An introduction to mathematics, by A. N. Whitehead.

8 INTRODUCTION TO MATHEMATICS
pages of some elementary mathematical
treatises.
The reason for this failure of the science to
live up to its reputation is that its fundamental ideas are not explained to the student
disentangled from the technical procedure
which has been invented to facilitate their
exact presentation in particular instances.
Accordingly, the unfortunate learner finds
himself struggling to acquire a knowledge of
a mass of details which are not illuminated
by any general conception. Without a
doubt, technical facility is a first requisite
for valuable mental activity: we shall fail
to appreciate the rhythm of Milton, or the
passion of Shelley, so long as we find it necessary to spell the words and are not quite
certain of the forms of the individual letters.
In this sense there is no royal road to learning. But it is equally an error to confine
attention to technical processes, excluding
consideration of general ideas. Here lies
the road to pedantry.
The object of the following chapters is not
to teach mathematics, but to enable students
from the very beginning of their course to
know what the science is about, and why it is
necessarily the foundation of exact thought
as applied to natural phenomena. All allusion in what follows to detailed deductions
in any part of the science will be inserted