Crelle (Journal für die reine und angewandte Mathematik)

Crelle (Journal für die reine und angewandte Mathematik)
Title	Journal für die reine und angewandte Mathematik
Other titles	Crelle
Discipline	Mathematics
Language	German
Abbreviation	J. reine angew. Math.
Publisher	Verlag Hirschfeld / Akademie Verlag
Country	Germany
History	1826–present
Frequency	Irregular / Quarterly
Issn	0075-4102

Crelle (Journal für die reine und angewandte Mathematik) is a long‑running mathematical journal founded in the Kingdom of Prussia that became a central venue for dissemination of research in analysis, algebra, number theory, and geometry. From its establishment in the 1820s the journal published original work by leading figures associated with universities and academies across Europe, influencing developments tied to institutions and prizes and fostering correspondence among mathematicians in Berlin, Göttingen, Paris, and London.

History

Established in 1826 during the era of the Kingdom of Prussia and the reign of Frederick William III of Prussia, the journal emerged amid intellectual movements connected to the University of Berlin and the Prussian Academy of Sciences. Early publication coincided with the careers of scholars linked to the Humboldt University of Berlin, the University of Göttingen, and the École Polytechnique, and the period saw exchanges with mathematicians associated with the Royal Society and the Académie des Sciences (France). Throughout the 19th century the journal navigated political changes such as the Revolutions of 1848 and the unification under the German Empire (1871–1918), while contributing to networks that included the Société Mathématique de France and the London Mathematical Society.

Founding and Editorial Leadership

The journal was founded by the bookseller and publisher August Leopold Crelle, who established the periodical in competition with contemporaneous serials like those edited by Carl Friedrich Gauss's correspondents and by editors at the Journal de Mathématiques Pures et Appliquées. Editorial stewardship passed through figures tied to the Humboldt University of Berlin, including mathematicians who worked with the Prussian Academy of Sciences and collaborators of Peter Gustav Lejeune Dirichlet, Niels Henrik Abel, and Évariste Galois. Later editors maintained links to the German Mathematical Society and to academic centers such as Leipzig University and Heidelberg University, shaping the journal’s scope alongside prize committees for awards like the Crelle Prize and other recognitions administered by learned societies.

Influence and Notable Publications

The journal published papers that influenced fields associated with scholars like Carl Friedrich Gauss, Bernhard Riemann, Georg Cantor, Leopold Kronecker, David Hilbert, and Felix Klein, and thus became entwined with advances presented at venues such as the International Congress of Mathematicians and discussions within the Royal Society of London. Seminal contributions in complex analysis, elliptic functions, and algebraic number theory appeared alongside works that informed the development of the Hilbert problems and the theories later advanced at the Institute for Advanced Study. Cross‑referencing occurred with journals such as Acta Mathematica, Mathematische Annalen, and the Proceedings of the London Mathematical Society, amplifying impact through citation networks tied to major libraries like the Bayerische Staatsbibliothek and the British Library.

Publication Format and Indexing

Originally issued in quarto and later in formats compatible with academic publishers such as Springer Science+Business Media and Wiley‑VCH, the journal’s volumes featured articles in German with abstracts used by indices maintained by organizations like Mathematical Reviews and Zentralblatt MATH. Archives are held by repositories including the Staatsbibliothek zu Berlin and digitized collections utilized by scholars affiliated with the Max Planck Institute for Mathematics and university libraries at University of Göttingen and Humboldt University of Berlin. The journal is indexed in major bibliographic services connected to the Deutsche Forschungsgemeinschaft and appears in catalogues of the Union Catalogue of Serials.

Notable Contributors and Papers

Contributors included prominent figures: early papers by Niels Henrik Abel and Carl Gustav Jacobi; foundational articles by Bernhard Riemann and Leopold Kronecker; later works by Georg Cantor, David Hilbert, Emmy Noether, Hermann Minkowski, Ferdinand von Lindemann, Richard Dedekind, Ernst Zermelo, Kurt Gödel, André Weil, Henri Poincaré, Sofia Kovalevskaya, Jacques Hadamard, Émile Picard, Issai Schur, Ernst Kummer, Gustav Roch, Otto Hesse, Karl Weierstrass, Ludwig Prandtl, Ernst Fischer, Paul Dirac, John von Neumann, Norbert Wiener, Alexander Grothendieck, Jean-Pierre Serre, Jean Leray, Israel Gelfand, Hjalmar Schacht, Max Noether, Wilhelm Killing, Sophus Lie, Élie Cartan, Hermann Weyl, Salomon Bochner, Hermann Schwarz, Jacques Tits, Klaus Friedrich Roth, Harish-Chandra, and Atle Selberg. Notable papers addressed problems in number theory, topology, and analysis that later informed awards such as the Fields Medal and the Abel Prize.

Legacy and Impact on Mathematics

The journal’s legacy is reflected in its role connecting mathematicians across institutions such as the University of Cambridge, the University of Oxford, the Sorbonne University, and the University of Chicago and in fostering dialogues that shaped curricula at the École Normale Supérieure and research agendas at the Max Planck Society. Its archive documents the evolution of themes later central to departments at the Institute Henri Poincaré and the Courant Institute of Mathematical Sciences, and its influence persists in citation trails found in works by laureates of the Nobel Prize‑adjacent scientific community and recipients of major prizes administered by the International Mathematical Union and national academies.

Category:Mathematics journals Category:German-language journals Category:Publications established in 1826