Klein's encyclopedia

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Klein's encyclopedia is a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Meyer were organizers of the encyclopedia. Its title in English is Encyclopedia of mathematical sciences including their applications, which is Enzyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen (EMW). It is 20,000 pages in length (6 v. published in 22 or 29 parts) and was published by B.G. Teubner Verlag, publisher of Mathematische Annalen. Today, Göttinger Digitalisierungszentrum provides online access to all volumes, while archive.org hosts some particular parts.


Walther von Dyck acted as chairman of the commission to publish the encyclopedia. In 1904 he contributed a preparatory report on the publication venture in which the mission statement is given.

The mission was to present a simple and concise exposition, as complete as possible, of the body of contemporary mathematics and its consequences, while indicating with a detailed bibliography the historical development of mathematical methods from the beginning of the nineteenth century.

The preparatory report (Einleitender Bericht) serves as the Preface for the EMW. In 1908 von Dyck reported on the project to the International Congress of Mathematicians in Rome.[1]

Nominally, Wilhelm Franz Meyer (1856 — 1934) was the founder president of the project and assembled part 1, "Arithmetic and Algebra", that appeared between 1898 and 1904.

Part 2, the "Analysis" series printed between 1900 and 1927 had coeditors Wilhelm Wirtinger and Heinrich Burkhardt. Burkhardt condensed his extensive historical review of mathematical analysis that appeared in the Jahresbericht of the German Mathematical Society for a shorter contribution to the EMW.

Part 3 on geometry was edited by Wilhelm Meyer. These articles were published between 1906 and 1932. Significantly, Corrado Segre contributed an article on "Higher-dimensional space" in 1912 that he updated in 1920. The latter was reviewed by T.R. Hollcroft.[2]

Part 4 of EMW concerned mechanics, and was edited by Felix Klein and Conrad Müller. Arnold Sommerfeld edited part 5 on "Physics", a series that ran until 1927.

Part 6 included two sections: Philipp Furtwängler and E. Weichart coedited "Geodesy and Geophysics", which ran from 1905 to 1922. Karl Schwarzschild and Samuel Oppenheim coedited "Astronomy", publishing until 1933.


In 1916 George Abram Miller noted:[3]

One of the great advantages of this large encyclopedia is that it tends to avoid duplication by establishing a higher minimum of general mathematical knowledge. ... The vastness of the new [mathematical] literature, combined with the fact that some of the new developments appeared first in somewhat obscure places, has often made it difficult for an author to determine whether his results were new. While some of this difficulty remains, yet the large encyclopedia, in which related important results are carefully associated, tends to reduce the difficulty materially.

Librarian Barbara Kirsch Schaefer wrote:[4]

Despite its age it remains a valuable source of reference, for its period of publication spans one of the most fruitful periods of mathematical research. Noted for its comprehensive treatment and well-documented scholarly articles, it is aimed at the specialist.

In 1982 a history of aeronautics noted the following:

As organizer and editor of the monumental Encyclopedia of Mathematical Sciences Including Their Applications, [Klein] compiled a collection of definitive studies that became the standard reference in mathematical physics. Early in the thirty-year enterprise Klein solicited the esteemed Sebastian Finsterwalder, professor of mathematics at the Munich polytechnic (and incidentally, one of Prandtl’s teachers), to write an essay on aerodynamics. This review article is significant in the history of aerodynamics because of its comprehensive scope and because it was submitted in August 1902. The date is more than a year before the Wrights achieved their powered flights at Kitty Hawk, North Carolina, and two years before Prandtl introduced his theory of the boundary layer. It is therefore kind of a prenatal record of the science we now call aerodynamics. More to the point, however, it was then a rare compendious account of the state of the art of aerodynamics, a first reference to be found in much subsequent research in the field. Klein’s encyclopedia as a whole, moreover, provided the model for the later publication of Aerodynamic Theory, the six-volume encyclopedia of the science of flight that William F. Durand edited in the mid-1930s…[5]

Ivor Grattan-Guinness observed in 2009:[6]

Many of the articles were the first of their kind on their topic, and several are still the last or the best. Some of them have excellent information on the deeper historical background. This is especially true of articles on applied mathematics, including engineering, which was stressed in its title.

He also wrote, "The mathematicians at Berlin, the other main mathematical pole in Germany and a citadel for pure mathematics, were not invited to collaborate on the EMW and are reputed to have sneered at it."


  1. ^ Walther von Dyck (1908) "E m W", Proceedings of the International Congress of Mathematicians, v 1, pp 123–134
  2. ^ Hollcroft, T. R. (1936). "Review: Mehrdimensionale Räume, by C. Segre". Bulletin of the American Mathematical Society. 42 (1, Part 2): 5–6. doi:10.1090/s0002-9904-1936-06226-9. 
  3. ^ George Abram Miller (1916) Historical Introduction to the Mathematical Literature, pp 63,4, Macmillan Publishers
  4. ^ Barbara Kirsch Schaefer (1979) Using the Mathematical Literature: A Practical Guide, p 101, Marcel Dekker ISBN 0-8247-6675-X
  5. ^ Paul A. Hanle (1982) Bringing Aerodynamics to America, pages 39,40, The MIT Press ISBN 0-262-08114-8
  6. ^ Ivor Grattan-Guinness (2009) Routes of Learning: Highways, Pathways, Byways in the History of Mathematics, pp 44, 45, 90, Johns Hopkins University Press, ISBN 0-8018-9248-1


  • Hélène Gispert (1999) "Les débuts de l'histoire des mathématiques sur les scènes internationales et le cas de l'entreprise encyclopédique de Felix Klein et Jules Molk", Historia Mathematica 26(4):344–60.
  • Virgil Snyder (1936) Indexing EmW Bulletin of the American Mathematical Society v42.

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