Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics

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. (Sept.)