`Creative mathematics' – real or rhetoric?

The notion of creativity has its natural home in the fine arts, where the artist literally creates something that can be perceived by the senses. The products of mathematical activity are clearly not of this kind, yet some distinguished mathematicians have claimed that mathematics offers considerable scope for creativity. The title of the book under review, and some claims to be found in it, suggest that creativity can indeed be associated with mathematics, and that young children may experience it in the classroom. We suggest that the word creative is being used in rather different senses in these different contexts, yet the meanings associated with the arts, say, are in danger of being applied to mathematical situations for rhetorical purposes.This revised version was published online in September 2005 with corrections to the Cover Date.