How is it that *Homo sapiens* - evolved to meet the raw contingencies
of life on the African savannas - came to have brains capable of handling
calculus and trigonometry, or the arcane abstractions of topology and group
theory? The mystery of humankind's mathematical ability has become the
focus of intense research and speculation in recent years, as few of our
abilities seem so extravagantly unnecessary from a Darwinian point of view.
Brian Butterworth, Professor of Cognitive Neuropsychology at University
College London, is the latest to weigh in on this fascinating subject with
his new book, "The Mathematical Brain".

Until recently, Butterworth notes, significant mathematical ability was
regarded as a talent vouchsafed to relatively few individuals. One either
had it or one didn't, was the prevailing view - and most believed they
didn't. Butterworth wants to release us from this myth. At the heart of
this deeply humanist work is the message that the ability to do mathematics
is a primary human trait that every one of us possesses in abundance.
From his own research, and that of a growing group of scientists studying
both human and non-human facility with numbers, Butterworth has concluded
that "we are born with brain circuits specialized for identifying small
numerosities" - that is, the number of things in a group (such as the
number of deer at a water hole). He calls this set of circuits "the number
module", and it is, he writes, "the start-up kit for all our mathematical
abilities". As evidence for the innateness of at least some mathematical
ability, Butterworth surveys a wide swath of cultures and finds none in
which this ability is totally absent. The Aranda people of central Australia
have no words for numbers above three, but they answer the question "How
many?" by drawing lines in the sand. Likewise, the Yupno people of highland
Papua New Guinea have no specific number-words, but they count using
their bodyparts, including fingers, toes, facial features, and testicles.
No culture we know of is without a sense of number, Butterworth says.

There is even evidence that our *Homo erectus* ancestors were able
to count. Recent research has also revealed that babies only a few months
old are able to distinguish between one and two objects, and infants of
eighteen months can do simple addition and subtraction. Moreover, the
basics of a mathematical brain are not confined to humans; birds have
been taught to match numerosities by choosing a box with the same number
of dots as on a card, lions can count the number of foes in an enemy pride,
and a chimp named Sheba has learnt both to add and to use the first three
Arabic numerals.

But if nature provides us with the rudiments of a neuronal mathematical
machinery, that still leaves open the question of higher mathematical
function. For Butterworth, the key is not in neuronal structure but in
culture. Thus, New Guinea highlanders are no less mathematically able than
Westerners, they are just less practised, largely because, Butterworth
says, the contingencies of their environment have produced little pressure
for the development of this skill.

Likewise, Butterworth believes that mathematical geniuses of any culture
do not have different brains from the rest of us. The secret to being a
Gauss or a Ramanujan is practice, he says. As with great musicians, so,
too, great mathematicians spend vast amounts of ti playing with numbers,
learning their mathematical scales, as it were.

"Prodigies work very hard to learn the tricks of their trade." If all of
us - except certain stroke victims and those with rare neuron aberrations
(who form an invaluable research cohort) - have an innate mathematical a
ability then why are so many of us so bad at basic maths? According to
Butterworth, the answer lies in our educational system; most children
are taught mathematics in a way almost guaranteed to stamp out enthusiasm
for the subject. is particularly incensed by the practice of forcing ch
children to learn tables and rules by rote. What Butterworth would like to
see is revolution in mathematics education where focus would shift to
making maths fun and to reinforcing children's already sophisticated though
often idiosyncratic, mathematical intuitions and "street" learning.

Much of Butterworth's book covers similar territory to Stanislas Dehaene's
wonderful "The Number Sense" (reviewed in the *TLS* on September 11,
1998). Both conclude with call to arms for the revitalization of maths
education by building on, rather than denying children's innate number instincts.
Both should be read by anyone interested in the future of education.

© Times Literary Supplement, 1999.