Ibrāhīm al-Balīshṭār's book of arithmetic (ca. 1575): Hybridizing Spanish mathematical treatises with the Arabic scientific tradition

Abstract

We present an Arabic treatise on arithmetic, penned in Cherchell (Algeria) around 1575, of which five manuscripts are extant. The author, Ibrāhīm al-Balīshṭār, is a hitherto unknown Morisco mathematician from Aragon. After sketching his biography, we show that his treatise, claimed by him to be the translation of a book by a Christian priest, is actually an elaborate personal work, resulting from the intertwining of two Spanish treatises–those by Marco Aurel and Juan de Ortega–and of material drawn from Arabic authors such as al-Ghurbī, al-ʿUqbānī and Ibn al-Bannāʾ. It is therefore an original attempt to create a Euro-Islamic hybrid knowledge.

Résumé

Nous présentons un traité d'arithmétique en arabe, rédigé à Cherchell (Algérie) vers 1575, dont cinq manuscrits subsistent. L'auteur, Ibrāhīm al-Balīshṭār, est un mathématicien morisque jusqu'ici inconnu, originaire de l'Aragon. Après avoir esquissé sa biographie, nous montrons que son traité, qu'il dit être la traduction d'un livre d'un prêtre chrétien, est en réalité un travail personnel élaboré, résultant de l'entrelacement de deux traités espagnols – ceux de Marco Aurel et Juan de Ortega – et d'éléments tirés d'auteurs arabes comme al-Ghurbī, al-ʿUqbānī et Ibn al-Bannāʾ. Il s'agit donc d'une tentative extraordinaire de création d'un savoir hybride euro-islamique.

Introduction

Over the past few years, some attention has been paid to early stages of the transfer of modern European science to Islamic countries.¹ Much of the research has focused on translation, which represents the most tangible evidence of knowledge transfer. Most of the time, little is known about the translators. What can be gleaned from sources reveals a wide range of cultural go-betweens with diverse backgrounds and experiences: travellers, merchants, missionaries, converts, captives, exiles, interpreters, native scholars, translation pairs consisting of a native and a non-native, and so forth. The case reported in this article goes back to the sixteenth century: it is the earliest encounter we know of between Islamic mathematics and European mathematics, two long-separated sister traditions. Its specificity lies in the fact that the mediator attempted to create a hybrid between the two.

The origin of our research goes back to 1986, when one of us (H. H.) discovered at the National Library of Tunisia a previously unknown Arabic language arithmetical treatise, containing many original problems on commercial transactions. He immediately noticed an unusual and intriguing fact: the author of the treatise, a certain Ibrāhīm al-Balīshṭār living in Cherchell (Algeria), claims to have translated a book by a Christian priest. He analyzed the mathematical content of the treatise in some detail, but other occupations prevented him from publishing his observations, which remained in the form of handwritten notes in Arabic. It was not until 2018 that he announced this discovery at the Colloque maghrébin d'histoire des mathématiques arabes in Tunis (Hedfi, 2019) and, simultaneously, in the catalogue of a collection of scientific manuscripts kept in the National Library (Abdeljaouad and Hedfi, 2018, 111-115, 148-152). At this point, the author of the treatise remained mysterious and his sources unidentified. During the Colloque maghrébin, we decided to combine our efforts towards a better understanding of this intriguing treatise. This article sums up the main results of our joint research. Sections 1 and 2 cover the context in which al-Balīshṭār's treatise was written and what we could determine about its author. Section 3 describes its five extant copies, with a tentative stemma codicum. Sections 4 and 5 discuss its European and Arabic sources. Section 6 describes its contents, with special focus on two chapters which seem to us to be representative of the whole project. The article rounds out with an epilogue aimed at clarifying some confusion in historiography.

We are currently preparing a complete critical edition of al-Balīshṭār's treatise, including a French translation and extensive historical and mathematical comments. The reader is referred to this edition for more details.