Nature
"The quality of mathematical exposition is high, a sense of excitement is strongly conveyed."

From Booklist
Pledged by a wealthy amateur math enthusiast, $1 million per problem awaits whoever can solve the seven problems mathematician Devlin describes in this work. A similar proposition, minus the money, was made in 1900 by the German mathematician David Hilbert, who listed two dozen math mysteries he hoped would be dispelled in the coming century. All but one were, and that one, called the Riemann hypothesis, carries over to the new set of conundrums. The Riemann hypothesis is comprehensible to an advanced high-school math student, thanks to Devlin's clarity as well as his experience in popular exposition as the author of books such as The Math Gene (2000) and NPR's explainer of all things mathematical. As to the rest of the conjectures, Devlin directly states that no one without a doctorate could understand them, let alone crack them. But as a skilled guide pointing out the shape of the problems, and the practical implications of their solutions, Devlin's intriguing book will appeal to the lay reader curious about the abstract frontiers of math. Gilbert Taylor. Copyright © American Library Association. All rights reserved

From School Library Journal
In May, 2000, the Clay Mathematics Institute posted a million-dollar prize to anyone able to solve any of what it considered the seven most important mathematical problems of the 21st century. They were chosen not for theoretical beauty alone, but because many of them deal with concepts in fields like physics, computer science, and engineering, and exist because practitioners in those fields are already using theoretical or practical design solutions that have not been mathematically proven. Devlin, "The Math Guy" from NPR's Weekend Edition, does a good job explaining the background of the problems and why theoretical mathematics as a discipline should matter to a general audience. Each problem has a chapter of its own and is given a treatment that, where applicable, extends back to the ancient Greeks. A passing knowledge of mathematics is important for taking in Devlin's work but a major in the subject is not, and this book should satisfy anyone looking for a layman's guide to modern theoretical mathematics. Or hoping to win a million dollars. Sheryl Fowler, Chantilly Regional Library, VA

SELECTED REVIEWS FOR
The Math Gene

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 things—from 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 books—one 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.
Copyright 2000 Reed Business Information, Inc.

From Library Journal
This book is not about mathematics or genetics or why some people are good at math and others are not. Rather, Devlin (Goodbye, Descartes) asks and attempts to answer the question, "How and why did human beings evolve the ability to do mathematics?" His point is that mathematics is more than arithmetic. Real mathematics involves making logical arguments about abstract objects. Devlin briefly outlines Chomsky's theory that we are all born with "hard-wired" linguistic ability. He then explains that the mental process of making logical connections between abstract objects and the mental process needed to construct sentences have the identical structure. Thus, we can see that the genetic heritage that gives us all the ability to communicate by language also gives us the ability to do mathematics. I am convinced that Devlin is correct, and, if you read this book, you will be, too. For all math and science collections. Harold D. Shane, Baruch Coll. of CUNY
Copyright 2000 Reed Business Information, Inc.

Bookpage
"I am hooked again. Mathematics is understandable."


Ian Stewart, author of Nature's Numbers and Life's Other
". . . an instant antidote to math phobia and a pleasure to read."

SELECTED REVIEWS FOR
INFOSENSE

Pending...

SELECTED REVIEWS FOR
Mathematics

Mathematical Association of America
Excellent . . . . He presents us with a series of colorful personalities and seminal ideas [and] conveys all of the power, beauty and excitement of mathematics . . . . Well-written, informative.

SELECTED REVIEWS FOR
Goodbye, Descartes

From Booklist , January 1, 1997
Devlin traces the history of logic, particularly mathematical logic, over two-plus millennia and the shorter history of Chomsky's Cartesian linguistics to explain why at least some "mathematicians and scientists have come to realize that the truly difficult problems of the information age . . . concern ourselves what it is to think, to reason, and to engage in conversation." Despite their remarkable accomplishments, he argues, logic and linguistics don't adequately explain the most characteristic human acts. (Thus, artificial intelligence seems beyond our reach.) Logic and linguistics (and Western culture itself), Devlin maintains, are limited by the eternal "desire to explain knowing how in terms of knowing that, to reduce skills to facts and rules, to explain the composite in terms of its constituents." But this approach ignores important issues; e.g., in linguistics, meaning, context, cultural knowledge, and the structure of conversation. Not a simple read, but accessible enough for the sort of reader likely to be drawn to this subject. Mary Carroll
Copyright© 1997, American Library Association. All rights reserved

"[Goodbye, Descartes] is certain to attract attention and controversy . . . a fascinating journey to the edges of logical thinking and beyond."—Publishers Weekly(P).

"A masterly survey of Aristotelian and Stoic logic, of George Boole's 19th-century "algebra of thought," [and] of the contemporary project to produce a talking computer."—Wall Street Journal.

"Superb historical analysis of how 'mind' and natural language came to be understood as products of a logic machine. . . . This is frontier science, conveyed by a practitioner who cares about and knows how to enliven the relevant history."—Wilson Quarterly.