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

~ (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.

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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: #526,439 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.

22 of 27 people found the following review helpful:

1.0 out of 5 stars Useless and Weak Thesis, November 27, 2000

By	Gary Rubinstein "author of 'Reluctant Discipl... (New York, NY United States) - See all my reviews (REAL NAME)

As an avid teacher and student of Mathematics, I was excited by the title of this book. It seemed like it would demonstrate why all humans have an aptitude for Math, and maybe how those who are 'innumerate' could tap into this inborn potential.

Unfortunately, this is not at all what the book delivered. It was basically a description of the evolution of the Human brain, specifically with regard to language acquisition.

With about 30 pages left in the book, he finally launches into his Thesis, which is that we are natrually good gossips, and that Math, to real Mathematicians, is very much like gossip. Mathematicians know numbers like they are people, and know their properties and relationships deeply.

That was it. No clue as to how people who have struggled with Math can use this gossip ability to help them learn and appreciate Math at any level.

Really a disappointing book. Don't waste your time, as I did mine.