## Mathematics in the Medieval Maghrib: General Survey on Mathematical Activities in North Africa 1/5

### Introduction

The text that we will present here is the first part of a study which attempts to present the essential aspects of mathematical activity in North Africa since the 9^{th} century. The abundance of material has obliged us to report, in a future article, the study dedicated to mathematical activities in Egypt during the same period. The whole work, as soon as concluded, will constitute the second volume of the study “Recent research on the history of Mathematics in Africa: an overview”, by A. Djebbar and P. Gerdes, whose first volume has already been published (Gerdes 1992: 3-32, 1994) [1].

This work is just a first outline that needs to be completed by the presentation of certain activities which abundantly used the different mathematical disciplines and were sometimes considered more important than mathematics. Essentially this refers to Astronomy, Astrology, and the Science of Succession Division or Science of Inheritance. We have satisfied ourselves by evoking certain of their aspects, or certain authors who are particularly distinguished, hoping to deal with them more fully in a later study.

However, so as to avoid eventual misunderstandings or ambiguities, it seems useful to make some remarks about the terminology that will be used in the different parts of this study.

First of all we need to specify what we understand by “scientific tradition”. As soon as we begin to deal with the contents of scientific, and more particularly mathematical activities, which take place in the context of the Arab-Islamic civilisation, it is not possible to speak of a specific tradition in the Maghrib (as opposed to that of Muslim Spain or that of the East). In fact we may speak of one overall tradition, that of Arabic mathematics – that is mathematics that has been thought about, written and taught in the Arabic language (also called Mathematics of the countries of Islam) -, which has developed in the East since the end of the 8^{th} century, and that has been partially transmitted to the cities of the Muslim West and of Central Asia, and later to southern Europe, by means of translations (essentially Latin and Hebrew). This tradition has been assimilated, revived and enriched by the scientific environments of the different countries of Islam that gave it, sometimes, certain specific mark at the level of this or that research and teaching orientation, as well as at the level of composition of the contents of the works, of the terminology, or of the classification of the studied disciplines. But, as far as we know, this internal process of differentiation has not lead to the emergence, at local or regional level, of a new mathematical tradition characterised by its own concepts and paradigms. The scientific traditions which are evoked in this study are such in an externalist sense that takes scientific practice in relation to its environment into account.

The same remark applies to the contents of the mathematics produced or taught in each of the five vast regions that constituted, in the Middle Ages, North Africa, that means the Extreme Maghrib, the Central Maghrib, the Oriental Maghrib that at that time was called Ifr¥qiyya, Egypt and the extended sub-Saharan zone of Muslim confession that went then by the name of BilŒd as-S’dŒn [Countries of the Sudan]. The analysis of the scientific texts which have come to us does not allow us to speak of regional specificities either at the level of content itself or at the evolution of its contents. On the contrary, we observe, following the epochs, notable differences between the regions, at the level of the number of mathematicians or of their works, of the vitality of this or that taught discipline, of the dynamism of the different scientific foyers of each of these regions.

It is also necessary to explain what we here understand by “Maghribian mathematicians”. In bio-bibliographic treatises, in particular those written by oriental authors, one finds a certain number of scholars, poets and writers who are referred to as “Maghribian” without being born in the Maghrib. That is the case, for example, of scholars native to Muslim Spain. That is also the case of those whose parents are native of the Muslim West but who have grown up or have been educated in the East. In addition, there are persons whose origin is not Maghribian but who have played a role in the scientific activity of the Maghrib. Thus, in the case of mathematicians, it is necessary to specify that only one category is representative of the mathematical production of the Maghrib. This concerns those who lived there during a given period of their life and who, through their teaching or through their production, contributed to the development or the perpetuation of a local or regional mathematical activity. As an example of this type of scholar, one may cite al-Qatrawānī (15^{th} century), who was born in Egypt and who lived for a certain time in Tunis where he wrote one of the books that we will mention later [Lamrabet 1981: 41-91; Djebbar 1986a: 118-19; Hadfi 1989, 1992: 138-39].

With respect to the others, one may classify them into two categories: the first regroups all who were natives of the Maghrib and who have left it in order to install themselves in another region of Africa (such as Egypt or the Sub-Saharan regions of the continent). Among the representatives of this category, one finds al-îasan al-MurrŒkush¥, one of the greatest specialists of astronomy in the 13^{th} century, who lived essentially in Egypt [Sédillot 1834-35, 1844; Souissi 1982; Murrākushī 1984].

The second category regroups all those who were born in or were natives of the Maghrib but who were, in reality, educated in the cities of the East or of Muslim Spain, and who spent the largest part of their life there. One of the most eminent representatives of this category is as-Samaw<al al-Maghrib¥ (d. 1175) who was born in Baghdad to a Jewish family native of the Extreme Maghrib, more precisely from Fez [Anbouba 1970: 80]. His major contributions, which concern the theory of polynomials and decimal fractions, seem not to have been known by the Maghribian mathematicians of the 12^{th}-14^{th} centuries [Rashed & Ahmad 1972; Rashed 1984].

As these mathematicians or astronomers have not participated, in any way, in a scientific activity in the Maghrib and as these have not been vectors of this activity, we have not judged it useful to mention their different contributions here.

*By Prof. Ahmed Djebbar, to be continued…*

### Table of contents

**1. Introduction****2. Birth and first developments of mathematical activities in the Maghrib (9**^{th}-11^{th}centuries)- 2.1. The Andalusian tradition
- 2.2. The Maghribian tradition
**3. Mathematics in the Maghrib during the Almohad epoch (12**^{th}-13^{th}centuries)- 3.1. The contribution of al-Qurashī
- 3.2. The contribution of al-Hassār
- 3.3. The contribution of Ibn al-Yāsamīn
- 3.4. The contribution of Ibn Mun‘im
**4. Mathematical production in the Maghrib during the 14**^{th}-15^{th}centuries- 4.1. The contribution of Ibn al-Bannā
- 4.2. The continuators of the tradition of Ibn al-Bannā
**5. The mathematicians of the Maghrib after the 15**^{th}century**6. Conclusions****7. History of Mathematics in the Medieval Maghrib: Survey of the Scholarship**

### End Note

[1] See also the volume published recently: *Mathematics in African History and Cultures: An Annotated Bibliography* by Paulus Gerdes and Ahmed Djebbar, African Mathematical Union, 2004 (430 pp., ISBN 978-1-4303-1537-7). New updated and extended edition, 2007 (Chief Editor).