[1] The "top ten" of these topics, as listed by reviewer Ian Stewart, are, in order: Other common topics for crankery, collected by Dudley, include calculations for the perimeter of an ellipse, roots of quintic equations, Fermat's little theorem, Gödel's incompleteness theorems, Goldbach's conjecture, magic squares, divisibility rules, constructible polygons, twin primes, set theory, statistics, and the Van der Pol oscillator.
[4] The book also attempts to analyze the motivation and psychology behind crankery,[1] and to provide advice to professional mathematicians on how to respond to cranks.
First, it found that by publishing his work on Cantor's diagonal argument, Dilworth had made himself a public figure, creating a higher burden of proof for a defamation case.
[6] Reviewer John N. Fujii calls the book "humorous and charming" and "difficult to put down", and advocates it to "all readers interested in the human side of mathematics".
[2] Although complaining that famous mathematicians Niels Henrik Abel and Srinivasa Ramanujan might have been dismissed as cranks by the standards of the book, reviewer Robert Matthews finds it an accurate reflection of most crankery.