Mathematical Reviews

Mathematical Reviews
Discipline	Mathematics
Publisher	American Mathematical Society
Country	United States
History	1940–present

Mathematical Reviews is a comprehensive bibliographic database and review journal covering the global literature of mathematics and related fields. Published by the American Mathematical Society, it provides expert, peer-reviewed summaries of research articles, books, and conference proceedings. Its mission is to offer researchers critical evaluations and guides to the vast output of mathematical scholarship, facilitating discovery and scholarly communication across the discipline.

History and development

The publication was conceived in the late 1930s by Otto Neugebauer, a historian of mathematics, and John von Neumann, a foundational figure in numerous fields, amid concerns over the fragmentation of mathematical literature following the rise of Nazism in Europe. With initial funding from the Rockefeller Foundation and support from the American Mathematical Society, the first issue appeared in 1940 under the editorship of Raymond Wilder. Early operations were significantly aided by mathematicians fleeing World War II, such as Einar Hille and William Feller. Its establishment paralleled other major reviewing efforts like Zentralblatt MATH, published in Berlin. Over decades, it expanded its scope and linguistic coverage, moving its editorial offices to Ann Arbor, Michigan, and becoming a cornerstone of the American Mathematical Society's publishing enterprise.

Content and coverage

It systematically covers pure and applied mathematics, including core areas like algebraic geometry, topology, number theory, and mathematical analysis, as well as interdisciplinary fields such as mathematical physics, computer science, statistics, and theoretical economics. The database includes reviews of articles from thousands of serials, including major journals like Annals of Mathematics, Inventiones Mathematicae, and Journal of the American Mathematical Society. It also covers monographs, proceedings from conferences like the International Congress of Mathematicians, and doctoral theses from many institutions. The coverage is international, encompassing literature from publishers in Russia, China, Japan, France, and Germany.

Editorial process and indexing

The editorial process relies on a global network of thousands of active mathematicians who serve as reviewers, selected for their expertise by a staff of professional editors, often PhDs in mathematics. Upon receipt of a published item, an editor assigns it to a reviewer, who produces a concise summary and evaluation, not merely an abstract. These signed reviews are then edited for clarity and consistency. Each item is meticulously indexed using the Mathematics Subject Classification scheme, a hierarchical system co-developed with Zentralblatt MATH. This classification, along with author and title indexing, allows for precise searching and discovery of literature across subfields.

Impact and significance

It has profoundly shaped modern mathematical research by providing a centralized, critical filter for the exponential growth of literature. It is considered an indispensable tool for researchers at institutions like the Institute for Advanced Study, University of Cambridge, and Massachusetts Institute of Technology. Its authoritative reviews often serve as the first point of contact with new work, influencing the direction of research and the dissemination of ideas. The service has been recognized by awards from organizations such as the Association of American Publishers. Its significance is comparable to other major scientific indexing services like Chemical Abstracts Service or PubMed.

Electronic access and MathSciNet

The electronic version, launched in 1996, is a vastly enhanced relational database offering powerful search capabilities, citation linking, and direct links to original articles via services like JSTOR and Project Euclid. It features author profiles, citation data, and collaboration graphs. Access to is typically provided through institutional subscriptions to the American Mathematical Society. The platform is continuously updated, incorporating reviews and records shortly after publication, and represents the primary mode of access for the global mathematical community.

Related services and publications

The produces several derivative products and collaborates on related initiatives. These include the annual index volumes and the, a curated database of highly cited and influential articles. The collaborates with similar organizations worldwide, such as the European Mathematical Society and the Society for Industrial and Applied Mathematics. Its classification system is used by major publishers including Springer Science+Business Media and Elsevier. Other related review services in adjacent fields include zbMATH Open, ACM Computing Reviews, and JSTOR.

Category:Mathematics journals Category:American Mathematical Society Category:Bibliographic databases Category:Academic publishing