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

NATURE OF MATHEMATICS 13
sensations, the most serviceable part-from
its clearness, definiteness, and universalityof what is left is composed of our general
ideas of the abstract formal properties of
things; in fact, the abstract mathematical
ideas mentioned above. Thus it comes about
that, step by step, and not realizing the full
meaning of the process, mankind has been
led to search for a mathematical description
of the properties of the universe, because in
this way only can a general idea of the course
of events be formed, freed from reference to
particular persons or to particular types of
sensation. For example, it might be asked
at dinner: "What was it which underlay my
sensation of sight, yours of touch, and his of
taste and smell?" the answer being "an
apple." But in its final analysis, science
seeks to describe an apple in terms of the
positions and motions of molecules, a description which ignores me and you and
him, and also ignores sight and touch and
taste and smell. Thus mathematical ideas,
because they are abstract, supply just what
is wanted for a scientific description of the
course of events.
This point has usually been misunderstood,
from being thought of in too narrow a way.
Pythagoras had a glimpse of it when he proclaimed that number was the source of all
things. In modern times the belief that the