Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

30 MATHEMATICAL PHILOSOPHY
of genius to which it appeals. The growing literature
of the subject is large. Fortunately, it is not necessary,
except for the historian, to examine it all, for it has been
refined, assimilated, and, all but the later developments,
superseded in the monumental work of Whitehead and
Russell-Principia Mathematica-the present culmination of the movement. This work, however, which has
not yet been completed, the philosopher must examine
minutely if he would understand, as a philosopher ought
to understand, the fundamental nature of mathematics as
disclosed in the best light that has been thrown upon it
and especially if he would realize the hope of being able
to improve the light, which is not yet perfect. The
symbols are at first repellent; they tend to frighten but
are not in fact difficult to master.
They are things of so frightful mien
That to be hated need only be seen.
But often seen, familiar with their face,
We endure them first and then embrace.
Theoretically, the symbols are not essential, a sufficiently powerful god could get along without them; but
practically they are indispensable as instruments for
economizing our intellectual energy.l
No kind of work, whether philosophic or scientific,
can be severer in its demands. None surpasses it in re.
spect of the toil involved, nor in patience, nor in depth
of penetration, nor in subtlety, nor imagination, nor analytic finesse, nor in the demand it makes upon the constructive faculty, and none can give to the competent
student a serener vision of eternal things. If on this
1In relation to the early history and importance of symbolism do not
fail to read Professor David Eugene Smith's beautiful essay, "Ten Great
Epochs in the History of Mathematics," in Scientia, June, I921.