The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip [Paperback]

Keith Devlin (Author)

Book Description

Publication Date: May 17, 2001

Why is math so hard? And why, despite this difficulty, are some people so good at it? If there’s some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can’t we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it’s a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can’t we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don’t recognize when we’re using mathematical reasoning.

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 --This text refers to the Hardcover edition.

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. --This text refers to the Hardcover edition.

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Product Details

• Paperback: 352 pages
• Publisher: Basic Books; Reprint edition (May 17, 2001)
• Language: English
• ISBN-10: 0465016197
• ISBN-13: 978-0465016198
• Product Dimensions: 5.3 x 0.9 x 8 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (31 customer reviews)
• Amazon Best Sellers Rank: #398,238 in Books (See Top 100 in Books)

More About the Author

Dr. Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. (Archived at http://www.stanford.edu/~kdevlin/MathGuy.html.)

He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition.

He writes a monthly column for the Mathematical Association of America, "Devlin's Angle": http://www.maa.org/devlin/devangle.html

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Most Helpful Customer Reviews

25 of 26 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

Format:Hardcover

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.

29 of 33 people found the following review helpful

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

By Mike Christie

Format:Hardcover

"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.

8 of 9 people found the following review helpful

3.0 out of 5 stars Ok, So We All Have a Math Gene, But... December 20, 2005

By Allen Moore

Format:Hardcover

The author presents a carefully crafted theory of how language developed in humans, and links our innate mathematical abilities to this skill with language. Although his position is that everybody has some level of mathematical skill beyond number sense, he never really addresses in detail why some people have an aptitude for math and others don't, other than to mention the mathematician's ability to cope with abstraction.

This is the second book by Devlin I've read, and I'm impressed by his boldness in escorting the reader through difficult mental terrain. If you find the topic of language development interesting, and you're willing to exert some mental effort to keep up with his arguments, you'll find this book a thought-provoking read. However if you want to know why high-school algebra gave you such trouble, you'll have to look elsewhere for the answer.