Everything counts: Margaret Wertheim
The Mathematical Brain by Brian Butterworth
446pp. Macmillan. £20.
0333735377
Times Literary Supplement
December 24th 1999: Page 24How 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.The Guardian
The Washington Post
Scientific American
Nature
The Financial Times
Dr.Jonathan Miller
Professor Steve Jones
Dr. Oliver Sacks
Times Literary Supplement
London Review of Books
American Scientist
abcnews
Journal for Research in Mathematics Education
British Journal of Healthcare Computing & Information Management
Plus Magazine
amazon.com
Kirkus
Summary