Fallacies in Mathematics

As Dr Maxwell writes in his preface to this book, his aim has been to instruct through entertainment. 'The general theory is that a wrong idea may often be exposed more convincingly by following it to its absurd conclusion than by merely announcing the error and starting again. Thus a number of by-ways appear which, it is hoped, may amuse the professional, and help to tempt back to the subject those who thought they were losing interest.' The standard of knowledge expected is fairly elementary. In most cases a straightforward statement of the fallacious argument is followed by an exposure in which the error is traced to the most elementary source, and this process often leads to an analysis which is often of unexpected depth. Many students will discover just how mathematically minded they are when they read this book; nor is that the only discovery they will make. Teachers of mathematics in schools and technical schools, colleges and universities will also be sure to find something here to please them.

Table of Contents:
Preface; 1. The mistake, the howler and the fallacy; 2. Four geometrical fallacies enunciated; 3. Digression on elementary geometry; 4. The 'Isosceles triangle' fallacy analysed; 5. The other geometrical fallacies analysed; 6. Some fallacies in algebra and trigonometry; 7. Fallacies in differentiation; 8. Fallacies in integration; 9. Fallacy by the circular points at infinity; 10. Some 'Limit' fallacies; 11. Some miscellaneous howlers.

Review :
'The scope is wide and the fallacies are examined at considerable depth. This book should provide a valuable stimulus to those who follow the byways of mathematics out of sheer interest. It deserves a place on the bookshelf of every teacher of mathematics at sixth form or equivalent levels, and will prove a useful addition to the mathematics section of the school or college library.' Technical Education 'Dr Maxwell is the unchallenged master of fallacious argument (if he will pardon this way of putting it), and his book must not be regarded merely as a diversion, a Chamber of Horrors, a manual of oddities. University teachers often complain that pupils leave school equipped with techniques but with little idea of what mathematics is really about, and also that they show poor appreciation of the need for logical precision … by showing mathematics in sickness this book can help teachers to show it in health.' Mathematics Teaching 'It is hard to imagine a more pleasant way of arousing a class to an appreciation of the importance and even the fascination of mathematical rigour. Besides, teachers will be well advised to master the book before it comes into the hands of pupils.' Technology 'Enjoyment as well as enlightenment is provided by trying to detect the fallacies, or at least by reading the solutions given by the author of this lovely little work.' Science 'This is a book for every sixth-form mathematics classroom, and indeed for anyone who is at all interested in mathematics. There is no other book like it.' The Times Educational Supplement