Preface to the First German Edition
And furthermore, a presentation that follows the historical develop-
ment has the advantage of making many mathematical abstractions
seem the natural consequence of individual investigations, so that one
never gets the impression of starting with an unmotivated definition
somehow descended from heaven in a completely arbitrary manner.
At the same time, we are able to leave out a great deal of material
that would be necessary to include in a work seeking great generality.
However, we must mention a significant drawback to our approach:
Many complicated calculations will be necessary, even if they are of
an elementary nature, whose results would be more simply derived
from a qualitative point of view on the basis of general principles.
In order to make this book as distinct as possible from mathe-
matical textbooks, I have chosen the same style of presentation as in
my book Luck, Logic, and White Lies. Every chapter begins with a
simple, usually more or less rhetorical, question that gives the reader
an idea of the nature and level of difficulty of the chapter ahead, even
if the chapter usually goes far beyond simply answering the ques-
tion posed. This structure should also offer the more mathematically
sophisticated reader, for whom the overview offered here will often
be too superficial and incomplete, a quick way of determining which
parts of the book are of particular interest, after which the references
to the literature will indicate a path of additional reading.
The topics of the individual chapters are too closely woven to-
gether to make it possible to read the chapters independently of one
another. Nevertheless, the reader who is interested in only a partic-
ular aspect of the subject is encouraged to plunge directly into the
relevant chapter. Even if one then encounters a reference to another
chapter, at least the details of the calculations carried out there will
be unnecessary for an understanding of the following chapters. Of
course, the beginning of every chapter offers the opportunity to start
over if the details of the previous chapter became too difficult.
The reader who wishes to keep the very abstract passages at a
greater distance might adhere to the following plan:
• In Chapters 1 through 6 the proofs in the set-off sections may