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Think of a number by Malcolm E. Lines, Hilger, pp 163, Pounds sterling
7.50 pbk

THIRTY years ago, Malcolm Lines was undergoing an oral examination in
an Oxford college. After successfully dealing with some questions relating
to Green’s functions in mathematics, he was asked by an eminent, but nonscientific
fellow of the college: ‘How would you explain one of these Green’s functions
you have been talking about to a medieval historian?’

Lines recalls this experience in the preface of Think of a Number, and
it underlines his laudable view that ‘someone who claims to understand,
and be excited by, any aspect of science – including mathematics – ought
to be able to pass on the essence of that knowledge with enthusiasm to any
reasonably intelligent layperson who is interested’. He certainly practises
what he believes in this eminently readable and thought-provoking book.

Lines is that rare author who conscientiously respects his claim ‘that
little or no prior knowledge of mathematics is required’. All that is necessary
is accepting that letters can stand for numbers, and an understanding of
the basic arithmetical operations plus the use of signs and indices. A useful
introductory chapter covers even these basic points in an intelligible way
for those who may have forgotten all their schoolwork. Some may hiccup at
the end of this chapter when – perhaps unnecessarily as it does not appear
again – but one respects the author’s trait of not ducking awkward issues
and of anticipating some of the questions that his writing stimulates.

Of course, the book does not read like a novel, and I (at least) had
to invest some mental effort to appreciate fully and follow some of the
concepts he introduces. But the author’s erudition makes this effort well
worthwhile.

Besides ‘intelligent lay persons’ the book should appeal to many mathematicallly
literate scientists and engineers. While there is a fresh look at perennial
topics such as Fibonacci numbers, statistics, map colouring, space-time
curvature and Gauss’s clock numbers, other sections deal with such matters
as hailstone numbers, cryptography and computer security problems, Golomb’s
rulers, chaos theory and fractals.

The author, a solid-state physicist who has worked on computers at Bell
Labs, is also fas cinated by what ‘number crunching’ with computers has
done for some previously intractable mathematical problems, and how it has
opened up new lines of research.

Peter Wymer is a freelance science writer.