The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip (First Published in Great Britain in 2000 by Weidenfeld & Nic) (Hardcover)

by Keith Devlin (Author) "I HATED MATHEMATICS when I was in elementary school..." (more)
Key Phrases: hominid brain growth, innate number sense, animal coat patterns, Linguistic Eve, Out of Our Minds, Mitochondrial Eve (more...)

Editorial Reviews

Amazon.com Review
For many, the mere word "mathematics" is enough to conjure memories of incomprehension at school, and fear and loathing ever afterward. Countless otherwise well-educated people see mathematics as the skeleton in their intellectual closet--the one key subject demanding a talent that they so obviously did not possess.

Or so it seems to anyone who has felt very much on the outside of the subject. British mathematician Keith Devlin is certainly on the inside, and in The Math Gene, he has wonderful news for everyone: we can all join him there. For Devlin argues that we all possess the ability to cope with mathematics--if only we recognize what's required. While a number of recent books, notably Stanislas Dehaene's The Number Sense, have focused on numerical ability, the scope of Devlin's book is much larger. He examines the evidence that we all possess, if not literally a gene, then at least an inherent ability not just for arithmetic but for real mathematics: algebra, calculus, and the rest. Devlin even puts forward a Darwinian explanation for the origin of this ability, based on the idea that being able to handle abstract ideas and relationships confers key evolutionary advantages.

Mathematics merely involves a relatively high level of abstraction--but one we can all cope with, if we work at it. "Doing mathematics is very much like running a marathon," writes Devlin. "It does not require any special talent, and 'finishing' is largely a matter of wanting to succeed."

In its wealth of wonderful examples supporting the central argument, The Math Gene bears comparison with Steven Pinker's The Language Instinct, and its plain common sense about this most misunderstood of subjects is inspirational. Thoroughly recommended for anyone seeking to rid their intellectual closet of the skeleton of mathematical "incompetence." --Robert Matthews, Amazon.co.uk

From Publishers Weekly
Recently, luminaries like Steven Pinker have shown lay audiences neat theories about how language works and how our "language instinct" evolved. In the same years, writers like David Berlinski have made higher math entertaining and accessible. Here, prolific math writer and NPR commentator Devlin (The Language of Mathematics) has joined these two strands of popular science writing. Using up-to-date cognitive psychology, along with the history of math, Devlin aims to unfold our "innate sense of number" and to show what it has to do with language. He also hopes, more ambitiously, to win readers over to his own hypothesis about how our language and math "instincts" arose. Experiments show that chimps, like us, "use symbols to denote numbers," though human toddlers are far better at it. Combining a number sense with symbolic abilities, we use abstractions to manipulate quantities, leading to arithmetic and potentially to calculus and number theory. After several stellar chapters devoted largely to psychology experiments, Devlin switches gears to higher math, giving examples of how abstract models describe concrete thingsAfrom rotating clock faces to rattlesnake skins. The book takes another sharp turn, into the stimulating but quite crowded field of hypotheses about how our brains came to be. While responsibly laying out several hypotheses, Devlin favors the idea that enhanced symbolic abilities let early hominids think "off-line," asking and answering "what if" questions about tools, predators, habitats or prey. Some may wish Devlin had written two booksAone about math and language, the other about language and evolution; the former would likely ace the latter. Most readers, though, will appreciate the broad, accessible syntheses he does provide. 35 illus. (Sept.)
Copyright 2000 Reed Business Information, Inc.

See all Editorial Reviews

Product Details

• Hardcover: 328 pages
• Publisher: Basic Books; 1 edition (January 15, 2000)
• Language: English
• ISBN-10: 0465016189
• ISBN-13: 978-0465016181
• Product Dimensions: 9.8 x 6.5 x 1.2 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 3.3 out of 5 stars See all reviews (23 customer reviews)
• Amazon.com Sales Rank: #1,036,848 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

19 of 20 people found the following review helpful:

5.0 out of 5 stars An exploration into the origins of mathematical ability, October 4, 2000

By A Customer

Devlin's "The Math Gene" is a wonderful book, well worth reading if you've an interest in how we think, and absolutely essential if your interest extends further to why we can do mathematics.

