56 
Proceedings of the Royal Irish Academy. 
the last five years, with the corresponding number for the five years 
immediately preceding, and you will find the same phenomenon. 
Again, there is another cause, which has always rendered the 
number of Papers on Pure Mathematics very uncertain — namely, the 
small number of labourers employed in that field. IN^ot now, for the 
first time, have we to remark upon the paucity of such communi- 
cations. If you examine the records of the Academy for the years 
1836 to 1840, you will find that Pure Mathematics had well nigh 
disappeared. And yet those were the days of Hamilton and M'Cul- 
lagh. Again, if you examine our records for the period during 
which these communications were most numerous — the decade, 
namely, 1850-60 — you will find how largely we were then indebted to 
the illustrious mathematician just mentioned, and to our former Pre- 
sident, the present Bishop of Limerick. JsTor are we singular in the 
smallness of our purely Mathematical School. The records of the 
Eoyal Society have a story to tell which is very similar. I may 
mention as a remarkable fact, that their Proceedings for the Session, 
1868-69, contain but three Papers in Pure Mathematics, all of which 
come from the same author. Professor Cayley. 
The truth is, that the brilliancy which of late years has marked 
the track of experimental discovery — the more striking, popular, may 
I add, intelligible, character of the truths of experimental science — 
has proved too powerful an attraction. The splendour of these disco- 
veries appeals to the imagination of the younger student with a force 
which is wholly beyond the reach of Pure Mathematics. And the 
mathematician must be, as a student, absolutely unselfish. Every 
motive to exertion — the hope which brightens the commencement 
of his toil — the reward which crowns its close — must be found in 
the study itself. All the external incentives to labour^ — the wonder 
with which the outer world follows the path of the astronomer — the 
vigorous, noisy, almost polemical, energy, which attends the specula- 
tions of the geologist — these are not for him. He may be enthusiastic 
in his pursuit ; but his enthusiasm will wear, in the eyes of the outer 
world, somewhat of a grotesque aspect. They can understand and sym- 
pathize with the ardour of other scientific men — the passionate longing 
with which the astronomer strives to penetrate the secrets of the vast 
abyss — with which the geologist seeks to unrol (if I may call them so) 
Nature's autobiographic records ; but who, say they, could grow en- 
thusiastic over a differential equation? And when we reflect how 
earnestly we all desire the sympathy and admiration of our fellow- 
men, can we wonder that few are found to devote their lives to a pur- 
suit so essentially lonely ? Is it not rather wonderful that there are 
so many ? 
And if the mathematician works unsympathized with, he works too 
unaided. All those external appliances, essential to the experimental 
philosopher — which a society like ours can, and does supply — he 
does not need. All that we can do for the mathematician is, to listen 
with respectful attention to any communication which he makes to us, 
