zbMATH — the first resource for mathematics

Overview

Zentralblatt MATH (zbMATH) is the world’s most comprehensive and longest-running abstracting and reviewing service in pure and applied mathematics. It is produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH (FIZ Karlsruhe). Editors are the European Mathematical Society (EMS), FIZ Karlsruhe, and the Heidelberg Academy of Sciences and Humanities. zbMATH is distributed by Springer.

The zbMATH database contains more than 3.5 million bibliographic entries with reviews or abstracts currently drawn from more than 3,000 journals and serials, and 170,000 books. The coverage starts in the 18th century and is complete from 1868 to the present by the integration of the “Jahrbuch über die Fortschritte der Mathematik” database.

About 7,000 active expert reviewers from all over the world contribute reviews to zbMATH.

Scope

zbMATH provides easy access to bibliographic data, reviews and abstracts from all areas of pure mathematics as well as applications, in particular to the natural sciences, computer science, economics and engineering. It also covers history and philosophy of mathematics and university education. All entries are classified according to the Mathematics Subject Classification Scheme (MSC 2010) and are equipped with keywords in order to characterize their particular content.

zbMATH covers all available published and peer-reviewed articles, books, conference proceedings as well as other publication formats pertaining to the scope given above. For the list of journals and book series covered see the Journals search.

Publishers who would like their journals to be indexed in zbMATH are encouraged to contact our editorial office at editor@zentralblatt-math.org. Provided that the suggested journal falls within the scope described above, our staff will contact the publisher for the arrangement of a suitable data delivery procedure.

Reviewers

The content and quality of zbMATH highly relies on contributions from our reviewers. We are very grateful for their help and we encourage active mathematicians to join them. If you are interested in becoming a reviewer or want to suggest a colleague, please visit our Reviewer Service or contact us at editor@zentralblatt-math.org.

Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is a classification scheme maintained by Mathematical Reviews and zbMATH. It is used by these reviewing services and many others to categorize items in the mathematical sciences literature.

The MSC is updated every 10 years, the current version being MSC2010. See the MSC-search or download MSC2010 (PDF).

Links to full texts

The database zbMATH contains about 2.1 million direct links to electronic versions of the indexed publications, to the publishers’ websites and/or to electronic libraries with open access to the full texts (in particular to ElibM and EuDML).

Within current electronic library activities, more retrospective data of journals are made available, too, even prior to 1868, that give also links to full texts. For instance, coverage of Crelle’s journal (Journal für die Reine und Angewandte Mathematik) has been extended in this way back to Vol. 1 (1826).

For articles from about 550 journals, lists of references are delivered, with links to their zbMATH entries as well as their electronic versions via DOI.

Update schedule

zbMATH is updated daily with new bibliographic data and abstracts. Reviews are also updated on a daily basis after initial editorial work has been carried out. The final editorial work on reviews and abstracts is subsequently done as quickly as possible.

New interface

The main aim of the new zbMATH interface is to offer detailed and easily accessible information, with the potential to incorporate results of recent and future developments. New features include:

  • Separated tabs allow an easy navigation among different search facets: documents, authors, journals, classification codes and software. The search results are interlinked in the sense of the content structure.
  • Clickable drop-down menus and mouse-over functionalities help to provide a clear and intuitive design.
  • Results of a query are filtered by authors, journals, classification codes and publication years according to frequency. This new functionality helps you to refine your original search as well as to formulate complex queries. For instance, you can now determine who are the most prolific authors in the top mathematics journals or analyse how research topics have evolved over the years.
  • For every author, a profile page with an analysis of her publications according to co-authors, journals and mathematical subjects is generated. The publications are displayed in chronological order as a clickable diagram for easy visualization of the author's scientific output.
  • New journal profiles offer aggregated information on all indexed journals, particularly helpful for librarians or for scientific evaluation purposes.
  • The retrieval system is now based on HTML5, allowing a quick and correct display of mathematical formulae in MathML for almost all browsers.

Further developments

FIZ Karlsruhe is continuously improving the infrastructure of its databases.

