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

NATURE OF MATHEMATICS 9
merely for the purpose of example, and care
will be taken to make the general argument
comprehensible, even if here and there some
technical process or symbol which the reader
does not understand is cited for the purpose
of illustration.
The first acquaintance which most people
have with mathematics is through arithmetic.
That two and two make four is usually taken
as the type of a simple mathematical proposition which everyone will have heard of.
Arithmetic, therefore, will be a good subject
to consider in order to discover, if possible,
the most obvious characteristic of the science.
Now, the first noticeable fact about arithmetic is that it applies to everything, to
tastes and to sounds, to apples and to angels,
to the ideas of the mind and to the bones of
the body. The nature of the things is perfectly indifferent, of all things it is true that
two and two make four. Thus we write
down as the leading characteristic of mathematics that it deals with properties and
ideas which are applicable to things just because they are things, and apart from any
particular feelings, or emotions, or sensations, in any way connected with them.
This is what is meant by calling mathematics an abstract science.
The result which we have reached deserves
attention. It is natural to think that an