xxvi Introduction

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

options.

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

important:

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-

uct.

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

1At

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.