The aim of the following projects is to enlarge the content and improve the search possibilities of zbMATH:

Scientific and editorial boards

zbMATH is edited by FIZ Karlsruhe, a non-profit organisation for scientific information and infrastructure, in collaboration with two academic institutions, the European Mathematical Society (EMS) and the Heidelberg Academy of Science. The Springer Publishing House is responsible for sales, marketing and invoicing.

Gert-Martin Greuel, zbMATH’s editor-in-chief
Dirk Werner, deputy editor-in-chief

Since 2012 Gert-Martin Greuel is the current editor-in-chief of zbMATH. He is a professor of mathematics at the University of Kaiserslautern since 1981 and the former Director of the Mathematical Research Institute Oberwolfach (2002–2013). His main areas of research are singularity theory, algebraic geometry and computer algebra. He is one of the developers of the computer algebra system SINGULAR.

The deputy editor-in-chief is Dirk Werner. He is a professor of mathematics at Free University Berlin. His main areas of research are functional analysis and operator theory with a special emphasis on the theory of Banach spaces.

Both are responsible for the scope and content of the database. Together with FIZ Karlsruhe and the other two editorial institutions, they develop long-term strategies for the future improvement of the service.

Scientific User Committee

The Scientific User Committee (SCUC) of zbMATH is a scientific advisory board consisting of renowned members of the mathematical community. They meet on a regular basis to propose recommendations for further developments of the database and its associated services.

Members:

  • Ingo Brüggemann
    (vice-chair)
  • Annalisa Buffa
  • Anand Dessai
  • Fuquan Fang
  • Sofia Lambropoulou
  • José Francisco Rodrigues
    (chair)
  • Katrin Wendland

Editorial board

The editorial office of zbMATH is located in Berlin. Most of the editors are researchers from scientific institutions of the Berlin area, contributing expertise in their areas of research.

Members:

  • Bernd Bank
  • Apostolos Damialis
  • Gertraud Ehrig
  • Alexander Frey
  • Hubert Gollek
  • Rainer Götz
  • Jan-David Hardtke
  • Georg Hebermehl
  • Karl-Eberhard Hellwig
  • Klaus Kiermeier
  • Detlef Krüger
  • Andreas Kühnemund
  • Jürgen Leiterer
  • Grit Malik
  • Olaf Ninnemann
  • Dieter Nowack
  • Octavio Paniagua
  • Aleksandar Perović
  • Lutz Recke
  • Karin Reich
  • Enzo Rossi
  • Nicolas Roy
  • Ragmar Rudolph
  • Hans-Jürgen Schmidt
  • Klaus Schneider
  • Wolfram Sperber
  • Olaf Teschke
    (managing editor)
  • Oleg Titow
  • Dirk Werner

International editorial organisations

In order to ensure a broad coverage of mathematical literature world-wide, zbMATH cooperates with the following international partners:

History of zbMATH

The history of zbMATH, from its origins as a monthly compilation of bibliographic data and reviews of mathematical publications to its current status as a comprehensive database in pure and applied mathematics, recounts a fascinating tale that spans decades of intense developments in information services for scientific literature.

Foundation and early years

The Zentralblatt für Mathematik und ihre Grenzgebiete was founded in 1931 with the aim to publish reviews of the entire world literature in mathematics and related areas. Zentralblatt became the second comprehensive review journal for mathematics in Germany after the Jahrbuch über die Fortschritte der Mathematik, established in 1868 and active until the 1940s. Although Zentralblatt had essentially the same agenda as the Jahrbuch, the latter maintained the principles of completeness and classification of all articles of one year, whereas Zentralblatt counted on promptness and internationality.

neugebauer
Otto Neugebauer
bohr
Harald Bohr
courant
Richard Courant
springer
Ferdinand Springer

The initiative for the foundation of a new mathematical reviewing journal came from mathematicians Otto Neugebauer, Richard Courant, and Harald Bohr, together with the publisher Ferdinand Springer. The rapidly growing number of newly published mathematics works in the 1920s and the scientists’ need for obtaining quick information on recent material motivated the decision to create an alternative service to the Jahrbuch.

