( OS prefers reducing animation! )

Research Blog

Home > Research > CI Research Blog > A Global Mathematical Literature

A Global Mathematical Literature

Creative Informatics PhD RA project

Michael Barany, Senior Lecturer in the History of Science, reflects on the outcomes of his recent project with a PhD research assistant funded by Creative Informatics. Find out more about PhD RA funding here.

Creative mathematical research depends on many different kinds of conversations in many different forms with many different interlocutors—from a chalk talk at a blackboard to a one-sided argument scrawled in the margins of a journal to hand- and type-written missives sent over land and sea in airmail envelopes or virtual email packets. The changing scales and forms of these conversations have defined many dimensions of the history of mathematics and its relationships to science, industry, art, society, and much else. A vital challenge for historians today is to find a way to see those often-ephemeral conversations across their often-intractable geographies to understand their often-complex effects on an often-mathematical world.

At the turn of the twentieth century, internationally-minded mathematicians dreamed of real-time access to the latest work from a research community that, in their new international imaginations, had begun to include fellow mathematicians in different countries and even different continents and hemispheres. Today, with the right digital tools, working mathematicians (even those not particularly internationally minded) expect and depend on something very much like the dreamed-of infrastructures of their counterparts more than a century ago, with tools that allow rapid retrieval and traversal of everything from unfinished future papers to searchable published documents from well before the era of born-digital mathematical communication.

Our project aimed to turn those present-day infrastructures in on themselves to understand the emergence and effects of new globe-crossing apparatus of mathematical communication in the mid-twentieth century. We focused on the Zentralblatt für Mathematik und ihre Grenzgebiete, whose launch in the 1930s marked a turning point in how a newly unified mathematical literature was assembled and made available to mathematicians around the world. Using the Zentralblatt’s open-access online database zbMATH together with backend metadata and files shared by its publisher, we explored approaches to analysis that would help a backward-looking database (very much used today by forward-looking researchers) to give insights into how past mathematicians developed and used the Zentralblatt as a past-, present-, and future-looking means of building both theories and communities.

Masthead of Zentralblatt für Mathematik, from FIZ Karlsruhe’s collection of scanned page images.

The central challenge for this part of the research was to use the zbMATH database to understand what the original print Zentralblatt journal would have conveyed to readers in the 1930s, 1940s, 1950s, and so on. We wanted, moreover, to understand the living perspective of Zentralblatt readers at scale, using data-driven methods to derive a sense of pace, frequency, coverage, classification, and other dimensions of Zentralblatt reading experiences aggregated over years and decades. These elusive readers were, of course, not in view and not around to answer questions. We had an indirect form of the paper journals they read in their offices, libraries, and elsewhere, and much of our focus ended up being on the relationship between the present-day zbMATH database and those paper journals. Because zbMATH is a working database for working mathematicians, it has been assembled and maintained in ways that prioritise what working mathematicians need from it, rather than the needs and priorities of historians.

Draft chart of entry dates (first and third quartile) by volume number, by Rodrigo Liscovsky, excerpted from project research notes.

Bringing the historian-relevant features into view was not always possible, and often required taking a creative perspective on features intended for mathematical research, such as the database’s evolving system of indexing and classification. Seemingly simple questions like how long it took items to be included in the Zentralblatt were difficult to answer directly. The above chart examines the interquartile range of dates covered in successive volumes of the Zentralblatt as a way of estimating typical spans of material covered without overemphasizing small numbers of outliers or imperfectly validated metadata. Even here, some apparent anomalies stand out against a wider pattern of volumes slowly but surely reflecting an ever more voluminous mathematical literature.

The Creative Informatics PhD RA fund supported Rodrigo Liscovsky (now Dr Rodrigo Liscovsky!) to work with Principal Investigator Dr Michael Barany at the University of Edinburgh’s Science Technology and Innovation Studies Subject Group to understand and probe the zbMATH database. Rodrigo’s PhD developed data science methods for understanding international networks in biological research. Michael’s major area of research is on the globalization of modern mathematics in the twentieth century. Rodrigo began working with Michael on this dataset under a 2019 Carnegie Trust for the Universities of Scotland grant, and the collaboration took a number of twists and turns as researchers around the world responded to the Covid pandemic. (Indeed, Covid’s effects have shed new light on many of the contemporary dimensions of global mathematical interconnectivity, including its limitations, which Michael is exploring through other projects.) We partnered with Olaf Teschke, who leads a number of efforts including data-driven research with the zbMATH database at its publisher, FIZ Karlsruhe, and with a fellow recent PhD student and recipient in STIS, Rhodri Leng.

This latest stage of research focused on bringing Rodrigo’s contributions to a state where we could identify key findings and where future researchers could pick up as Rodrigo continues his career post-PhD. We now have a much better sense of the existing database and some solid tools for understanding its dimensions and for exploring its potential implications. It was clear at the end of this stage that we still need to zoom in to the database before we are prepared to zoom out to the historical questions that motivated the study, and Rodrigo’s work sets the foundation for future analyses that put the database into conversation with digital images from FIZ Karlsruhe and physical volumes at the National Library of Scotland. Michael is looking forward to continuing to work with student researchers on this over the next several years as part of a UKRI Frontier Research grant (ERC Starting Grant backstop), titled Situating International and Global Mathematics, to launch in late 2022.