The enormous increase in mathematical activity and knowledge during the past half century has not been achieved without a corresponding increase in the number of terms which mathematicians use. Not only have names had to be given to new concepts and objects, for example categories and functors, but there has also been a need to attach new and/or more precise meanings to certain terms such as ‘function’ which have been used, in some sense or other, for centuries. Again, deeper insight into mathematical structure has often yielded an alternative way of approaching such well-established ideas as that of a derived function. This creation of new definitions and rewriting of old ones has not made life any the easier for the reader of mathematics. Certainly, an explanation of any of the terms can be found somewhere, but finding the correct source can be time consuming. The attractions of a reference book of definitions are, therefore, obvious.

Alas, the difficulties of compiling such a work are no less obvious! As soon as such a book were to appear it would be months out of date, for each issue of every mathematical journal can be expected to introduce at least one new term to the vocabulary of mathematics and frequently a new symbol – or an alternative usage of an old one – to accompany it. Moreover, talents equal to those of the troops of Bourbaki would be required to produce a comprehensive and authoritative work.