The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple bec… - Alfred North Whitehead

Seek simplicity and distrust it.

In a certain sense, everything is everywhere at all times. For every location involves an aspect of itself in every other location. Thus every spatio-temporal standpoint mirrors the world.

In the theory of well-ordered series and compact series, we have followed Cantor closely, except in dealing with Zermelo's theorem (*257 — 8), and in cases where Cantor's work tacitly assumes the multiplicative axiom. Thus what novelty there is, is in the main negative. In particular, the multiplicative axiom is required in all known proofs of the fundamental proposition that the limit of a progression of ordinals of the second class {i.e. applicable to series whose fields have ^{o terms) is an ordinal of the second class (cf *265). In consequence of this fact, a very large part of the recognized theory of transfinite ordinals must be considered doubtful.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.