I attempt to find a few general encyclopedic works on computer science such that looking up relevant terminologies is easily available ready to hand. I'm not familiar with the whole picture of computer science so I can't describe precisely the delicate character of what is a good encyclopedic reference to computer science. But I could list some extremely distinctive and appropriate(at least for my part) encyclopedic works on mathematics so as to provide a comparable template as suggetions for indicating that what type of general encyclopedic works on computer science are what I really desire. Any suggetions are really appreciated.

Some famous and useful Encyclopedias of Mathematics:

1. Encyclopedia of Mathematics

Encyclopedia of Mathematics(EOM for short), published by Kluwer Academic Publishers in 2002, maintained by Michiel Hazewinkel. The encyclopedia has been translated from the Soviet Математическая энциклопедия (Matematicheskaya entsiklopediya) (1977, Moscou, Sov. Entsiklopediya) originally edited by Ivan Matveevich Vinogradov. References listed in many articles seem heavily weighted in favour of Russian mathematicians, reflecting the works Russian origins. You can really consider EOM as professional, comprehensive and up-to-date reference or manual of Mathematics because at present EOM possesses its own online wiki. It's open access and you can look up through the following link: EOM, which is maintained by Springer, in cooperation with the European Mathematical Society. EOM is currently the most comprehensive, professional and up-to-date ONLINE mathematics reference work.

2. Encyclopaedia of Mathematical Sciences

Encyclopaedia of Mathematical Sciences(EOMS for short), published by Springer-Verlag. The series started as a joint effort with the Soviet publisher VINITI, and it then became the famous and high-quality mathematical Encyclopaedia, which presented a series of surveys in contemporary mathematics written by/with the cooperation of the foremost specialists worldwide. For example, one could have a look at this very good survey volume Basic Notions of Algebra(really appropriate for everyone to get a bird's eye view of the totality of modern algebra) written by a master Igor R. Shafarevich. The articles contained in volumes of EOMS report on a variety of topics in terms of the major concepts and results, without giving details of proofs. So if you find the explanations of some topic in EOM are not so deep and detailed you could try to consult EOMS alternatively.

3. 岩波数学辞典

岩波数学辞典(Iwanami Sūgaku Ziten, ISZ for short), published by 岩波書店(Iwanami Shoten). The 2nd and 3rd Japanese original edition had been translated into English volumes with title Encyclopedic Dictionary of Mathematics(EDM for short; Note: EDM_1=ISZ_2, EDM_2=ISZ_3). The latest Japanese revised version is the 4th edition(i.e., ISZ_4) and it has no other language translations so far.

First of all, it's well worthy of going through the following paragraphs extracted from the prefaces of ISZ_1 and ISZ_2 written by S.Iyanaga:

``One of the characteristics of 20th-century mathematics is the conscious utilization of the axiomatic method and of general concepts such as sets and mappings, which serve as foundations of different theories. Indeed, mathematics is being reorganized on the basis of topology and algebra. One such example of reorganization is found in Bourbaki's Eléments de mathématique; ...This encyclopedia, with its limited size, cannot contain proofs for theorems. However, we intend to present a lucid view of the totality of mathematics, including its historical background and future possibilities. Each article of this encyclopedia is of medium length sufficiently short to permit the reader to find exact definitions of notions, and sufficiently long to contain explanations clarifying how important concepts in the same field are related to each other.''

``It's an encyclopedic dictionary with articles of medium length aimed at presenting the whole of mathematics in a lucid system, giving exact definitions of important terms in both pure and applied mathematics, and describing the present state of research in each field, together with historical background and some perspectives for the future.''

