Ito K. (ed.) Encyclopedic Dictionary of Mathematics

Second Edition by the Mathematical Society of Japan. — MIT Press, 1993. — 2171 pp. — ISBN 978-0262590204This second edition of the Encyclopedic Dictionary of Mathematics is in substance an English version of the second edition of Iwanami Sügaku Ziten (in Japanese). We shall explain how these two versions are related to each other and how the present edition differs from the first English edition. For the sake of simplicity we abbreviate Encyclopedic Dictionary of Mathematics and Iwanami Sügaku Ziten to EDM and ISZ, respectively, and indicate the numbers of editions beyond the list by Arabic numerals.
The prefaces of the previous editions will clarify how ISZ, its augmented edition, ISZ2, ISZ3, and EDM came into existence in 1954, 1960, 1968, 1985, and 1977, respectively. EDM, published nine years later than ISZ2, consisted of its English translation and some new materials added to update its contents. In retrospect, it was felt that this procedure was not adequate to cope with the recent rapid progress of mathematics, and a suggestion was raised in the Mathematical Society of Japan that ISZ3 and EDM2 be produced simultaneously. The favorable reaction of the mathematical public to EDM encouraged us greatly. In 1978 an agreement was made among the Society, Iwanami Shoten, Publishers, and The MIT Press for the publication of ISZ3 and EDM2 . An editorial committee was established in the Society with the members named in the preface to ISZ3 . Manuscripts were prepared simultaneously in Japanese and English by each contributor, with Yuji Ito acting as linguistic consultant.
The English translation of this second edition published by The MIT Press has achieved international recognition. In the meantime, remarkable progress has been made in mathematical sciences: recognition of the interrelationships amongst various branches within mathematics has increased significantly, and the formulation of mathematics as a synthetic entity is in the making. Furthermore, advanced mathematical theories have been utilized frequently in the physical, biological, and social sciences, and expectations for mathematics to be the basis of a11 the sciences have been increasing. In order to cope with these developments, it was decided that the second edition of Sügaku Ziten should be further revised and an updated version be published as the third English edition.