Review by Choice Review
General histories of mathematics pose a formidable problem. One cannot expect to say everything, but how to choose what to exclude? How much mathematics is necessary to get the point across? What organizes the plethora of facts available? Grattan-Guinness is keenly aware of these problems; his solution is successful, lively, and rich. His choices revolve around the bulk of mathematics that requires discussion, namely, from post-Renaissance Europe. He gives short but adequately referenced accounts of mathematical progress outside Europe, especially in the periods from antiquity to the Renaissance. A special strength of this history is its account of applied topics, arguably indivisible from mathematical efforts in the 17th and 18th centuries. The notion of desimplification, how a mathematical model admits better and better details of the motivating phenomenon, organizes this part of the story nicely. Grattan-Guinness writes with wit and enjoyment throughout. The subtitle is a metaphor for the "stupendous variety" of mathematical activities, as well as the far-off place from which culture admires mathematics. As he writes, "unlike the real rainbow, mathematics stays still when approached, and readily admits the active inquirer into its world of many colours." A great place to begin; it deserves a place in every library. J. McCleary; Vassar College
Copyright American Library Association, used with permission.
