by Roy Wagner

ETH Zürich
Dep. of Humanities, Social and Pol.Sc.
roy.wagner@gess.ethz.ch

Medieval mathematics was a field spanning a wide range of knowledge from commercial calculations to high theory and from the practical and recreational to the philosophical and mystical. In the Mediterranean area, it was a cross-cultural endeavor, circulating in oral and written forms in Arabic, Latin and vernacular languages. The migration of Jews across different language environments in the Middle Ages gave rise to a substantial corpus of Hebrew mathematics, which included some original contributions and served as a link between Islamicate and Christian-European knowledge communities.

The Mispar (literally, number, https://mispar.ethz.ch/wiki/Main_Page) project emerged from Naomi Aradi’s PhD dissertation on medieval Hebrew arithmetic. During her PhD, Naomi performed an almost unimaginable feat: she transcribed the corpus of an entire mathematical culture – practically all that survives of medieval Hebrew arithmetic (ca. 40 treatises, ca. 2000 manuscript pages). This, combined with some innovative digital tools, allows us to ask new questions about mathematics as a field of knowledge and as a culture.

Traditionally, historians interested in Hebrew mathematics focused on the most impressive treatises or excerpts in order to edit and analyze them in depth. This helped us to understand some peaks of mathematical knowledge and creativity (such as those of Ibn Ezra and Levi ben Gershon), but did not tell us a lot about how mathematical knowledge was conceived or understood by the “average” medieval Jewish intellectual. What appears to be unusual when looking at a handful of high-quality texts may in fact turn out to be quite standard when looking at the average “textbook” or vice versa. Moreover, questions of transmission of mathematical knowledge that cannot be answered by looking at major treatises may be resolved by looking at minor ones or at the corpus as a whole.

These questions have led Naomi to trace out an even more ambitious vision: an online, open access database, which will include not only all the transcribed texts with (at least partial) translations, but also tailor-made search capacities that can track down mathematical terms, mathematical algorithms and “formulas,” and mathematical word problems. With this kind of integrative view, a whole mathematical culture is made accessible, integrating its highs and lows, regularities and exceptions.

In order to turn this vision into a reality, Naomi teamed up with Roy Wagner, professor of history and philosophy of mathematics at ETH Zurich. With the support of the René & Susanne Braginsky Stiftung, the Gedenkstiftung Rapaport, and the ETH Zürich Foundation, we could turn Naomi’s vision into reality.

Our first task was to choose a platform. Instead of following many other digital humanities projects in creating our own platform and running the risk of not being able to maintain it in the long run, we decided to use a wiki platform. We wanted a platform that was there to stay, that was regularly updated and adapted to the realities of personal computing, and that enabled easy crowd sourcing.

Behind this choice was the understanding that we will never be able to finish this database. There will always be mistakes, newly discovered manuscripts, alternate manuscripts, additional processing of the material (translations, formalizations) and, most importantly, new information to extract from the database, which will require new coding. The only way to keep the database at least potentially open for further processing and improvements without a guaranteed long-term budget was to put it on a crowd-sourced platform, such as Wikimedia.

Which leads us to another technical challenge. We wanted our system to include rich semantic tagging: mathematical terms, algorithm and “formulas”, and problems were to be associated with semantic categories organized in a tree structure. But since we do not think of our database as finished, we have to allow changes to the source text even after some of this text is already semantically annotated. Surprisingly (at least for me), this is not possible with any of the available semantic annotation systems that were relevant for out project. Fortunately, the ETH scientific software and data management unit created for us a dedicated annotation system, which is open source and available to anybody interested in it (thanks, Swen Vermeul, for this hard work!).

Our systems currently allow users to view the entire corpus as well as lists of mathematical terms (in Hebrew and English, linked to their occurrences in the various manuscripts), track down specific kinds of word problems across the entire corpus, and see what kinds of algorithms and “formulas” occur in our database. All of this is still under construction, but the partial information we have gathered is already available to users and updated regularly. Moreover, the database includes partial translations or English summaries of the texts, making them accessible to scholars who are not fluent in reading the Hebrew mathematical language. This aspect too is being developed as we go along.

In order to consolidate the lists of Hebrew mathematical terms, we have been cooperating with the Peshat project. The Peshat online lexicon of philosophic and scientific Hebrew terminology (https://www.peshat.org) is enriched by mathematical terms linked to examples in our database, and Mispar terms will eventually be linked to definitions in the Peshat lexicon.

We hope that the availability of this database will attract new scholars to this research area and stimulate new inquiries and teaching. We also hope to “recruit” professionals and amateurs who will help us improve the database: editing, translating and completing the tagging of terms, mathematical expressions and word problems. We also hope that our database will eventually be expanded to include other branches of Hebrew mathematics, as well as mathematical texts in Judeo-Arabic. In the long run, perhaps it will host an even richer, multi-lingual corpus. We also note that our format can be used for other corpora, and would be happy to advise researchers in implementing similar databases.

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