Translated into English as the Encyclopedic Dictionary of Mathematics 2nd ed. (MIT Press), this edition represents a thoroughgoing overhaul of the previous edition, firmly established as a world-level dictionary. Not only have the stunning advances in mathematics since the publication of the previous edition, including the solutions to Fermat’s theorem and the Poincaré conjecture, been reflected in this edition, the section structure has been renewed and the coverage of applied mathematics in the dictionary has been expanded to other scientific fields and various social issues by, for example, creating a new section on applied analysis. To systematically summarize the whole of mathematics in one compact dictionary, this edition adheres to the subheading method employed from the first edition, adding more than 140 new entries to the previous edition to bring the total number of subheadings to 515. Formulae associated with topics such as Lie algebra, topology, trigonometry, differentiation, q-series, special orthogonal polynomial, and integral transform have been added to the appendices along with new information in the numerical tables. This dictionary is an indispensable companion not only for researchers and students majoring in mathematics but for everyone working in related fields.

Where formulae are displayed, the JapanKnowledge edition has adopted TeX to enable use of the online dictionary for everyday study and in writing papers and reports. The English, French and German terms corresponding to each headword are shown, making it possible to know the definitive term for translation when writing papers or making translations.

All the appendices in the paper edition are available for browsing. Features have been created in the main text and appendices for quick access to information being sought by inserting links for reference entries and in cases where definitions and explanations of technical terms are given in other entries.