zbMATH Open : the first resource for mathematics

Give it a try now: zbmath.org

This short document targets mathematicians, from doctoral students to emeritus scholars. It was written on March 2021.

It aims to provide information as well as to help decision making.

In order to increase the impact of this page, we are actively encouraging institutions to translate this document, under licence CC-BY-NC-SA, in their own language.

zbMATH Open (formerly Zentralblatt für Mathematik) is the online version of the oldest bibliographic database in the world specialized in mathematics.

  • zbMATH Open allows to obtain reviews on articles and books
  • zbMATH Open allows you to get bibtex entries, DOI links, arXiv links, EuDML links, Numdam links and other digital repositories
  • zbMATH Open allows you to identify and disambiguate mathematicians and to browse their author profile
  • zbMATH Open allows to identity journals and to browse their serial profile
  • zbMATH Open allows you to find and identify research articles and books, navigate in their references, etc.

zbMATH Open is the European counterpart of MathSciNet, and is now open access in contrast to MathSciNet.

zbMATH Open is produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH (FIZ Karlsruhe).

The Editors of zbMATH Open are the European Mathematical Society (EMS), FIZ Karlsruhe, and the Heidelberg Academy of Sciences and Humanities.

You may take a look at the comprehensive frequently asked questions on zbMATH Open.

At the time of writing this text, zbMATH Open and MathSciNet are quite close in spirit and in features.

One of the current differences in favor of zbMATH Open is the fact that it is open access while the access to MathSciNet is in general expensive. zbMATH Open provides, for each paper in electronic version, not only a link to its DOI, but also, if it exists, a link to arXiv, Euclid, Numdam, EuDML, DigiZeitschiften, etc. This is not provided by MathSciNet.

One of the current differences in favor of MathSciNet is the large quantity of current reviews of articles and books, essentially due to the big number of reviewers they have.

The free access to zbMATH Open is supported by European institutions rather than by subscriptions.

zbMATH Open is willing to make its database entirely open under the terms of an open access license. This is more than just a free access to a service.

zbMATH Open has powerful tools that enable the user to make complex and precise queries: operators, fields and filters that can be combined at will. E.g., in zbMATH Open you can look for all papers where a given author is cited and then refine your search using all these tools.

The zbMATH Open database is older than the one of MathSciNet and has presently a better coverage of the period before 1939 (it starts from 1868).

Here are some common misconceptions about zbMATH Open:

  • zbMATH Open has lower quality compared to MathSciNet

    Incorrect. Some people may find that the articles and books reviews proposed by MathSciNet are better than the ones proposed by zbMATH Open. It is true that MathSciNet has more reviewers that zbMATH Open, nonetheless the number of reviewers of zbMATH Open is currently increasing after it became open access. A large part of researchers are not interested in these reviews and they use MathSciNet or zbMATH essentially to explore the citation links between articles and to get reliable bibtex entries and other metadata. MathSciNet, at least for certain periods of times, has put more efforts and human resources for data processing, while zbMATH has used more algorithmic data processing for a larger collection of serials. Maybe it can be said that MathSciNet was more innovative in the past regarding online services, but zbMATH Open has improved greatly. There are features that at the moment are only present in zbMATH Open: the information service for mathematical software swMATH, which provides a systematic collection of references to software-relevant mathematical publications. In zbMATH Open we have an interlinking with some other open access services such as MathOverflow; thanks to the fact that now zbMATH Open is an open access database, the author profiles have more external links and more open access services will be incorporated in this complex network of services. There is also the feature formula search allowing the user to find whether a specific formula is found in a paper.

  • zbMATH Open does not provide author profiles that are helpful for evaluation of research

    Incorrect, the author profiles in zbMATH Open are very complete. zbMATH’s staff has invested a lot of time and resources to obtain accurate and complete author profiles. It should be remarked that thanks the state funding of zbMATH Open it does not require the storing of extensive user data, which is usually the case of subscription-based services

  • zbMATH Open does not provide DOI links

    Incorrect in the present version. Besides, as already mentioned, zbMATH Open provides links for other digital libraries.

  • zbMATH Open does not provide enough and clickable references

    Incorrect.While it is true that MathSciNet historically had more references in their entries, the number of (clickable) references in zbMATH Open has increased significantly. Currently, by https://zbmath.org/about/#id_4 and https://mathscinet.ams.org/mathscinet/help/byTheNumbers.html, zbMATH Open has more than 20 million matched citations (compared to more than 17 million in MathSciNet) .

  • zbMATH Open is less used than MathSciNet

    In the last ten years the number of queries in zbMATH has increased more than tenfold: the current number is around 25 million queries per year.

  • zbMATH Open does not offer the citations of a given paper

    Incorrect. In zbMATH Open it suffices to click the button at the bottom right of the paper record. Overall, as it can be again checked at the figures pages, the numbers of cited articles are on par.

