Encyclopedia of Mathematical Sciences

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The encyclopedia of the mathematical sciences including their applications was an encyclopedia project of the mathematical sciences (in the broadest sense) including applications that was published by BG Teubner Verlag in Leipzig from 1898 to 1935.

Emergence

The idea for the project arose on a trip to the Harz Mountains by Felix Klein , Heinrich Weber and Wilhelm Franz Meyer in 1894. Leading mathematicians and physicists from the turn of the century to the 1920s took part, coordinated in particular by Felix Klein. Participation was international. B. also contributions from Italy, England and France. The academies in Munich, Leipzig, Göttingen and Vienna (not Berlin) were involved. In France there was a French edition at the same time (published 1904 to 1916 by Gauthier-Villars, editor Jules Molk ), some of the articles (especially on real analysis) of which were taken over into the German encyclopedia. The articles in the encyclopedia still provide valuable information on the history of mathematics today. Some of the articles are classics, e.g. B. that of Wolfgang Pauli on the theory of relativity , of Tatjana and Paul Ehrenfest on statistical mechanics and that of Max Dehn and Poul Heegaard on topology . The original plan to write the most concise overview articles possible, however, already partially dissolved with the contributions of Alfred Pringsheim , who brought his own research on the theory of functions to the encyclopedia. Ludwig Boltzmann gave a little insight into the organization .

In addition to mathematics (volumes 1, 2 and for geometry 3), z. B. Physics , mechanical engineering , hydrodynamics , geodesy and astrophysics are dealt with (mechanics in rows 4, physics in 5, geophysics and astrophysics in row 6). Arnold Sommerfeld supervised the physics volumes, in which famous theoretical physicists such as Hendrik Antoon Lorentz collaborated and in which quantum theory was also dealt with (Smekal 1925).

The volumes of the encyclopedia also contain the beginning of the triumphant advance of vector notation, as Karin Reich explained.

From 1939 until the 1950s, the project of a new encyclopedia was started, which was then abandoned. Although it was limited to pure mathematics, due to the great increase in mathematical knowledge (especially in the period after the Second World War) and the shift in the focus of mathematical research to countries other than German-speaking Central Europe, the time for such a project was up. In the 1970s, a similar project, the Matematicheskaya entsiklopediya, began in the Soviet Union under the direction of Ivan Matwejewitsch Vinogradow, from the 1990s in an expanded and updated English version as the Encyclopaedia of Mathematics at Kluwer Verlag (later Springer ), but without the broad term of Applications that Felix Klein in particular contributed to the encyclopedia project.

content

  • Vol. 2-2: William Fogg Osgood General Theory of Analytical Functions of One and Several Complex Variables (1901), Wilhelm Wirtinger Algebraic Functions and Their Integrals (1901), Robert Fricke Elliptical Functions (1913, using templates from James Harkness , Wilhelm Wirtinger ), Automorphic functions including the elliptic module functions (1913), Emil Hilb differential equations in complex areas, nonlinear differential equations (1916), Adolf Krazer , Wilhelm Wirtinger Abelian functions and general theta functions (1920).
  • Vol. 3-2-2b: Special algebraic surfaces: Wilhelm Franz Meyer third order surfaces (1928), fourth and higher order surfaces (1930), Luigi Berzolari Algebraic Transformations and Correspondences (1932).
  • Vol. 5-2: Arnold Sommerfeld , Richard Reiff electricity and optics - standpoint of action at a distance, elementary laws (1902), Hendrik Antoon Lorentz Maxwell's electromagnetic theory (1902), advanced training of Maxwell's theory - electron theory (1903), Richard Gans electrostatics and magnetostatics ( 1906), Friedrich Pockels The relationship between electrostatic and magnetostatic state changes on the one hand and elastic and thermal on the other hand (1906), Peter Debye Stationary and quasi-stationary fields (1909), Max Abraham Electromagnetic Waves (1906), Rudolf Seeliger Electron Theory of Metals (1921), Wolfgang Pauli Theory of Relativity (1920).