This is an intriguing question. After all, it's a fairly new part of human behavior - having been around maybe 10,000 years - that we all can do, at least a bit, and the rest of the animal kingdom can't, at least as far as we know.

Devlin's the first mathematician I know of who's looked deeply into this subject using recent research in the area; he's done a great job fitting the available data to a theory that starts to answer the question, how it is we can do mathematics?

First, though, you have to understand what mathematics really is. Devlin's definition is the "science of patterns" and he explains clearly and convincingly why it's the right one.

His premise, roughly, is that however we acquired language, and he stays mostly on the sidelines of the heated debates about that, mathematical ability came along for the ride. His reasoning is that "off-line reasoning" is an essentially equivalent to language, as you can't have one without the other, and that this plus some other abilities, such as a number sense and spatial reasoning, give us the ability to do mathematics.

He then explains why so many of us find the subject difficult. A simplified version is that we use language mainly to talk about interpersonal relationships. In a word, gossip. Note he's not claiming this to have been the purpose for it's development, just that it's what we mostly do with it now. And we're very good at gossiping. In fact, it's so easy we consider it to be a form of relaxation. To Devlin, you need to have the same kind of relationship with mathematical objects in order to be able to work with them.

The book's greatest strength, to my mind, is its gathering of results in cognitive psychology into a coherently developed thesis regarding the origins of mathematical ability. It's a worthy contribution to the discussion, even if the theory proposed is completely wrong, as it may well be. Devlin's open and clear about it being highly speculative.

I do have quibbles, but they're just that. Its major weakness, if the book can be said to have any, is that it doesn't make much by the way of predictions based on his theory, which would make it far more convincing. But this is a terrific starting point for other work.

27 of 31 people found the following review helpful:

4.0 out of 5 stars Fascinating, untestable, and plausible. Recommended., December 31, 2000

By	Mike Christie (Austin, TX USA) - See all my reviews (REAL NAME)

"The Math Gene" presents a theory of how mathematical ability and language are related, and how they might have evolved. Devlin starts by separating "number sense" from mathematical ability. Many animals as well as humans can estimate the quantity of something; rats can be taught to press a lever about sixteen times to get a reward. The "about" is significant though; it's an estimate, not an exact count, as far as the rats are concerned. So if number sense and mathematical ability are not the same, what else is needed for mathematics? Devlin lists eight other attributes, including algorithmic ability, a sense of cause and effect, and relational reasoning ability.

Then there's a fairly long discussion of mathematics from the inside--are mathematician's brains different? What is it mathematicians do?--including a moderately detailed description of the basics of mathematical groups. I think Devlin does this to provide non-mathematicians with a sense of what mathematics is about, to make the rest of the book more plausible. This section is well-written and fluent, but I found myself getting a little impatient for the meat of his argument, which comes in the last half of the book. I suspect any reader with a good mathematics background would react the same way.

The next piece of the argument is to demonstrate that language is unlikely to have developed solely as a result of evolutionary pressure towards communication. This is a subtle point I haven't seen made before, but Devlin (who acknowledges his debts to other workers in this area) makes the case quite convincing. In summary: apart from extremely simple messages like "Danger!" and "Mammoth here" you can't communicate what you don't have a mental representation of. The evolution of communication can't have driven representation; it must have always lagged a half-step behind. So mental representation must have evolved first. I am not doing this argument justice here, but Devlin buttresses it well.

The inference is that language is simply a natural but lucky result of our ability to represent the world in our minds. Devlin's key point, however, is that since mathematics is essentially the ability to construct and work with increasingly abstract representations, the same mental changes that gave rise to language have also given rise to mathematics. His conclusion is that we all have the ability to do mathematics: there is no "math gene" except in the same way there is a "language gene": it's universal.

