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

82 INTRODUCTION TO MATHEMATICS
reader's mind: What is the use of all this
elaboration? At this point our friend, the
practical man, will surely step in and insist on
sweeping away all these silly cobwebs of the
brain. The answer is that what the mathematician is seeking is Generality. This is an
idea worthy to be placed beside the notions
of the Variable and of Form so far as concerns
its importance in governing mathematical
procedure. Any limitation whatsoever upon
the generality of theorems, or of proofs, or of
interpretation is abhorrent to the mathematical instinct. These three notions, of the
variable, of form, and of generality, compose
a sort of mathematical trinity which preside
over the whole subject. They all really
spring from the same root, namely from the
abstract nature of the science.
Let us see how generality is gained by the
introduction of this idea of operations. Take
the equation x +1=3; the solution is x =2.
Here we can interpret our symbols as mere
numbers, and the recourse to "operations"
is entirely unnecessary. But, if x is a mere
number, the equation x+3=1 is nonsense.
For x should be the number of things which
remain when you have taken 3 things away
from 1 thing; and no such procedure is
possible. At this point our idea of algebraic
form steps in, itself only generalization under
another aspect. We consider, therefore, the