Magnificent Mistakes in Mathematics

August 1, 2013

Posamentier (mathematics education, Mercy Coll.) and Lehmann (formerly, mathematics, Humboldt Univ., Berlin), coauthors of several math books, present a compendium of mathematical errors, arranged by topic into five chapters. Only the first, on errors made by eminent mathematicians, has much narrative. Here, we see number-theoretic conjectures that were based upon a few examples and a lot of wishful thinking. In Chapter Two, the authors address errors in arithmetic based mostly upon misunderstandings of notations. Chapter Three deals with algebraic errors primarily caused by inadvertent division by zero or the introduction of extraneous roots. In Chapter Four we have errors in geometric proofs, mostly arising from deliberately misleading diagrams. The final chapter deals with probability, showing mistakes made by confusing the concepts of conditionality, independence, and mutual exclusivity of events. Many of the errors are clever and instructive, some are repetitive and uninteresting; only a few should be designated as "magnificent." VERDICT This volume could be useful to a teacher of mathematics as a source of examples that can hammer home important concepts. Beyond that, it will have a limited readership.--Harold D. Shane, Mathematics, Emeritus, Baruch Coll., CUNY

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