As a side note, not critical to his main argument, he points out that the most likely reason for the growth of representational ability in human brains was to foster understanding of other humans in the group; to encourage a sense of group-ness. For a creature that was more effective in group actions (e.g. hunting) there would have been a strong evolutionary advantage to having an emotional investment in the success of the group. Hence much of the early use of this ability would have been to represent others in the group; when language was added, it would have enabled people to talk about each other. In Devlin's words, "Having arisen as a side-effect of off-line thinking, language was immediately hijacked to facilitate gossip." (Off-line thinking is used to mean representational thinking that doesn't result in or from actions in the immediate environment.)

Two particular items in the book are worth mentioning. One is a followup to some famous experiments done by child psychologist Piaget in the 1930's. Piaget thought he'd demonstrated that children don't acquire a fully-developed number sense till around six years old. More recent work has demonstrated that children are much smarter than Piaget realized: there was a subtle and fascinating methodological flaw in Piaget's experiment. The second item is a little test of logical reasoning, presented with four cards on a table. Even mathematicians, who will probably get the test right, may be surprised at the coda to the test, which forms one of the few methods of direct verification of Devlin's claim that everyone can do mathematics.

The case is well-argued, but one problem with theories like these is that there *are* so few ways of finding out if they're true. "The Math Gene" is reminiscent of Julian Jaynes' "The Origin of Consciousness in the Breakdown of the Bicameral Mind" in this way; a fascinating argument that we may never be able to test. However, it's thought-provoking and plausible, and left me, at least, convinced of its likely truth.

26 of 32 people found the following review helpful:

1.0 out of 5 stars A poor rehash of old ideas, amatuerishly presented, February 24, 2001

By A Customer

Like a lot of people, I've been augmenting my reading lately with many of the scientific popularizations that have been coming out on neuroscience, biology, linguistics and information processing theory. These books generally fall into four camps: good science with bad prose (Edelman, Calvin, Llinas); bad science with good prose (Pinker, Bickerton, Lakoff & Johnson); good science with good prose (Deacon, Damasio's first effort, Tomasello, Ramachandran) and bad science with bad prose (anything to do with "memes" - and this book!)

Quite simply: no good argument here is new, and no new argument here is good (to paraphrase Samuel Johnson). For the "math gene" itself turns out to be nothing more than the "math version" of Chomsky's moribund and increasingly untenable "deaux ex machina" - an Innate and Universal Grammar, made even more implausible - if such a thing is possible at this late date - by the addition of Derek Bickerton's "catastrophic adaptation" model of how the "miraculous mutation" that "endowed" us with "syntax" (and thus with Universal Grammar and its "mathematical equivalent") took place.

Far worse from an intellectual standpoint is the uncredited and wholly superficial regurgitation of far more insightful authors' works, in particular Terrance Deacon, whose "Symbolic Species" is all but plagarized in the few coherent chapters of this book.

Too, it soon becomes obvious that the author of THE MATH GENE obviously never bothered to read any of the source materials. To give just one of many possible examples, the American philosopher C.S. Pierce posited eleven - not three - levels of interpretation between icon and symbol - but since Terrance Deacon (who is never credited anywhere in this book, not even in the bibliography, despite the many examples and their arguments - communication vs. language, symbol vs. index, the whole discussion of vervet alarm calls, etc. - that have been lifted whole from his work) deliberately limited his own discussion in The Symbolic Species to three, the author of THE MATH GENE dutifully reports that Pierce's orginal formulation was likewise three.

Lev Vygotsky similarly gets a perfunctory mention in the last two pages, though at no time throughout this book is any evidence whatsoever offered that would lead on to conclude that the author of THE MATH GENE has ever actually read any of Vygotsky's work (Vygotsky in that sense is becoming today what Freud was fifty years ago).

Finally, the author spends an unconscionable amount of time promising, heralding, and foreshadowing the upcoming appearance of his revolutionary explanatory "thesis" that - hold onto your hats for a mind-blowing challenge to 2500 years of received wisdom here - human beings are good at math beacuse the species has evolved a talent for "what I call 'off-line' thinking."

307 poorly written pages for that!

In short, I've read undergraduate students' term papers that had more original and well-argued thought.

And they cite their sources.