zbMATH Open (formerly known as Zentralblatt MATH) 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 FIZ Karlsruhe. 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 serving the public interest. Since January 2021, zbMATH Open has been available as an open access service.

zbMATH Open is set to become a crucial hub in the global network of mathematics information. It connects a large variety of mathematics-relevant information and information services in our open access interface, and aim to enable more links through our APIs. More details are outlined in https://dx.doi.org/10.4171/NEWS/116/12.

Currently, zbMATH Open contains around 5 million bibliographic entries with reviews or abstracts drawn from more than 5,000 journals and book series, and some 200,000 books. The coverage, which starts in the 18th century, is complete from 1868 to the present day, due to the integration of the “Jahrbuch über die Fortschritte der Mathematik” data. In 2024, mathematically relevant parts of the arXiv were integrated. zbMATH Open contains more than one million profiles of identified authors connected with various platforms, the swMATH information service about mathematical software, about 50 million references, links to mathematical research data, and connections to various full text and research data platforms or Q&A forums like MathOverflow.


zbMATH Open 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 2020) and are equipped with keywords in order to characterize their particular content.

zbMATH Open covers all available published and peer-reviewed articles, books, conference proceedings as well as other publication formats pertaining to the scope given above that present a genuinely new point of view. For the list of journals and book series covered see the Serials search.

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".


Published items are initially indexed in zbMATH Open based on metadata provided by publishers as pending items. They obtain a stable zbMATH Open ID after finalization. This may take several months, depending on the reviewing and editorial process.

Selected articles will be reviewed after the indexing procedure. More than 8,000 active expert reviewers from all over the world contribute reviews to zbMATH Open.

Reviewers are selected by the zbMATH Open 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 appreciated.

Every trained mathematician is very welcome to become a reviewer of zbMATH Open in their specific field of research, see our FAQ on "Becoming a reviewer" for more details.

Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is a classification scheme maintained by Mathematical Reviews and zbMATH Open. 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 MSC2020. See the classification search or download MSC2020 (PDF).

Links to full texts

The service zbMATH Open contains about 4 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 Open entries as well as their electronic versions via DOI.

User interface

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

Features include:

  • Separated tabs allow for an easy navigation among different search facets: documents, authors, serials, classification codes and software. The search results are interlinked according to the structure of the contents.
  • Results of a query are filtered by authors, journals, classification codes and publication years according to frequency. This 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 their 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.
  • Serial profiles offer aggregated information on all indexed journals and book series, particularly helpful for librarians or for scientific evaluation purposes.


The information service swMATH was created as 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. It is being further developed in cooperation with the Zuse Institute Berlin in the framework of the Forschungscampus Modal.

This enables a novel information service for mathematical software. It offers open access to comprehensive information on mathematical software, and provides a systematic collection of references to relevant mathematical publications. In 2022, the swMATH data were integrated into the zbMATH Open service.

arXiv Preprints

zbMATH Open displays arXiv preprints from a specified set of subcategories in the math category. The subcategories are chosen by analyzing how many preprints in them have actually been published within the zbMATH Open scope in the past. For more details see arXiv:2401.08297.

In contrast to published articles, preprints are not reviewed and mistakes in their metadata are not corrected. Furthermore, withdrawn arXiv preprints are displayed following the arXiv policy. If a preprint gets published, it is merged with the published version. The zbMATH Open entry for a merged preprint disappears and the arXiv version will just appear as an additional link.

It might happen that a preprint is published in a journal or conference that is not in the scope of zbMATH Open. In this case, the corresponding zbMATH Open entry will remain in its preliminary form. Such cases are limited by the choice of the displayed arXiv subcategories, but cannot be ruled out completely.

Links to arXiv preprints are assigned algorithmically to published articles. This algorithm is not perfect and might lead to missing or wrong arXiv links at a zbMATH Open document. We very much appreciate your help in correcting those errors. Please contact us using our Contact Form so that we can correct the mistake.

Scientific and editorial boards

photograph of Christian Bär
Christian Bär
photograph of Dirk Werner
Dirk Werner

zbMATH Open 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 Sciences and Humanities.

In January 2024, Christian Bär took over the responsibilities as editor-in-chief of zbMATH Open. He is a professor of mathematics at the University of Potsdam. His main areas of research are differential geometry and global analysis.

