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

SYMBOLISM OF MATHEMATICS 59
purposes, however, the history of the notation
is a detail. The interesting point to notice
is the admirable illustration which this
numeral system affords of the enormous importance of a good notation. By relieving
the brain of all unnecessary work, a good
notation sets it free to concentrate on more
advanced problems, and in effect increases
the mental power of the race. Before the
introduction of the Arabic notation, multiplication was difficult, and the division even of
integers called into play the highest mathematical faculties. Probably nothing in the
modern world would have more astonished a
Greek mathematician than to learn that,
under the influence of compulsory education,
the whole population of Western Europe,
from the highest to the lowest, could perform
the operation of division for the largest numbers. This fact would have seemed to him a
sheer impossibility. The consequential extension of the notation to decimal fractions
was not accomplished till the seventeenth
century. Our modern power of easy reckoning with decimal fractions is the almost
miraculous result of the gradual discovery of
a perfect notation.
Mathematics is often considered a difficult and mysterious science, because of the
numerous symbols which it employs. Of
course, nothing is more incomprehensible than