Digitized edition

Encyclopédie des sciences mathématiques pures et appliquées

The French edition of the Encyclopedie was published by Gauthiers-Villars. At the International Congress of Mathematicians in Paris in 1900, the publisher and Teubner agreed on a French edition that was created at the same time, but was not intended to be a mere translation, but was edited by leading French mathematicians. A reprint was published by Éditions Jacques Gabay in the 1990s. In addition to Jules Molk, Paul Appell was also the editor of some volumes . It was published from 1904 to 1916 in 8 volumes, each with partial volumes. After individual chapters had already been affected by the First World War, the entire edition was canceled in 1916 due to the war. As in the German edition, the partial volumes were partly published in continuation issues.

The cooperation between the author of the German edition and the French author took place by letter. First of all, the author of the German original sent supplementary suggestions with his text to the French author, who supplemented and edited and sent the text back to the original author, etc. Molk also organized a newsletter in which comments could be placed on all articles. In a few cases (as in Paul Langevin's adaptation of Max Abraham) a completely new text was created. Some of the contributions in the German edition, especially in analysis, were originally written by French mathematicians.

New edition from 1939 by Teubner

From 1939 the Academies of Sciences in Göttingen, Berlin, Vienna and Heidelberg and the BGTeubner publishing house planned a new edition. The editors were Helmut Hasse , Erich Hecke , Max Deuring and Emanuel Sperner . The following volumes have been published:

The volumes are available online as digital copies in the Göttingen State and University Library (SUB Göttingen) of the Georg-August-Universität Göttingen.

A presentation of the theory of algebras (then called hypercomplex numbers) by Richard Brauer , who emigrated to Canada during the Nazi era , which was available in manuscript in 1936 and was actually already accepted for publication, never appeared.

See also

literature

  • Walther von Dyck: Encyclopedia of the Mathematical Sciences. Lecture on behalf of Felix Klein at the International Congress of Mathematicians in Rome 1908, DMV annual report.
  • Hélène Gispert: 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, Volume 26, 1999, pp. 344-360.
  • Hélène Gispert, Jean-Luc Verley (editor): L'Encyclopédie des sciences mathématiques pures et appliquées, (1904–1916), traduire ou adapter l'entreprise de Felix Klein. Springer-France, 2000 (contributions from Gispert, Catherine Goldstein , Renate Tobies, among others ).
  • Hélène Gispert: The German and French Editions of the Burkhardt – Molk Encyclopedia: Images of the Mathematical Sciences at the Dawn of the Twentieth Century. In: Amy Dahan, Umberto Bottazzini (Eds.): Changing Images of Mathematics in History. Reading, UK: Harwood Academic, 1999.
  • David E. Rowe : Klein, Hilbert, and the Göttingen Mathematical Tradition, Osiris (2) 5 (1989), 186-213.
  • Jules Tannery: L'Encyclopédie des sciences mathématiques. Bulletin des sciences mathématiques 35 (1911), 296-297.
  • Paul Tannery: Encyclopédie des sciences pures et appliquées, notes historiques (1904–1906). Mémoires scientifiques, Paris-Toulouse, 1930.

