Mathematics and the Real World

July 14, 2014
Buried in stilted writing, dramatic mischaracterizations of evolution, and superficial biographical asides of famous mathematicians and scientists, Artstein, professor of mathematics at the Weizmann Institute of Science, occasionally provides some interesting discussions about the creation of mathematical reasoning. Beginning with the Greeks and extending to the current day, he explores the changing meaning of mathematics while always asking about the practical implications of new ideas. But Artstein has a larger goal in mind, linking the development of mathematics to the theory of evolution. As he explains it, “The discussion will be accompanied by the constant presence of the question regarding the extent of the effect of the evolution of the human race on the development of mathematics and its applications.” In fact, however, evolution only makes cameo appearances and when it does it bears little resemblance to the theory accepted by modern biologists. Instead, Artstein promotes the decades-old, discredited view that group selection rather than individual selection is primary and that evolution works at the species level. He concludes with an attempt to explain the best way to teach mathematics, but does so in such a convoluted fashion that his main point is lost in the details.

August 1, 2014

Artstein's short history of mathematics emphasizes how the subject has developed concurrently with its applications in the real world, endeavoring to convey the essence of different areas of study with a minimum of technical detail. Although the subtitle promises that the discussion will center on the role of evolution in the making of mathematics, that relationship is tenuous throughout most of the book. However, in the last chapter the author makes his intent clear: the book is a plea to those who develop school mathematics curricula to recognize that the subject should be taught in a way that is consistent with how we think. Published mathematical papers are written as polished wholes, he points out, with definitions, propositions, logical arguments, and final proofs. However, that is not the way mathematical concepts are learned, nor is it the way new mathematics is discovered. We must recognize that evolution did not equip us with brains that process information in that formalistic manner and avoid presenting the subject to students in that way. (according to the author?) VERDICT This title is recommended for those who want to learn about math; it also gives solid advice to educators.--Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

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