Journal für die reine und angewandte Mathematik (Crelle)

Journal für die reine und angewandte Mathematik (Crelle)
Title	Journal für die reine und angewandte Mathematik
Abbreviation	Crelle
Discipline	Mathematics
Language	German, English, French
Publisher	Brill Publishers; historically Julius Springer and others
Country	Germany
History	1826–present
Frequency	Quarterly
Issn	0075-4102

Journal für die reine und angewandte Mathematik (Crelle) is a long-established peer-reviewed mathematics journal founded in 1826 by August Leopold Crelle in Berlin and associated with successive editors and institutions including Carl Friedrich Gauss, Leopold Kronecker, Bernhard Riemann, Peter Gustav Lejeune Dirichlet, and later figures such as Gotthold Eisenstein, Felix Klein, and Emmy Noether. The journal has published foundational work by mathematicians of the 19th century and 20th century including contributions linked to Euler, Galois, Weierstrass, Hilbert, Minkowski, Noether, Dedekind, and Poincaré.

History

The journal was established by August Leopold Crelle with early editorial direction from Carl Gustav Jacobi and patronage in the intellectual milieu of Prussia and Berlin; subsequent editorial influence came from Peter Dirichlet and Leopold Kronecker, shaping publication of research connected to the development of number theory, analysis, and algebraic geometry. During the mid-19th century the journal printed work by Bernhard Riemann and Karl Weierstrass and interacted with institutions such as the University of Berlin and the Academy of Sciences. In the late 19th and early 20th centuries figures like Felix Klein, David Hilbert, Hermann Minkowski, and Emmy Noether appeared in its pages; the journal continued through political transitions including the German Empire, the Weimar Republic, the Nazi Germany era, and post-war reconstruction involving Max Planck Society and contemporary publishers. Editorial stewardship in the post-war period brought contributions from mathematicians linked to Hermann Weyl, Otto Toeplitz, Heinz Hopf, and later editors associated with Göttingen and Humboldt University of Berlin.

Scope and Content

Crelle publishes original research in areas historically central to its identity: number theory, complex analysis, real analysis, algebraic number theory, algebraic topology, differential geometry, partial differential equations, functional analysis, and mathematical physics—fields advanced by contributors such as Srinivasa Ramanujan, André Weil, Jean-Pierre Serre, Alexander Grothendieck, and John von Neumann. The journal has accommodated papers on classical themes tied to Gauss's Disquisitiones Arithmeticae, modern treatments related to Atiyah–Singer Index Theorem, and cross-disciplinary work connecting to Klein's Erlangen Program and developments by Évariste Galois and Niels Henrik Abel. Editorial selections emphasize rigorous proofs and original theorems, attracting submissions from scholars at institutions including Cambridge University, École Normale Supérieure, Princeton University, Institute for Advanced Study, and IHÉS.

Editorial Board and Publication Details

The editorial board has historically included leading academics from Germany, France, United Kingdom, and the United States, with editors drawn from University of Göttingen, University of Bonn, University of Paris, University of Cambridge, and Princeton University. Publication frequency evolved from irregular early volumes to a modern quarterly schedule under publishers such as Teubner and Brill Publishers. Peer review standards align with practices common at journals like Annals of Mathematics, Acta Mathematica, and Transactions of the American Mathematical Society; editorial processes engage external referees drawn from networks including members of the International Mathematical Union and prize committees for awards like the Fields Medal and Abel Prize.

Notable Articles and Contributions

Crelle's archive includes landmark papers by Bernhard Riemann on complex analysis and Riemann surfaces, foundational notes by Peter Dirichlet in number theory, and influential expositions by Leopold Kronecker and Karl Weierstrass. The journal has disseminated results related to the work of David Hilbert on invariant theory, Hermann Minkowski on convex bodies, Emmy Noether on ring theory and Noetherian rings, and later breakthroughs connected to Hecke, Eisenstein, Dedekind, Poincaré, Hardy, Littlewood, and Selberg. More recent notable contributions include papers by mathematicians such as Jean-Pierre Serre, Alexander Grothendieck, Enrico Bombieri, Andrew Wiles, and Gerd Faltings addressing problems in Diophantine geometry, modular forms, and arithmetic geometry.

Abstracting and Indexing

The journal is indexed in major bibliographic services and abstracting databases alongside comparable journals like Journal of the American Mathematical Society and Inventiones Mathematicae, and appears in catalogs maintained by Mathematical Reviews, Zentralblatt MATH, and indexing systems associated with the Web of Science and Scopus. Institutional library holdings include collections at British Library, Bibliothèque nationale de France, Library of Congress, Staatsbibliothek zu Berlin, and university libraries at University of Oxford, Harvard University, and University of Tokyo.

Impact and Reception

Crelle is regarded as one of the historically influential journals in mathematics, often cited in connection with seminal developments by Gauss, Riemann, Hilbert, and Noether. Its long publication record underpins historiography found in works by historians such as Carl Boyer, Hans Freudenthal, and Peter Pesic, and it features in bibliometric comparisons involving impact factor analyses and citation studies across outlets like Proceedings of the Royal Society and Communications in Mathematical Physics. The journal's prestige is reflected in its role in disseminating results that led to major recognitions including the Fields Medal and the Abel Prize for authors whose formative papers appeared in its pages.

Category:Mathematics journals