Foreword

Summary

Mathematics is a dangerous enterprise. Through hard experience, mathematicians have learned to subject even the most “evident” assertions to rigorous scrutiny, as intuition and facile reasoning can often lead them astray. However, the impossibility and impracticality of completely watertight arguments make it possible for errors to slip by the most watchful eye. They are often subtle and difficult of detection. When found, they can teach us a lot and can present a real challenge to straighten out.

For the mathematics teacher, one source of such errors is the work of students. While students are responsible for a certain amount of plain nonsense, a few more thoughtful ones make “good” mistakes that on the face seem to compel assent; sometimes it may only be a vague hunch of something not quite right that induces a marker to look more closely. Occasionally, a text book will weigh in with a specious result or solution. Presenting students with faulty arguments to troubleshoot can be an effective way of helping them critically understand material, and it is for this reason that I began to compile fallacies and publish them in the Notes of the Canadian Mathematical Society.

Almost a dozen years ago, I persuaded the editors of the College Mathematics Journal to publish a regular department devoted to fallacies and so provide a regular outlet for them that did not seem to exist elsewhere. The catchy title, Fallacies, Flaws and Flimflam came from the editors, Professors William and Ann Watkins.