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| Enzyklopädie der mathematischen Wissenschaften | |
|---|---|
| Title | Enzyklopädie der mathematischen Wissenschaften |
| Language | German |
| Country | German Empire |
| Discipline | Mathematics |
| Editors | Felix Klein; Walther von Dyck |
| Publisher | Teubner |
| First | 1898 |
| Last | 1935 |
| Volumes | 23 (main), supplements |
Enzyklopädie der mathematischen Wissenschaften is a comprehensive German-language mathematical encyclopedia issued at the turn of the 20th century that aimed to survey contemporary David Hilbert-era research across analysis, algebra, geometry and applied topics. Conceived in the milieu of the German Empire and edited by leading figures associated with institutions such as the University of Göttingen and the Technische Hochschule München, the work sought to coordinate contributions from a constellation of European and international mathematicians and engineers. Its pages record interactions among scholars connected to schools in Paris, Cambridge, St. Petersburg, Moscow, Rome and Zurich and reflect the institutional networks of the period, from the Kaiser Wilhelm Society to the Prussian Academy of Sciences.
The project was launched under the leadership of Felix Klein with editorial collaboration from Walther von Dyck and publication by B. G. Teubner Verlag in Leipzig; initial volumes appeared in 1898 and serial publication extended into the 1930s. Production coincided with major mathematical events such as the International Congress of Mathematicians and the rise of research centers including University of Göttingen and ETH Zurich. The encyclopedia was arranged as alphabetized and thematic articles published in multi-part volumes, responding to contemporary initiatives like Encyclopaedia Britannica and national reference projects supported by academies such as the Royal Society and the Académie des Sciences. Periods of interruption and supplement volumes mirrored political disruptions including those surrounding World War I and institutional reconfigurations in the Weimar Republic.
Editorial oversight combined the reputations of Felix Klein and Walther von Dyck with advisory input from figures tied to the Hamburgische Wissenschaftliche Stiftung and the Sächsische Akademie der Wissenschaften. Contributors were drawn from diverse locales: protagonists of Hilbert's school in Göttingen (including followers of David Hilbert and Hermann Minkowski), analysts and algebraists from Paris affiliated with Élie Cartan-influenced circles, geometers from Milan and Rome connected to Tullio Levi-Civita, and specialists associated with Princeton University and Columbia University. The editorial model resembled collaborative enterprises like those surrounding Acta Mathematica and periodicals edited by Hermann Schapira and Felix Klein-era journals, structuring articles to balance expository surveys with research-level treatments by authors such as Emmy Noether, Henri Poincaré, G. H. Hardy, Émile Picard, L. E. J. Brouwer, Carl Runge, Ernst Zermelo, Richard Dedekind, Félix Klein-affiliates, and other prominent mathematicians of the era.
Entries cover branches represented in contemporary curricula and research programs: topics linked to David Hilbert's problems and to developments in Calculus of Variations associated with Leonida Tonelli and Óscar Zariski-era algebraic geometry; themes treated include functions and series studied by Karl Weierstrass, differential equations handled in the style of Sofia Kovalevskaya, probability treatments influenced by Andrey Kolmogorov precursors, and applied mathematics with bearings on engineering problems addressed at Technische Hochschule München and Darmstadt. The encyclopedia integrates historical sketches invoking the work of Carl Friedrich Gauss, Leonhard Euler, Joseph-Louis Lagrange, Adrien-Marie Legendre, and modern contributions by Élie Cartan, Jacques Hadamard, Norbert Wiener, John von Neumann, and Emil Artin. Specialized sections treat topics in Non-Euclidean geometry as advanced by Nikolai Lobachevsky and Bernhard Riemann, algebraic structures in the tradition of Richard Dedekind and Emil Artin, and numerical methods comparable to those discussed by Carl Runge and Martin Kutta.
Contemporaneous reception among institutions such as the Prussian Academy of Sciences and the Austrian Academy of Sciences praised the encyclopedia for synthesizing the output of mathematicians affiliated with centers like University of Göttingen, University of Paris, and Moscow State University. Reviews in periodicals tied to Acta Mathematica and journals edited by Heinrich Weber and Leopold Kronecker highlighted both the pedagogical utility for students at University of Berlin and the research value for mathematicians at Princeton University and Cambridge University. Criticisms emerged about uneven coverage and national biases in contributor selection, voiced in forums linked to International Congress of Mathematicians meetings and correspondence between figures such as David Hilbert and Felix Klein.
The original German editions were reprinted in multiple impressions by B. G. Teubner Verlag and later issued in collected forms with supplements during the interwar years; portions were translated or summarized in outlets associated with Encyclopædia Britannica-style projects and in national bibliographies curated by the Royal Society and the National Academy of Sciences (United States). Reprints circulated in academic libraries at institutions including Harvard University, University of Chicago, Sorbonne University, and University of Tokyo, and influenced subsequent multilingual reference efforts coordinated by bodies like the International Mathematical Union.
Notable contributions include survey articles and research expositions by scholars in the orbit of Felix Klein and David Hilbert as well as standalone treatments authored by Emmy Noether, Henri Poincaré, Jacques Hadamard, Élie Cartan, John von Neumann, Ernst Zermelo, Emil Artin, G. H. Hardy, L. E. J. Brouwer, Andrey Kolmogorov, Norbert Wiener, Erwin Schrödinger (on mathematical physics topics), and Tullio Levi-Civita. These pieces often synthesized prior work by Carl Friedrich Gauss, Leonhard Euler, Bernhard Riemann, Joseph-Louis Lagrange, and Augustin-Louis Cauchy while framing emerging directions linked to Hilbert's program and axiomatic approaches.
The encyclopedia shaped subsequent reference works and influenced curricular planning at universities such as University of Göttingen, ETH Zurich, Princeton University, and University of Cambridge. Its model of long-form survey articles by leading researchers informed later projects associated with the Encyclopedia of Mathematics and reference volumes coordinated by the International Mathematical Union and national academies. Traces of its editorial philosophy are visible in monograph series sponsored by Birkhäuser and in specialist handbooks produced under the auspices of the American Mathematical Society and the London Mathematical Society. Category:Mathematics encyclopedias