Author accepted manuscript, accepted 27 January 2025, version of record to be published in Mathematische Semesterberichte, https://doi.org/10.1007/s00591-025-00388-7.

Review by Michael J. Barany, University of Edinburgh, m.barany@ed.ac.uk

Klaus Hulek, Octavio Paniagua Taboada, and Olaf Teschke (eds.) 90 Years of zbMATH. EMS Press, 2024.

Since its first print volume in 1931, the Zentralblatt für Mathematik und ihrer Grenzgebiete and its successor resources have reshaped how mathematicians understand and interact with the international published literature of their discipline. The abstracting journal, originally published by Springer Verlag, was distinguished from its earliest days by an editorial ambition to review the entire world’s mathematics literature (‘die gesamte Weltliteratur der Mathematik’) efficiently enough to provide a dynamic view of current research, rather than a static retrospective of past research. At once an idealistic international collaboration and daunting technical and logistical accomplishment, the journal has been strongly marked across its history by the geopolitical calamities and divisions of the twentieth century as well as the changing circumstances of science research and scientific information.

For the eightieth anniversary of what had by then been remade into the zbMATH database, the editors compiled a core sample of one review for each year, together with author profiles from the database and a brief survey by Silke Göbel of the publication’s remarkable history.¹ No longer published by Springer and now distributed open access as zbMATH Open, the project celebrated (a few years late) in 90 Years of zbMATH exhibits a decade of dramatic changes that are the focus of a rather more forward-looking volume.

The slim book is available from the European Mathematical Society’s EMS Press as an open-access PDF, and is perhaps overpriced at €29 in paperback (with neither the advantage of being able to click any of more than a hundred hyperlinks in the footnotes and elsewhere, nor the much crisper digital appearance of the colour figures). Short messages from representatives of the three bodies currently responsible for zbMATH Open, the European Mathematical Society, the Heidelberg Academy of Sciences and Humanities, and FIZ Karlsruhe - Institute for Information Infrastructure, are followed by nine short chapters and two longer ones. The authors come from a close research, editorial, and production community around zbMATH, and together offer an inside view of recent and anticipated challenges and developments for the enterprise.

Deputy editor-in-chief Dirk Werner contributed the two shortest essays, offering illuminating glimpses of the community of reviewers, the selection of indexed literature, and (in both essays) the roles of the former in evaluating the latter. Chapters on software indexing, full-text open access, formula search, author identification, integration with other platforms, and API tools, although quite technical at points, strikingly exhibit both the complex difficulties of contemporary mathematical bibliography and the enormous possibilities to be found in zbMATH’s data and software. Above all, these chapters highlight the transformation of zbMATH to emphasise linked information systems, with publication-focused data a vital part of a growing ecosystem of interrelated digital data about science.

Two chapters use zbMATH’s voluminous bibliographic data to provide critical quantitative insights into, respectively, the mathematics profession’s gender gap and the different patterns of authorship and citation that confound common indices of scholarly impact. Both chapters show a justified optimism in the potential of such data to provide insightful big pictures of the discipline while also evenhandedly presenting many of the difficulties and ambiguities that come with wrangling the zbMATH data.

Helena Mihaljević and Lucía Santamaría’s chapter on the gender gap comes from their work on a major international project funded from 2017-2020 by the International Science Council to develop means to measure and hopefully reduce gender gaps in access to and recognition in scientific careers. Inferring genders for more than four million author-publication pairs between 1970 and 2019 from the zbMATH data (more than a million could not be inferred), they derive several indicators of gender discrepancies in mathematical careers from associated patterns of publication. The authors find a silver lining in the tight academic job market with a somewhat narrowing gender gap among those who continue to publish ten years after having been active for five years–their proxy for transitioning into stable mathematical careers. Conversely, their data show grimly persistent gender gaps in high-profile journal publications.

The book’s final chapter, by recent zbMATH editor-in-chief Klaus Hulek and zbMATH managing editor Olaf Teschke, illustrate a variety of uses of publication, citation, authorship, and classification data while calling for further studies. Indeed, alongside the effort to convert zbMATH to a highly interlinked open access data platform, Teschke and collaborators have for some time been energetically piloting and demonstrating creative uses of zbMATH data and supporting a wider assortment of interested researchers. This chapter focuses on different ways to parse citation measures using the interlinked zbMATH data, challenging the validity of common science metrics based on short-term citations for mathematicians’ varied and somewhat distinctive publication and citation patterns.

One comes away from 90 Years of zbMATH with a sense of the living project of mathematical bibliography, transformed time and again in response to the questions, opportunities, challenges, and tools of each era of mathematical research. This volume joins that living history not by looking back but rather by looking around, finding emerging and potential ways that the latest developments in mathematical bibliography can foster and flourish from interactions with the varied worlds of mathematical and scientific communication and information. The volume evidences the vibrancy not just of the mathematical community that has long cultivated and used iterations of the Zentralblatt but also the multidisciplinary communities of mathematicians, data scientists, software engineers, social scientists, and more who are rethinking what zbMATH can offer. I look forward in those terms to the impending centenary.