The Story of Mathematics

Richard Mankiewicz Princeton University Press/Cassell: 2001. 192 pp. $24.95/£18.99

Integrating maths: these images of a celestial chart (top), roman and ordinary numerals (middle) and particle tracks are aesthetically pleasing, but do they make mathematical ideas more accessible?

The Story of Mathematics guides the reader from prehistoric times to the era of 'chaos and complexity' in 191 lavishly illustrated pages, many of which are magnificent reproductions of mathematical documents, instruments or visual evidence of mathematicians' work. No wonder that, as the preface concedes, ruthless selection was needed in the material covered. Indeed, the author has devoted some attention to the mathematics of most periods, and every ancient tradition in particular. But the severe selection has had a notable effect on the range of topics covered. Mathematics in the twentieth century, for example, has mainly been boiled down to four chapters dealing, respectively, with games, modern art, machines and chaos. So what principles guided the choice of the “key developments in mathematical ideas” in given historical periods?

Richard Mankiewicz's main concern seems to be to bridge the gap between mathematics and the general 'culture'. First, by showing how the development of the mathematical sciences in each civilization was related to the historical context, Mankiewicz hopes to contribute to shaping a “scientific culture” today. This aim probably accounts both for the criteria used to select the mathematical topics and the presence of historical description that cannot always be easily related to mathematics. His second strategy to bridge the gap between the 'two cultures' is to show the long-standing interaction between 'artistic sensibility' and mathematics.

Mankiewicz's reasoning seems to be as follows: the beauty of mathematics can be made accessible through its visual aspects. “All ideas,” Mankiewicz claims, “are born of a vision.” Hence the multiplicity of illustrations in the book. One might wonder, however, what mathematical ideas and inner conceptual beauty are conveyed by aesthetically pleasing pages of writings that are reproduced without explanation, and whose artistic qualities remain unconnected to their content. Is this the sense of beauty that does justice to mathematical ideas? Is this the way in which we want mathematics to become an integral part of the culture? Such photographs don't seem the best way of showing how mathematicians use visual auxiliaries, such as figures and models, to work on mathematics and to illustrate or produce their ideas. That would seem to me to be a more adequate use of illustrations to convey ideas, a point I do not find addressed in the book.

On a more technical front, the book contains inaccuracies of fact and interpretation. To mention just two of them, it is not the case that, as Mankiewicz states, in Babylonian mathematics, “arithmetical calculations were handled much as we would today”. Moreover, one cannot speak without qualification of the “justifications” that Babylonian mathematicians gave to their procedure for solving quadratic equations. The bibliography, which contains an odd selection of titles, is given without dates or publishers' names. The lack of care given to the text contrasts strangely with the undeniable magnificence of the illustrations.