Zentralblatt MATH (zbMATH) is the world’s most comprehensive and
longest-running abstracting and reviewing service in pure and
applied mathematics. It is edited by the
European Mathematical Society (EMS), the
Heidelberg Academy of Sciences and Humanities and
The editorial work is done by the Berlin office of FIZ Karlsruhe
which, as a member of the
Leibniz Association, is a non-profit company and a recognized
organisation of public interest. zbMATH is distributed by
The zbMATH database contains about 4 million bibliographic
entries with reviews or abstracts currently drawn from about 3,000
journals and serials, and 180,000 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
zbMATH provides easy access to bibliographic data, reviews and
abstracts from all areas of pure mathematics as well as
applications, in particular to 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
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
Editors and publishers are expected to follow the guidelines as
expounded in the
Code of Practice of the European Mathematical Society
together with the
Comments by the EMS Ethics Committee, or the
Best Current Practices for Journals as outlined by the
International Mathematical Union.
For more details concerning indexing decisions see
our FAQ on "Indexing decisions".
Selected articles will be reviewed after the indexing procedure.
About 7,000 active expert reviewers from all over the world
contribute reviews to zbMATH.
Reviewers are selected by the zbMATH editor in charge. The reviews
are not intended to serve as replacements for peer-reviewing. They
should instead give a well-balanced description of the content of
the paper within the context of current developments in the
corresponding subject area. Reviewers have, in principle, no
responsibility for checking the correctness or novelty of the
original, but if they discover that it contains a significant error
or that it overlaps significantly with other work, they should
mention the fact. References to related work are always
Every trained mathematician is very welcome to become a reviewer of
zbMATH in their specific field of research, see
our FAQ on "Becoming a reviewer" for more
The Mathematics Subject Classification (MSC) is a classification
scheme maintained by
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
classification search or
download MSC2010 (PDF).
The database zbMATH contains about 2.5 million direct links to electronic versions of the indexed publications, to the publishers’ websites and/or to electronic libraries and repositories with open access to the full texts (in particular to arXiv, 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 600 journals, lists of references are delivered, with links to their zbMATH entries as well as their electronic versions via DOI.
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.
The main aim of the zbMATH interface is to offer detailed and easily accessible information, with the potential to incorporate results of recent and future developments. New features include:
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:
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.
In April 2016, Klaus Hulek took over the responsibilities as editor-in-chief of zbMATH. He is a professor of mathematics at Gottfried Wilhelm Leibniz Universität Hannover. His main area of research is algebraic geometry.
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.
From 2005-2016, the Scientific User Committee (SCUC) of zbMATH served as a scientific advisory board on behalf of the EMS. Under the guidance of its chairs Jean-Pierre Bourguignon, Stephan Klaus, and José Francisco Rodrigues, it consisted of renowned members of the mathematical community, which met on a regular basis to propose recommendations for further developments of the database and its associated services.
Since 2017, the newly formed EMS Committee for Publications and Electronic Dissemination has assumed the duties of SCUC.
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.
In order to ensure a broad coverage of mathematical literature world-wide, zbMATH cooperates with the following international partners:
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.
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.
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.
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.
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.
The editor-in-chief was Hermann Ludwig Schmid, who played an important role in the reconstruction of Zentralblatt, reviving contacts with former colleagues, inviting many of them to work again as editors or reviewers and finally succeeding in restarting publication. Following Schmid’s appointment as professor in Würzburg in 1953, Erika Pannwitz, who had worked as an editor for both the Jahrbuch in the 1930s and Zentralblatt since 1947, took over the editorship.
The construction of the Berlin Wall in 1961 caused a renewed division in Zentralblatt. The barrier cut off West-Berlin from the Eastern part of the city, causing many complications for Zentralblatt and its editors. While the editorial office was located in Adlershof (East Berlin) on the premises of the German Academy of Sciences, Zentralblatt’s publishing house Springer and about half of its staff members, including Pannwitz, were located in the Western districts. To make communication and the exchange of material between Zentralblatt’s office and Springer possible, Pannwitz and two other members of staff were given special permits by the German Democratic Republic to enter East Berlin without strict control.
