the limit of what is worth learning about mathematics? Where is
mathematics to be found in the “real world”?
In two years I was able to cover a wide spectrum of topics, as
can be seen from a perusal of the table of contents. There is the
contemporary and there is the classical; there are hors d’oeuvres and
main courses. And in many places the reader will learn how math-
ematics penetrates our lives, whether in the lottery, cryptography,
computer-aided tomography (CAT), and the evaluation of securities
Even before the ﬁnal column appeared, I received a proposal from
the publisher Vieweg to collect the columns in a book. There were
many good reasons to begin at once. First, many regular readers of
the column had inquired about such a book. Second, a newspaper
column is conﬁned to a ﬁxed size, so that every column had to have
the same length, regardless of the topic.1 For some of the topics, the
space limitation meant that important information had to be omitted,
leaving the author with a guilty conscience. Therefore I am pleased
that the book format allows such limitations to be overcome. And
ﬁnally, the luxury of space in a book means that the word can be sup-
plemented by the image: photographs, drawings, graphs, tables. . . .
In writing the column there were three aspects that I considered
Mathematics is useful: It should be made clear why our tech-
nologically based world could not function without mathematics. A
label reading “mathematics inside” could be placed on many a prod-
Mathematics is fascinating: Aside from its utility, mathematics
oﬀers a very special intellectual appeal. The irrepressible compul-
sion to see the solution of a problem through to the end can release
enormous amounts of energy.
Without mathematics one cannot understand the world: Accord-
ing to Galileo, “The book of nature is written in the language of
mathematics.” At his time, that was no more than a vision. Today
it is known that mathematics is the bridge that leads us across the
least that is what the author was told. Every now and then, the exigencies
of the page layout required that the column be trimmed a bit.