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Rating: 
Summary: Mathematical impossibility does not deter some people.
Review: 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.
Rating: 
Summary: The best math book of 1992
Review: 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.
Rating:
Summary: A very fun book
Review: 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.
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