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

INTRODUCTION 13
the bear to ride a bicycle, or the seal to balance a staff
upon its nose or to twirl a disc.
These considerations are no doubt obvious. I should
not dwell upon them at so great length but for the fact
that in the excitement and confusion of our industrial
age the most obvious of important facts and the most
evident of important principles are so commonly lost
sight of that they require to be cited again and again
and again. Nowhere is the confusion of the time more
evident than in the somewhat noisy and sometimes acrimonious discussion that has been recently and still is going on throughout our country regarding the value of
mathematics as a subject in secondary and collegiate education. The instigators of the discussion, those, that is,
who advocate so reducing mathematical requirements as
practically to abolish the subject from curricula of general
education, are not malicious nor insincere; many of them,
I do not doubt, are well-meaning citizens. And if their
rather voluminous discourses are often singularly lacking
in coherence, in clarity and in depth, the defects are not
due to evil intentions but rather, I suspect, to confusion
and a lack of just that sort of discipline which the subject
the authors are engaged in depreciating is peculiarly
qualified to give. Perhaps we should not be astonished.
If the saying of Sir Oliver Lodge be true that "the mathematical ignorance of the average educated person has
always been complete and shameless," one ought not, I
suppose, to be too much astonished if in a vast, crude,
formless, sprawling democracy like ours, a way to educational "leadership" is sometimes found by men whose
innocence, not only of mathematics but of the other great
subjects, including the principles of education, is wellnigh complete and shameless, And yet, despite famil