuit; we know by a long trial that we do wisely 
to vield ourselves to a love of beautiful things, and 
to the joy of making them. Well, pure mathematics, 
as such, is an art, a creative art. If its past triumphs 
of achievement fill us with wonder, its future scope for 
