xx Preface to the English Edition
a number of amplifying remarks (from which future German editions
will also proﬁt).
David has also added a number of observations of particular in-
terest to the English-speaking world, and if that weren’t enough, he
found a number of typographical errors in the German edition that
had somehow eluded everyone else.
In my opinion, his masterpiece is the translation of Chapter 20. In
second place are some of the chapter and section titles, such as “The
Butterfly That Fluttered By” and “Both a Borrower and a Lender
Be.” You can’t do much better than that.
I wish you, dear reader, much pleasure in perusing these “Five-
Minute” morsels of mathematics, and I hope that those among you
who may be skeptical about anything at all to do with mathematics
will be disabused of the beliefs that everything interesting has already
been discovered and that mathematics is nothing more than a bone-
dry collection of facts and techniques.