The above citations might be distilled into two crucial points:

  • Embracing Bourbaki's point of view on mathematics. The domain of mathematics has been becoming a tower of Babel, in which autonomous disciplines have been becoming more and more widely separated from one another, not only in their aims, but also in their methods and even in their language. Bourbaki, which is in fact the collective pseudonym of a group of younger French mathematicians with a deeply integrative sense of mathematics who set out to publish an encyclopedic work covering most of modern mathematics, undertook the task of presenting the whole picture of mathematical knowledge in a systematic and unified fashion. The right paradigm or pattern of doing mathematics in the light of Bourbaki's philosophy is to recognize, specify and study the diverse structures. Bourbaki regards mathematical research as a research of structures in relation to three mother-structures which are precisely algebra, topology and order. Actually algebraic and topological structures are indeed two of the most important mathematical structures, and algebra and topology were probably the branches on which Bourbaki exerted his most profound influence. However, good structuralist approach does not search for the formal structuralism(just as done in Théorie des ensembles), but for the right structuralism(just as done in Groupes et algèbres de Lie). ISZ assimilated, to the greatest extent possible, the best of Bourbaki's structuralist ideas, i.e., the algebra & topology-based structuralist approach.

  • Adopting the organization method of ``Article with Medium Length''. Here the Article is exactly the incarnation of the Entry in Encyclopedia. Keep this equation Article = Entry in mind. The text of ISZ_4, on the one hand, puts the whole of mathematics into 23 divisions(regarded as 23 branches of mathematics), for example, IV theory of numbers, VI algebraic geometry, on the other hand, consists of 515(i.e., the numerical order in Systematic List of Articles(SLA for short)) articles arranged alphabetically. Most of these articles are divided into sections, indicated by A, B, C, ..., AA, BB, .... Citations in the indexes are also given in terms of article and section numbers. We might consider the classification scheme mentioned above as an ISZ Tag System. Every article or section of article is tagged with a unique symbol sequence. Take an example for brief demonstration: the section generalized Jacobi variety is numbered 261 (VI-2) H, which means that the path of the item on generalized Jacobi variety in the ISZ Tag System is designated by SLA-261/division-VI/article-2nd/section-H. Adopting the Article with Medium Length in the sense of ISZ endows the dimension of article or section of article with flexibility in organizing them with scalable length.

Compared to the ISZ_3, the ISZ_4 edition adds more than 140 new entries, and many of the older entries have been either completely deleted or substantially revised. The number of entries has increased from 450 in the ISZ_3 to 515 in the ISZ_4. The new added entries are mainly related to the modern and mainstream concepts, the prominent and extraordinary achievements obtained in the second half of the twentieth century. ISZ_4 is as complete and comprehensive a magnum opus as one could wish for. It's succinctly but thoroughly covers all areas of mathematics, from the basics to the most advanced, for instance, the latest results such as Fermat's theorem and Poincaré conjecture, as well as an ever-expanding range of applications in recent years.

Within its 2000-plus pages(2016 pages in the 4th Japanese edition, 2007) are elegant explanations of Riemann surfaces, Fourier series, Hodge theory, l-adic cohomology, and so forth. What's more, many of entries start at elementary level, builds into intermediate level and culminates with advance level. Each entry is accompanied by a list of the most recent references. In addition to the 515 entries, a detailed index serves as a collection of technical terms. So it's very convenient to look up terminologies occurring in your specific textbook in hand, which seems somewhat like you making use of a word dictionary such as the OED. You could thus get a lot of pleasure out of reading those well written entries, many of which are treated in depth, and require solid mathematical background and great maturity on self-study. The ISZ_4 as an excellent reference will definitely meet the expectations of those people who are specialist or common researchers working at the doctoral level, as well as readers who are involved in mathematics in some way.


1 Answer 1


The art of computer programming by Don Knuth is more similar to the Bourbaki type work you mention (containing more than an encyclopedia). It is currently one of the best resources available on CS and akin to Euclid's elements for geometry. For a young field such as computer science (less than a century as a scientific area) it is arguably one of the most complete overviews of key aspects of the field (though by no means all encompassing).

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    $\begingroup$ Thanks a lot for your recommendation. I'll take a look at Don Knuth's classic series. I once read his another nice book with title Concrete Mathematics with which I was impressed. $\endgroup$
    – GL_n
    Commented Dec 4, 2021 at 15:20

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