Zentralblatt’s first editorial board consisted of Pavel S. Alexandrov, Julius Bartels, Wilhelm Blaschke, Richard Courant, Hans Hahn, Godfrey H. Hardy, Friedrich Hund, Gaston M. Julia, Oliver Kellogg, Hans Kienle, Tullio Levi-Civita, Rolf H. Nevanlinna, Hans Thirring, and Bartel L. van der Waerden. Otto Neugebauer became the first editor-in-chief, directing Zentralblatt from Göttingen, while the editorial office was installed on the premises of the Springer publishing house in Berlin. Distinguished mathematicians from various countries belonged to the large group of reviewers.

Unfortunately, a large amount of the editorial correspondence documenting the foundational era of Zentralblatt got lost in the turmoil of the Second World War and the post-war period. Nevertheless, it is a fact that within very few years Zentralblatt became a successful journal, with 18 volumes appearing between 1931 and 1938.

The years 1933–1945

A letter by Ludwig Bieberbach from 1938, requesting Helmut Grunsky, Jahrbuch’s main editor, to dismiss all Jews from the board of reviewers.
A letter by Ludwig Bieberbach from 1938, requesting Helmut Grunsky, Jahrbuch’s main editor, to dismiss all Jews from the board of reviewers.

Neugebauer directed the new periodical for several years until the political situation in Germany made his position as editor-in-chief unsustainable. In 1933, shortly after the Nazi party rose to power, a law was enacted which banned Jews and political enemies from holding jobs as civil servants. A call to dismiss Courant, Neugebauer, Landau, Bernays, and Noether appeared in a local newspaper and, soon afterwards, Courant escaped to the UK and later moved to New York. Due to this pressure, Neugebauer decided to resign from his post at Göttingen University and in 1934 took up a professorship in Copenhagen, from where he continued his work for Zentralblatt.

The struggle to produce the reviewing journal became more difficult throughout this period, however, for the Nazis tried to influence the editorial policy. Neugebauer eventually gave up his position as editor-in-chief in 1938 after a series of incidents, including Levi-Civita being dismissed from the editorial board without his knowledge. Following his withdrawal, other letters and telegrams of resignation were sent to Springer by editorial board members Bohr, Hardy, Courant, Tamarkin, and Veblen, and by a very large number of reviewers. English-language contributions to zbMATH were greatly reduced by the middle of 1939 and all but gone by the beginning of 1940.

Neugebauer moved to the USA in 1939, accepting an offer at Brown University which had been arranged by its dean Roland G. D. Richardson, who was also the secretary of the American Mathematical Society and saw the opportunity to use Neugebauer's expertise in the American project of founding a reviewing journal of their own. Upon leaving Europe, Neugebauer burnt most of the editorial correspondence of Zentralblatt and records of the journal except for the cumulative index. The first issue of the Mathematical Reviews, the American-based mathematical reviewing journal modeled on Zentralblatt, saw the light in January 1940.

In 1939 the Prussian Academy of Sciences and the German Mathematical Society took over the management of Zentralblatt. Harald Geppert, a mathematician and devoted Nazi, was nominated as managing editor ("Generalredakteur") of both the Jahrbuch and Zentralblatt, with Ludwig Bieberbach, also a devoted Nazi, as supervising editor. Until 1945, the editorial offices of the two journals continued working independently of each other, but sometimes they shared information, scientific literature and reviews.

A new beginning in 1947

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Hermann L. Schmid
pannwitz-dueball-szotowski
Erika Pannwitz with Elisabeth Szotowski and Fritz Dueball

The collapse of Germany after World War II led to a temporary suspension of the work at Zentralblatt. Berlin evolved as a divided city: West-Berlin (sectors of the Western Allies) and East-Berlin (Soviet sector). The Soviet administration took responsibility for the Prussian Academy of Sciences, which was reopened in 1946 as the German Academy of Sciences. Due to the initiative of the Academy and of Springer, Zentralblatt came to life again in 1947, while around the same time it was decided not to revive the Jahrbuch, of which the last volume (covering the year 1942) had been published in 1944.

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