The brief essays in A MATHEMATICIAN READS THE NEWSPAPERS (most are two to four pages) provide John Allen Paulos’ perspectives on how mathematics is used and misused in the popular media. Many of the essays discuss how reports of numbers are misleading or inaccurate. Misperceptions sometimes are created benignly, but writers with agendas sometimes choose to present numbers to their advantage. Writers wishing to boost the seriousness of some condition, for example, might provide absolute numbers, while those wishing to downplay the same condition might report percentages. Two thousand cases of an illness sound more serious than the same illness affecting less than .01 percent of the U.S. population.
Paulos also attacks approaches to news reporting. He is particularly critical of presentations of sets of opinions that give the impression of being representative when they are not. Such opinions might be obtained at the scene of an event at which only one side of an issue is represented or through a self-selecting process, such as calling a 900 number to express a viewpoint. Paulos asserts that such samples of opinions are samples of only the most vehement people on one or the other side of an issue.
The sections of the book parallel those of a newspaper. Paulos thus discusses mathematics in relation to national and international news; local news; business and social issues; lifestyle; science; and features, such as sports reporting and reviews. In each case, he cautions readers to be wary in reading numbers and bemoans the fact that numbers are not provided where they would be appropriate. He concludes by stating that journalists should be taught to address more than the traditional questions of who, what, where, when, why, and how; they should also discuss how many, how likely, and what fraction, as well as relating how quantities relate to other similar quantities and how quickly numbers are changing.
The mathematics applied in the book is relatively straightforward, and once Paulos provides the clues of what to look for, the problems in his examples of news stories became apparent. Although Paulos relies primarily on arithmetic, fractions, and percentages, he makes a few excursions into more advanced topics, such as chaos theory and game theory.