Try holding up your fingers to represent the number three. The result is more informative than you
might expect, as Brian Butterworth demonstrates in "The Mathematical Brain" (Papermac, 446
pages, published in US as "What Counts", Free Press). If you flourished your index,
middle and ring fingers, he states, you are from Northern Europe or one of its former colonial
outposts; if instead you raised your thumb, index and middle fingers, then you hail from the
Mediterranean.

This simple test shows that cultural difference plays an important role in the ways people
formulate numbers. So is numeracy solely a learnt skill? Certainly not, argues Butterworth, who is
a neuropsychologist: his invigorating book fleshes out an idea that number knowledge is innate
and universal, a basic capability to be ranked alongside seeing and feeling.

According to his hypothesis, we are born with a mathematical toolkit genetically hardwired into our
brains, which Butterworth calls the Number Module. Its operation is automatic, enabling us "to
categorize the world in terms of numerosities - the number of things in a collection." A baby, for
instance, will have no idea of what pineapples are, but should be able to identify that there are
two of them. More advanced abilities, from puzzling over restaurant bills to solving Fermat's last
theorem, are built onto this starting-point, and the scale of their development depends mainly on
cultural factors.

Butterworth sets out his case by first exploring the origins of number perception. It is a dazzling
tour, stretching back to prehistoric times, in which he elucidates the etymology of number words,
the emergence of Arabic numerals and the use of body-parts as counting aids. Non-linguistic
methods of keeping score are embedded in the terms many people use to describe numbers:
indeed, "score" is one such example, as is "digit".

In subsequent steps, he attempts to isolate the part of the brain in which the Number Module
might reside. This involves work with individuals who suffer from forms of number-blindness: a
stroke sufferer, for example, who could only count to four. Similar examples of localised brain
damage allow him to isolate a particular lobe, which in turn leads him to discuss why some people
loathe maths and others love it. Forcing blank-eyed children to learn multiplication tables by rote,
it turns out, is not the best way to stimulate further interest in the world of numbers.
Butterworth's book is itself the perfect panacea for anyone to whom maths is a distant or
unpleasant memory. Despite its complexities, he handles his subject matter with great deftness
and good humour, while his argument sweeps in epic style from mathematical habits around the
globe to the inner working of the brain's hemispheres.

Ludovic Hunter-Tilney

© The Financial Times, 2000