Web links

Wikisource: Encyclopedia of Mathematical Sciences  - Sources and full texts

Individual evidence

  1. ↑ Encyclopédie des sciences mathématiques pures et appliquées. A detailed comparison of the German and French editions by Hélène Gispert and Catherine Goldstein is in preparation (2004).
  2. ^ Ludwig Boltzmann : Journey of a German professor to the Eldorado. In: Popular Writings. Johann Ambrosius Barth, Leipzig 1905, pp. 403-435, there pp. 405-407.
  3. ↑ Karin Reich: The role of Arnold Sommerfeld in the discussion about vector calculation, presented using the sources in the estate of the mathematician Rudolf Mehmke. From: Joseph W. Dauben (Ed.) History of Mathematics: states of the art. San Diego 1996, pp. 319-341.
  4. ^ Nabl, 1876–1953, assistant to Boltzmann.
  5. ↑ Jean Dhombres : Vicissitudes in Internationalization: International Networks in Mathematics until the 1920s. In: Christophe Charle, Jürgen Schriewer, Peter Wagner (eds.): Transnational intellectual networks. Campus Verlag, 2004, 81–114.
  6. ^ Jean Dhombres: National conditions of mathematical culture in Germany and France in the years around 1900. In: Lothar Jordan, Bernd Kortländer: National borders and international exchange. Niemeyer, Tübingen 1995, pp. 312-333.
  7. ^ Raymond Le Vavasseur, received his doctorate from the Sorbonne in 1893 (Sur le système d'équations aux dérivées partielles simultanées auxquelles satisfait la série hypergéométrique à deux variables). Published in 1908 in the Annales de l´université de Lyon on number theory and in 1904 on group theory. During this time he was maitre de conférences at the University of Lyon.
  8. ↑ Actuarial mathematician at the life insurance company Compagnie L'Union in Paris; he died in 1913.
  9. ^ Gallica.
  10. ^ Gallica.
  11. ^ Gallica.
  12. ^ Gallica.
  13. ^ BNF, Gallica.
  14. ^ Armand Lambert (1880-1944), astronomer, head of the Service Méridien of the Paris Observatory. Murdered in Auschwitz.
  15. ^ Sauveur Carrus (* 1873), received his doctorate in Paris in 1906 (Familles de surfaces à trajectoires orthogonales planes) and was then in Lille from 1907 to 1909. Was an examiner at the Ecole Polytechnique and later Professor of Analysis in Algiers. 1931/32 published a two-volume analysis textbook ( Cours de Calcul Différentiel et Intégral. Méthode de formation au raisonnement mathématique, Eyrolles, Paris).
  16. ↑ Auguste-Clément Grévy (born July 1, 1865 in Paris - 1930), studied at the Ecole Normale Superieure and received his doctorate in 1894 under Gabriel Koenigs in Paris with a thesis on the iteration of complex functions (described in Daniel Alexander A history of complex dynamics, Aspects of Mathematics, 1994 - according to Alexander his four works from 1892 to 1897 are almost his entire contribution to mathematical research). Wrote textbooks on algebra (Paris, Vuibert 1905), trigonometry (1929), arithmetic (1917) and geometry ( Géométrie théorique et pratique, Complements de géométrie 1905). From 1897 until his death he was a teacher at the Lycée Saint-Louis .
  17. ↑ Lucien Lévy (1853–1912), professor of mathematics at the Lycée Louis-le-Grand , examiner at the Ecole Polytechnique, father of Paul Lévy .
  18. ^ Fascicule 1, Gallica.
  19. ^ Fascicule 2, Gallica.
  20. ^ Gallica.
  21. ^ Frédéric Marie Emmanuel Vallier (born December 23, 1849 in Versailles), artillery officer, corresponding member of the Academie des Sciences, author of several books on ballistics.
  22. ↑ Camille Benoît (born October 27, 1856 in Maule), officer of the artillery (from February 1917 first lieutenant). As general in 1931 published Histoire Militaire de L'Afrique Occidentale Française .
  23. ^ Hubert Cassien Fernand François Gossot (1853-1935), General.
  24. ^ Roger Liouville, examiner at the Ecole Polytechnique. Studied differential equations and mechanics and posthumously published the work of Pierre-Henri Hugoniot on shock waves.
  25. ↑ Volume 4-1 in Ed. Gabay.
  26. ^ Encyclopedia of Mathematical Sciences, including its applications . State and University Library Göttingen (SUB Göttingen). Retrieved March 27, 2019.