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Mathematical Cranks (Spectrum) Paperback

ISBN-13: 978-0883855072 ISBN-10: 0883855070

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Product Details

  • Series: Spectrum
  • Paperback: 384 pages
  • Publisher: The Mathematical Association of America (September 1, 1992)
  • Language: English
  • ISBN-10: 0883855070
  • ISBN-13: 978-0883855072
  • Product Dimensions: 9.3 x 6.2 x 0.8 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #1,250,618 in Books (See Top 100 in Books)

Editorial Reviews


'A delightful collection of true accounts of individuals who claim to have achieved the mathematically impossible ... It is hard to put down and provides topics for an unending series of interesting discussions. The organization and breadth of the book are impressive, supported by a helpful index and a list of resources that encourage further explorations. A classic.' Choice

'Dudley Underwood extracts insights from an astonishing variety of examples.' Robert Matthews, New Scientist

Book Description

A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem) and people with very eccentric views (thinking that second-order differential equations will solve all problems of economics, politics and philosophy).

More About the Author

Underwood Dudley was born in New York City quite a number of years ago. He got bachelor's and master's degrees (mathematics) at what was then the Carnegie Institute of Technology. After working for a time for the Metropolitan Life Insurance Company, he gave up his promising future as an actuary to flee back to academia, attaining the Ph.D. degree (number theory) at the University of Michigan in 1965. After two years at the Ohio State University and thirty-seven at DePauw University (Greencastle, Indiana) he lay down his chalk and eraser and retired to Tallahassee, Florida, never again to grade a calculus test.

He has done quite a bit of editing in his time--the College Mathematics Journal for five years, the Pi Mu Epsilon Journal for three, the Dolciani Mathematical Expositions book series (six years), and the New Mathematical Library book series (three years). As a result he has a complete grasp of the distinction between "that" and "which" (very rare) and the conviction that no writing, including this, should appear before the public before passing through the hands, eyes, and brain of an editor. Take that, bloggers!

He believes that there is no greater achievement of the human intellect than mathematics, and that the study of mathematics provides great benefits, even to people who think that they hate it.

None of his four children or six grandchildren has entered the family business, but that's the way it goes.

Customer Reviews

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Most Helpful Customer Reviews

9 of 9 people found the following review helpful By Daniel H. Bigelow VINE VOICE on April 22, 2005
Format: Paperback
In this book, math professor Underwood Dudley catalogues the characteristics and errors of mathematical cranks. These are the people, usually mathematical amateurs, who believe they have done the impossible: squared the circle, calculated a different value of pi (or in some cases, several different values), and so forth. Math has the advantage over darn near every other human system that one can absolutley prove these people are wrong, but that doesn't stop a true crank.

I am no math whiz, and a lot of this book is over my head. But I am a crank enthusiast (if you are, too, the best World Wide Web cranks can be found at Crank.net, with which I have no affiliation). What interests me most in this book, other than Dudley's enthusiastic and deft writing, are his catalogues of crank behavior -- for instance, how they can go from enthusiastic amateur to demented conspiracy theorist rather than simply admit nobody's paying attention to them because they're wrong. The math-oriented parts of the book are interesting case studies, and the crank-oriented parts have general application to all cranks, even of the non-mathematical variety. This makes for a useful and entertaining book.
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6 of 6 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on April 22, 2004
Format: Paperback
It is a very rare occasion when a writer addresses a topic that is largely unexplored.
Add the additional condition that it be done in a thoughtful, engaging manner and a jewel is created. This is such a book. Few people, in and out of mathematics, realize that there are people who believe themselves capable of doing the mathematically impossible. They do exist, and Dudley describes them and their obsessions in a frank and engaging manner.
Thankfully, such people have always existed and hopefully that state will continue. For they are the ones who often provide the driving force for positive change. Unfortunately, some cross that ill-defined line and refuse to consider the evidence contradicting their claims. Many fail to understand that mathematical truth is incommensurate with physical theory. The proofs found in the Elements of Euclid are just as true today as they were when first written. The alteration of physical theory over time is largely due to the refinements of the experiments. Of course, this does not stop them from appealing to the changes that have taken place in physical theory over the years. The persecution of Galileo is often cited by cranks as an example of eventual vindication.
Even mathematicians are not immune to the disease of crankery . Some of the people described in this book possessed a high degree of mathematical education (including professors!), but even that failed to vaccinate them against this strange malady.
Since the vast majority of cranks are attracted to the simple problems of squaring the circle or trisecting the angle, the mathematical level is fairly low. Some experience in calculus is necessary to understand all of the material, although much of that written by the cranks is incomprehensible.
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5 of 5 people found the following review helpful By A Customer on December 29, 1998
Format: Paperback
Underwood Dudly's book is great fun, especially if if you have ever tried to argue with someone impervious to reason. His very funny tales of encounters with mathematical cranks will probably sound familiar. You will also learn a lot about mathematical and scientific reasoning along with hilarious examples of how not to do mathematics. The author's points on how to identify and avoid cranks can serve readers well in all walks of life, not just mathematics.
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4 of 4 people found the following review helpful By A Customer on January 7, 1999
Format: Paperback
A mathematical proof of the impossibility of doing something does not deter some people from claiming that they have done it. Dudley labels such people as cranks, and he describes many of them in this book. While the reading is entertaining, it is also somewhat depressing, in that no amount of logic or reason can convince a crank that their work is flawed. They give so many different reasons for why their work is rejected. Unfortunately, a crank never arrives at the real reason, namely that their work is simply wrong.
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