  • zbMATH Open is just an imitation of MathSciNet

    Incorrect, Zentralblatt für Mathematik und ihre Grenzgebiete was founded in 1931 by Otto Neugebauer, among other mathematicians. MathSciNet is the online version of the Mathematical Reviews, which was founded also by Otto Neugebauer in the USA in the late 1930s to protest against the anti-semite behavior regarding the management of the ancestor of zbMATH Open at that time in the Nazi Germany, see the article on Wikipedia and references therein. zbMATH Open has incorporated the Jahrbuch which started in 1868.

  • zbMATH Open is as expensive as MathSciNet

    Incorrect, zbMATH Open is now free worldwide while MathSciNet’s subscriptions fees increase year after year.

  • zbMATH Open and MathSciNet are redundant and this is a pity

    Mostly incorrect, zbMATH Open influences MathSciNet to improve itself, and the converse is true. Moreover, the article and book reviews, when available, are not written by the same person in general, and it is good to have multiple points of view.

The economical models of zbMATH Open and MathSciNet are presently distinct:

  • zbMATH Open is funded by European public institutions and its access is free worldwide.
  • MathSciNet is a commercial product run by the American Mathematical Society who uses the fees to run its own other projects related to mathematics including research grants. In a sense the AMS collects a payment worldwide and decides how it spends the funds. MathSciNet provides AMS points to the contributing reviewers, usable to buy AMS books for instance. The reviewers in zbMATH Open at the present time have privileges for buying books from EMS Press. Nowadays, the reviews written for zbMATH Open are open access, while the ones written for MathSciNet are accessible only to subscribers.
  • Before 2021, zbMATH was not open access, it ran using a similar business scheme as MathSciNet. Springer Verlag was a long commercial partner for distributing zbMATH and therefore many people thought it was a commercial product of Springer. Maybe this was the reason why some institutions were more inclined to give their money to the AMS rather than to Springer.

In the case of all automated services like Google Scholar, Semantic Scholar and Microsoft Academic there is neither a consistent development nor independent reviews by experts. Also, another big problem is that in these automated services the profiles could easily be rigged. Google Scholar (1) is an automated product, in contrast with zbMATH Open (2) which is maintained by professional curators. In particular, Google Scholar (1) has problems in merging or making distinct authors and documents. zbMATH Open (2) aims to provide unique authors and document identifiers, which is useful for profiling. Nevertheless, using Google Scholar (1) is a good complement to zbMATH Open (2) for articles and authors profiling. The author profiles on Google Scholar (1) are maintained by the authors themselves, in contrast with the ones on zbMATH Open (2). Google Scholar (1) also provides bibtex entries, but their quality and accuracy is lower than on zbMATH Open (2).

(1) as well as Semantic Scholar and Microsoft Academic. (2) as well as MathSciNet.

Microsoft Academic is the Microsoft version of Google Scholar in a sense.
Semantic Scholar is the Allen Institute version of Google Scholar. It features graphical influence analysis.
ArXiv and the French HAL are something else for the moment, essentially preprint databases, with preprint bibtex entries, references exploration, limited author profiles and publication metadata.

If you are a PhD student, you should test and explore zbMATH Open, at least to understand how it works and what it provides.

If you are a young mathematician, it is likely that you do not feel the need for a database like zbMATH Open or MathSciNet and you probably use Google Scholar for the exploration of bibliographies and to get bibtex entries. Nevertheless, you could try zbMATH Open out of curiosity, you will find for free a better quality than on Google Scholar and you will find complementary information. Google is making Google Scholar free in order to encourage users to create a Google profile and to enter the Google consumerism and at minimum you will pay with your (meta)data.

If you are an experienced mathematician, it is likely that you already have your habits, and that you also have to evaluate research and colleagues. zbMATH Open can help you getting bibliographic exploration, bibtex entries, and author profiles, while being free access.

So if you do not know what is zbMATH Open or if you have tested it years ago, it is worth to give it a try (again)!

It depends on the budget pressure, if an institution has the resources to pay the subscription, then it is fine that it subscribes to MathSciNet and let the users to explore it and compare it with zbMATH Open, since they have different strengths. This competition will lead to services of better quality. If the budget is tight, zbMATH Open is a very strong alternative in all cases, especially when it is compared with other automated services such as Google Scholar, etc.

The cost of MathSciNet for a department depends on several parameters (close to 10K€/year) and should be compared with subscription costs for journals for instance.

zbMATH Open is open access and has a unique coverage of the period 1868-1939. MathSciNet was less automated and has a high quality of reviews for certain period of time.

By helping your colleagues / department to shift even temporarily to zbMATH Open, you can contribute to encourage the AMS to question its model.

Some mathematics departments have already decided to stop their MathSciNet subscription, such as the one of Université Grenoble Alpes in France.



This short document was set up by the RNBM, and benefited from the feedback of several colleagues and collaborators including people from Cellule Mathdoc.

We are actively encouraging institutions to translate this document in their own language.

This work is licensed under a Creative Commons Attribution 4.0 International License.

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