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the culminating philosophical outcome, of 
a century’s effort to ascertain what mathe- 
matics, in its intimate structure, is. This 
conception of what mathematics is comes 
to its fullest expression and best defense, 
as you doubtless know, in such works as 
Schroeder’s ‘‘ Algebra der Logik,’’ White- 
head’s ‘‘Universal Algebra,’’ Russell’s 
“‘Principles of Mathematics,’’ Peano’s 
“‘Hormulario Mathematico,’’ and especially 
in Whitehead and Russell’s monumental 
‘“Principia Mathematica.’’ I cite this 
literature because it tells us what, in a defi- 
nitional sense, the science in which the nor- 
mal mathematician is exclusively engaged, 
is. If we wish to be told what that science 
humanly signifies, we must look elsewhere; 
we must look to a mathematician like 
Plato, for example, or to a philosopher like 
Poinearé, but especially must we look to 
our own faculty for discerning those fine 
connective things—community of aim, in- 
terformal analogies, structural similitudes 
—that bind all the great forms of human 
activity and aspiration—natural science, 
theology, philosophy, jurisprudence, relig- 
ion, art and mathematics—into one grand 
enterprise of the human spirit. 
In the autumn of 1906 there was pub- 
lished in Poet Lore a short poem which, 
though it says nothing explicitly of mathe- 
matics, yet admits of an interpretation 
throwing much light upon the human 
significance of the science and indicating 
well, I think, the normal mathematician’s 
place in the world of spiritual interests. 
The author of the poem is .my excellent 
friend and teacher, Professor William Ben- 
jamin Smith, mathematician, philosopher, 
poet and theologian. I have not asked his 
permission to interpret the poem as I shall 
invite you to interpret it. What its orig- 
inal motive was I am not informed—it may 
have been the exceeding beauty of the 
ideas expressed in it or the harmonious 
SCIENCE 
[N.S. Vou. XXXV. No. 904 
mingling of their light with the melody of 
their song. The title of the poem is ‘‘The 
Merman and the Seraph.’’ As you listen 
to the reading of it, I shall ask you to re- 
gard the merman as representing the nor- 
mal mathematician and the seraph as rep- 
resenting, let us say, the life of the emo- 
tions in their higher reaches and their finer 
susceptibilities. 
I 
Deep the sunless seas amid, 
Far from Man, from Angel hid, 
Where the soundless tides are rolled 
Over Ocean’s treasure-hold, 
With dragon eye and heart of stone, 
The ancient Merman mused alone. 
II 
And aye his arrowed Thought he wings 
Straight at the inmost core of things— 
As mirrored in his Magie glass 
The lightning-footed Ages pass,— 
And knows nor joy nor Earth’s distress, 
But broods on Everlastingness. 
‘Thoughts that love not, thoughts that hate not, 
Thoughts that Age and Change await not, 
All unfeeling, 
All revealing, 
Scorning height’s and depth’s concealing, 
These be mine—and these alone! ’’— 
Saith the Merman’s heart of stone. 
III 
Flashed a radiance far and nigh 
As from the vertex of the sky,— 
Lo! a Maiden beauty-bright 
And mantled with mysterious might 
Of every power, below, above, 
That weaves resistless spell of Love. 
IV 
Through the weltering waters cold 
Shot the sheen of silken gold; 
Quick the frozen Heart below 
Kindled in the amber glow; 
Trembling Heavenward Nekkan yearned 
Rose to where the Glory burned. 
‘¢Deeper, bluer than the skies are, 
Dreaming meres of morn thine eyes are 
All that brightens 
Smile or heightens 
Charm is thine, all life enlightens, 