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 zbMATH Open. Together with FIZ Karlsruhe and the other two editorial institutions, they develop long-term strategies for the future improvement of the service.

EMS Committees

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 our services.

Since 2017, the newly formed EMS Committee for Publications and Electronic Dissemination has assumed the duties of SCUC.

Editorial board

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


  • Steven Damelin
  • Gertraud Ehrig
  • Kıvanç Ersoy
  • Alexander Frey
  • Georg Hebermehl
  • Karl-Eberhard Hellwig
  • Klaus Kiermeier
  • Thilo Kuessner
  • Andreas Kühnemund
  • Jürgen Leiterer
  • Grit Malik
  • Olaf Ninnemann
  • Dieter Nowack
  • Octavio Paniagua
  • Volker Perlick
  • Aleksandar Perović
  • Matteo Petrera
  • Lutz Recke
  • Karin Reich
  • Enzo Rossi
  • Nicolas Roy
  • Klaus Schneider
  • Olaf Teschke
    (managing editor)
  • Oleg Titow
  • Frank Viola
  • Dirk Werner

International editorial organisations

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

History of zbMATH Open

The history of zbMATH Open, from its origins as a monthly compilation of bibliographic data and reviews of mathematical publications to its current status as a comprehensive service 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.

photograph of Otto Neugebauer
Otto Neugebauer
photograph of Harald Bohr
Harald Bohr
photograph of Richard Courant
Richard Courant
photograph of Ferdinand 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 scan of a typewritten letter by Ludwig Bieberbach.
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 Open 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

photograph of Hermann L. Schmid
Hermann L. Schmid
photograph of Erika Pannwitz, Elisabeth Szotowski, and Fritz Dueball
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.

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.

A black-and-white photograph of 10 people in front of bookshelves filled with file folders and Zentralblatt volumes.
Zentralblatt’s editorial board in 1965

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 and Humanities 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

photograph of Ulrich Güntzer
Ulrich Güntzer
photograph of Bernd Wegner
Bernd Wegner

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 of Sciences and Humanities. 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 of Sciences and Humanities 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 of Sciences and Humanities, 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.

photograph of Gert-Martin Greuel
Gert-Martin Greuel

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 starting 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 the addition of the software layer, and 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.

Becoming an open access service

photograph of Klaus Hulek
Klaus Hulek

Klaus Hulek served as editor-in-chief from 2016 to 2023. This period was marked by significant transformations – most notably, the transition to an open service, the integration of mathematical research data, and of the arXiv.

After a concerted effort by zbMATH stakeholders and based on a recommendation by the Leibniz Association, the Joint Science Conference (Gemeinsame Wissenschaftskonferenz) agreed in the first week of December 2019 that the Federal and State Governments of Germany would support FIZ Karlsruhe to transform zbMATH into an open platform. As a result zbMATH Open has become a freely accessible research tool for the mathematical community worldwide since January 2021.

This step was inspired by the International Mathematical Union's 2014 vision of a Global Digital Mathematics Library: "to provide a coherent and sustainable open platform in which all mathematics-relevant information and data can be brought together, comprehensively accessed and used free of charge under a uniform interface".

In the future, zbMATH Open will connect mathematical services and platforms in such a way that considerably more content will be available for further research and new research questions for collaborative work in mathematics and related fields.

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 Open an indispensable tool for researchers in their search for accurate and high-quality information on mathematics publications.

Facts & Figures

Documents: 4,866,444 items indexed for documents search with publication years between 1826 and 2024, including
Authors: 1,269,540 authors indexed for authors search, including
Serials: 4,995 journals and 2,626 book series indexed for serials search, including
Classification: 4,280,188 items classified by MSC 2020
Software: 45,959 software packages indexed for software search
referenced by 287,759 documents
Formulæ: 160,809,572 formulae indexed for formula search
Reviewers: 8,032 active reviewers
1,174,472 reviews since 1868
Full Text Links: 4,010,121 full text links for 3,622,799 documents, including
References: 49,544,297 references
including 29,724,669 references matched within 1,953,088 items
listed for 2,026,071 documents from 1,581 journals & series

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