Customer Reviews

Mathematical Cranks (Spectrum)

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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.

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.
A fascinating description of disturbed personalities that somehow found their way to mathematics, Mathematical Cranks is entertaining and thought provoking. It is the most interesting book that I have read this year.

Published in Journal of Recreational Mathematics, reprinted with permission.

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.

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.

On the one hand, mathematics is the great leveler of the sciences. Anyone can do mathematical research, with no equipment but pencil and paper. On the other hand, mathematics is the only science where something can be proven, irrefutably and for all time, to be impossible. These two ingredients make mathematics one of the most fertile grounds for inspiring crankery.

This book is not only entertaining, the broadness of its examples provides a fascinating insight into the mind of cranks. I couldn't put it down.

The author means well but is himself a crank. Albert Einstein said, "From the very beginning there has always been present the attempt to find a unifying theoretical basis for all these single sciences, consisting of a minimum of concepts and fundamental relationships, from which all the concepts and relationships of the single disciplines might be derived by logical process." Would the author call Einstein a "neo-Kantian"? Doubtful, but that's what he calls supporters of Dewey B. Larson--and these actually follow the philosophical teachings of Samuel Alexander, not Kant. Obviously the author has not carefully studied Larson's Reciprocal System--if he had, he would not have labeled Larson's work that of a "conceptual" crank. The real cranks in science are the modern physicists and astrophysicists who've given us the nuclear theory of the atom, black holes, worm holes, neutron stars, string theory, and quarks. It's time for real scientists to take their profession back from the fruits and nuts.