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.
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 email@example.com. 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.
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 firstname.lastname@example.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.
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.
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 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.
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:
- swMATH is a joint project with the Mathematical Research Institute Oberwolfach (MFO), funded by the Leibniz Association, with the aim of building a freely accessible information service for mathematical software.
- DeLiVerMath focuses on the development of (semi-)automatic procedure to create and maintain controlled vocabularies and thesauri and to use those for indexing and classifying of mathematical documents. This is a joint project with the German National Library of Science and Technology TIB/UB and the L3S Research Center.
- MathSearch aims at developing tools for the automatic analysis and retrieval of mathematical formulae for the database zbMATH. Together with the Jacobs University Bremen as project partner, concepts and methods will be developed for the retrieval together with an intuitive user interface for mathematical expressions.
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.
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.
- Ingo Brüggemann
- Annalisa Buffa
- Anand Dessai
- Fuquan Fang
- Sofia Lambropoulou
- José Francisco Rodrigues
- Katrin Wendland
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.
- 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
- 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:
- Library of Chinese Academy of Sciences (Beijing, China)
- Mathematical Institute of the Serbian Academy of Sciences and Arts (Belgrade, Serbia)
- Mathematical Institute of the Slovak Academy of Sciences (Bratislava, Slovakia)
- Simion Stoilov Institute of Mathematics of the Romanian Academy (Bucarest, Romania)
- Institute of Mathematics of the University of Debrecen (Debrecen, Hungary)
- Institute of Mechanics of the National Academy of Sciences of Ukraine (Kiev, Ukraine)
- Russian National Public Library for Science and Technology (Moscow, Russia)
- Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk, Russia)
- Institute of Mathematics of the Academy of Sciences of the Czech Republic (Prague, Czech Republic)
- Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences (Sofia, Bulgaria)
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.
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
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
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.
Zentralblatt – a German-German cooperation
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.
Transformation into a reference database
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. In 2012 Gert-Martin Greuel was appointed the new editor-in-chief of zbMATH; he has since started new initiatives with the aim of enhancing the online service. Since 2013 zbMATH has a new logo and look and is 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.