Together with other West Berlin editors, she set up an additional temporary editorial office within the Springer house at Heidelberger Platz. The split-up of editorial responsibilities for Zentralblatt became official with the cooperation agreement between the German Academy of Sciences and the Heidelberg Academy of Sciences in 1965. The academies agreed to continue Zentralblatt with the editing duties to be shared equally by both Berlin offices, with printing and distribution to be done by Springer. Walter Romberg was in charge of the Eastern editorial board, while Pannwitz continued as editor-in-chief of the Western office. She stepped down from this position in 1969, and Ulrich Güntzer became her successor.
This remarkable German-German cooperation lasted until 1977 and resulted in Zentralblatt renewing its international standing in mathematical reviewing, despite the complicated political constellation.
During the decade of the 1970s the annual production of mathematical publications doubled, reaching a volume that could no longer be handled by hand. Simultaneously, advances in computer science and databases called for a modernization of Zentralblatt. Güntzer entered several partnerships with various scientific institutions to benefit from their computing facilities for the editorial work at Zentralblatt. Bernd Wegner, who took over the position of editor-in-chief for the West Berlin office in 1974, further developed the ideas of technically advancing the service. Recording of the text started being done on magnetic tapes and, from these, the printed version of Zentralblatt was produced.
Due to the reorganization of all information and documentation centers in West Germany and the intended integration of Zentralblatt into one of these, the Academy of Sciences of the GDR, formerly German Academy of Sciences, terminated its cooperation contract with the Heidelberg Academy. The reviewers from the GDR had to quit their services for Zentralblatt, and from then on all processing of literature was handled solely by the West Berlin editorial staff.
In 1979 the West Germany government established the Fachinformationszentrum Energie, Physik, Mathematik (the current FIZ Karlsruhe – Leibniz Institute for Information Infrastructure) in Karlsruhe. The Zentralblatt Berlin office was incorporated as a subsidiary, while the Heidelberg Academy remained responsible for content and Springer stayed in charge of printing, marketing and distribution.
With the fall of the Berlin wall in 1989, the political circumstances changed again. The Academy of Sciences of the GDR was reorganized and some former members of the East Berlin editorial office resumed their work for Zentralblatt. The Heidelberg Academy, FIZ Karlsruhe, and Springer continued as editors and publisher. Since 1999 the European Mathematical Society has been involved in Zentralblatt as an additional editorial institution.
The revolutionary developments in information technology and computer science enormously helped to improve Zentralblatt’s services. The first release of the database as an offline version on CD-ROM called CompactMATH was published in 1990. Soon afterwards TeX was introduced for the typesetting of complex mathematical formulas. The transition of Zentralblatt to a service accessible through the Internet was accomplished in 1996; the database was named MATH and subsequently renamed zbMATH.
In 2004 all records from the Jahrbuch were digitized and incorporated as an extension to the database. Moreover, the complete bibliographic data of Crelle’s Journal (Journal für die reine und angewandte Mathematik) were added from its first issue of 1826. This makes zbMATH unique as the most comprehensive source of mathematical information from 1826 to the present. From 2012 to 2015 Gert-Martin Greuel was serving as editor-in-chief of zbMATH. This period has been marked by many substantial developments to enhance the online service; perhaps most notably, he put special emphasis on significantly improving the author database, the integration of reference data, and profile functions. Since 2013 zbMATH has had a new logo and look and has been distributed only in electronic form.
The qualitative demands of the academic community regarding coverage of mathematical literature have not changed over the decades since the publication of the first Jahrbuch and the foundation of Zentralblatt. The criteria of completeness, timeliness and objectivity remain a fundamental goal for mathematics reviewing organs. The incorporation of modern technologies into the core of the service, including linkage to complementary material, semantic enhancement, author disambiguation and inclusion of mathematical software, make zbMATH an indispensable tool for researchers in their search for accurate and high-quality information on mathematics publications.