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The Penguin dictionary of mathematics (2nd edn) , edited by David Nelson. Pp. 461. £7.99. 2000. ISBN 0 14 051342 6 (Penguin).

The Penguin dictionary of mathematics (2nd edn), edited by David Nelson. Pp. 461. £7.99. 2000. ISBN 0 14 051342 6 (Penguin). This is an expanded second edition of a mathematics dictionary that does not seem to have been reviewed previously in the Gazette. Aimed at school and undergraduate mathematics students and interested non-specialists, the entries are of a uniformly high standard across all subject areas. They are clear, authoritative, upto-date (without being gimmicky) and unusual in a dictionary discursive rather than terse, so there are no cryptic one-line definitions which mystify rather than inform. The best dictionaries (and, make no mistake, this is one of the best) squarely address the 'four Rs' Recall, Revision, Reference and Revelation with a heady cocktail for the reader of things half-remembered, things now forgotten, things never learnt and things met in passing; thus they tend to offer 'two books for the price of one' by giving the definition sought together with an unsolicited tasty morsel. An unusual, and unusually attractive, feature of this dictionary is its biographical entries on well known (and some lesser known!) mathematicians: in the latter category I'd place Joseph Moxon (p. 287) who apparently published the first mathematical dictionary in English in 1679. Indeed, there is a refreshing historical awareness in the entries which both roots them in context and allows for unfinished business to be alluded to in a natural way: we thus learn (p. 4) that the trigonometric addition formulae were originally derived from Ptolemy's theorem and (p. 267) that the local connectedness or otherwise of the Mandelbrot set is an open problem.