Zentralblatt MATH (zbMATH) is the online version of the oldest bibliographic database in the world specialized in mathematics.

• zbMATH allows to identify research articles and books, navigate in the references, …
• zbMATH allows to get reviews on articles and books
• zbMATH allows to get bibtex entries, DOI links, arXiv links, EuDML links, Numdam links, …
• zbMATH allows to identify mathematicians and to browse their author profile
• zbMATH allows to identity journals and to browse their serial profile

zbMATH is the European counterpart of MathSciNet, and is now Open Access contrary to MathSciNet.

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

The Editors of zbMATH 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.

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

One of the current differences in favor of zbMATH is the fact that it is Open Access while the access to MathSciNet is expensive.

One of the current differences in favor of MathSciNet is the high quality of reviews of articles, books, and author profiles for certain periods of time.

zbMATh 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.

Everything has a cost, the free access to zbMATH does not mean that zbMATH has no cost, it means that the cost is supported by institutions rather than by subscriptions.

zbMATH 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.

The zbMATH database is older than the one of MathSciNet and has presently a better coverage of the period before 1939 (goes up to 1870).

Here are some common misconceptions about zbMATH:

• zbMATH is low quality when compared to MathSciNet
  Partly incorrect. Many people find that the articles and books reviews proposed by MathSciNet are better than the ones proposed by zbMATH. Many people do not really care about these reviews and use MathSciNet or zbMATH essentially to explore the citation links between articles and to get reliable bibtex entries. 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. From this point of view, MathSciNet is a higher quality product than zbMATH.
• zbMATH does not provide author profiles that are helpful for evaluation of research
  Incorrect with the present version
• zbMATH does not provide DOI links and clickable bibliographies
  Incorrect with the present version
• zbMATH is less used than MathSciNet
  Correct, MathSciNet is the de facto first standard, but who cares?
• zbMATH does not allow to search for documents that quote a given paper
  Incorrect. It suffices to click on the button at the bottom right of the paper record.
• zbMATH is just an imitation of MathSciNet
  Incorrect, zbMATH incorporates the Jahrbuch and is older than MathSciNet, but MathSciNet was more innovative in the past regarding online services. Actually in terms of imitation, it is historically the contrary. Namely, MathSciNet is the online version of the Mathematical Reviews, started historically in the USA in the late 1930s to protest against the anti-semite behavior regarding the management of the ancestor of zbMATH at that time in the nazi Germany, see the article on Wikipedia and references therein.
• zbMATH is as expensive as MathSciNet
  Incorrect, zbMATH is now free worldwide while MathSciNet subscriptions fees are increasing year after year.
• zbMATH and MathSciNet are redundant and this is a pity
  Mostly incorrect, zbMATH leads 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 and MathSciNet are presently distinct:

• zbMATH is funded by European public institutions and its access is free worldwide.
• MathSciNet is a commercial product run by the American Mathematical Society who is using the fees to run its own other projects related to mathematics including research grants. In a sense the AMS collects a MathSciNet tax worldwide and decides what it wants for spending the funds. MathSciNet provides AMS points to the contributing reviewers, usable to buy AMS books for instance. zbMATh does the same but the reward is lower and some people reported that it is less interesting. On the other hand, the reviews written for zbMATH are Open Access, while the ones written for MathSciNet are accessible only to subscribers.
• Before 2021, zbMATH was not open access, run using roughly the same economical scheme as MathSciNet. Actually it was a commercial product of the publishing company Springer, and people were more inclined to give their money to the AMS rather than to Springer.

Google Scholar(1) is an automated product, in contrast with zbMATH(2) which is maintained by professional curators. In particular, Google Scholar(1) has problems in merging or making distinct authors and documents. zbMATH(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(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(2). Google Scholar(1) also provides bibtex entries, but their quality and accuracy is lower than on zbMATH(2).

(1) as well as Semantic Scholar and Microsoft Academic. (2) as well as MathSciNet. zbMATH was more automated than MathSciNet and had less curators.

Microsoft Academic is the Microsoft version of Google Scholar in a sense.
Semantic Scholar is the Allen Institute version of Google Scholar in a sense. 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 authors profiles and publication metadata.

If you are a PhD student, you should test and explore zbMATH, 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 or MathSciNet and you probably use Google Scholar for the exploration of bibliographies and to get bibtex entries. Nevertheless, you could try zbMATH out of curiosity, you will find for free a better quality than on Google Scholar and often 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 can help you getting bibliographic exploration, bibtex entries, and author profiles, while being free access.

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

It depends on the budget pressure, on the type of mathematics, on the habits of colleagues, and on the arbitrage between short term and long term vision.

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 is Open Access and has a unique coverage of the period 1939-1870. 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, 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.

The official version of this document is on https://www.rnbm.org/zbmath-open-the-first-ressource-for-mathematics/