Klein's encyclopedia is a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Franz 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. It is 20,000 pages in length 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.
Overview
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 preparatory report serves as the Preface for the EMW. In 1908 von Dyck reported on the project to the International Congress of Mathematicians in Rome. Nominally, Wilhelm Franz Meyer was the founder president of the project and assembled volume 1, "Arithmetic and Algebra", that appeared between 1898 and 1904. D. Selivanov expanded his 20-page article on finite differences in Volume 1, Part 2 into a 92-page monograph published under the title Lehrbuch der Differenzenrechnung. Volume 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. Volume 3 on geometry was edited by Wilhelm Franz Meyer. These articles were published between 1906 and 1932 with the book Differentialgeometrie published in 1927 and the book Spezielle algebraische Flächen in 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. Volume 4 of EMW concerned mechanics, and was edited by Felix Klein and. Arnold Sommerfeldedited volume 5 on "Physics", a series that ran until 1927. Volume 6 consisted of 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.
Mentions
In 1905 Alfred Bucherer acknowledged the influence of the encyclopedia for establishment of appropriate notation for vector analysis in the second edition of his book: In 1916 George Abram Miller noted: In his review of the Encyclopedic Dictionary of Mathematics, Jean Dieudonné raised the specter of Klein's encyclopedia while denigrating its orientation to applied mathematics and historical documentation: Librarian Barbara Kirsch Schaefer wrote: In 1982 a history of aeronautics noted the following: Ivor Grattan-Guinness observed in 2009: 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." In 2013 Umberto Bottazzini and Jeremy Gray published Hidden Harmony in which they examined the history of complex analysis. In the final chapter concerned with textbooks, they used Klein's and Molk's encyclopedia projects to contrast the approaches in Germany and France. In 1900 an element of an algebra over a field was known as a hypercomplex number, exemplified by quaternions ℍ which contributed the dot product and cross product useful in analytic geometry, and the del operator in analysis. Explorative articles on hypercomplex numbers, mentioned by Bottazzini and Gray, written by Eduard Study and Elie Cartan, served as advertisements to twentieth century algebrists, and they soon retired the term hypercomplex by displaying the structure of algebras.
French edition
was the editor-in-chief of the Encyclopédie des sciences mathématiques pures et appliquées, the French edition of Klein's encyclopedia. It is a French translation and re-writing published between 1904 and 1916 by Gauthier-Villars. According to Jeanne Peiffer, the "French edition is notable because the historical treatment is more extensive, and often more precise than the original German version."
