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

60 INTRODUCTION TO MATHEMATICS
a symbolism which we do not understand.
Also a symbolism, which we only partially
understand and are unaccustomed to use, is
difficult to follow. In exactly the same way
the technical terms of any profession or trade
are incomprehensible to those who have never
been trained to use them. But this is not
because they are difficult in themselves. On
the contrary they have invariably been introduced to make things easy. So in mathematics, granted that we are giving any serious
attention to mathematical ideas, the symbolism is invariably an immense simplification. It is not only of practical use, but is
of great interest. For it represents an analysis of the ideas of the subject and an almost
pictorial representation of their relations to
each other. If any one doubts the utility of
symbols, let him write out in full, without any
symbol whatever, the whole meaning of the
following equations which represent some of
the fundamental laws of algebra:x+y =y+x (1)
(x+y)+z=x+(y+z) (2)
xXy=yXx (3)
(xXy) xz=x (yxz) (4)
x x (y+x) = (x xy) + (x xz) (5)
Here (1) and (2) are called the commutative
and associative laws for addition, (3) and (4)