2. Birth and first developments of mathematical activities in the Maghrib (9th-11th centuries)

Taking into account the very close economical, political and cultural links which were woven between the Maghrib and Muslim Spain throughout the Middle Ages, and taking into account the quantitative and qualitative importance of the transmission of the scientific production of each of these regions to the other, it seemed necessary for us to briefly recall the genesis and the most important aspects of the development of mathematical activity in the cities of Muslim Spain. This could also help the reader to better appreciate the strong lines of orientation of mathematical activity in the Maghrib by placing them into a larger – but more natural for the epoch – cultural and scientific context, that is that of the Muslim West.

In fact, the period that extends from the end of the 8^th century to the end of the 11^th century is characterised by the development, in the Maghrib and in Muslim Spain, of two more-or-less linked scientific traditions encouraged by scholars who, beyond the social contradictions and the differences of statute or of religion, were relatively united both by the way of life of the Islamic city and by the cultural and scientific environment that had been established favouring different human contributions and multiple contacts with the scientific foyers of the Muslim East [Vernet 1978; Vernet & Samso 1981; Samso 1992].

Having said this, we have to note immediately that the birth and the first steps of scientific activities in Muslim Spain and in the Maghrib are not well known. In fact, and to limit ourselves to our discipline, one has to recognise that testimonies concerning the beginning of mathematical activities in these two regions of the Muslim West are rare and not very specific. Speaking of the scientific activities during the period that follows the Muslim conquests in Spain, the bio-bibliographer of the 11^th century, Sā‘id al-Andalus¥, says that “the country remains indifferent to all sciences, with the exception of those of Law and the Arabic language, until the day that the power passes definitely to the Umayyads”, that is around the middle of the 8^th century [Sā‘id 1987: 120]. For his part, Ibn Juljul, another Andalusian bio-bibliographer who lived in the 10^th century, leaves us to understand that, until the epoch of the fourth Omeyyad caliph, >Abd ar-RaúmŒn II (826-852), the medical, philosophical and mathematical sciences did not have eminent representatives. But, in saying so, this author confirms implicitly the existence of men of science, understanding maybe that they had still not achieved the level of their colleagues of the East [Ibn Juljul 1955: 76].

However that may be, it seems reasonable to us to think that, during the period of installation and consolidation of Muslim power in the first cities of Spain and of the Maghrib, that Medicine and Calculation were the first scientific disciplines to have benefited from teaching followed by the publication of works, and this to respond to the needs of certain well-to-do ranks of society of the cities, or to the solicitations of lawyers for the solution of certain problems such as those involved in land measurement or in the partitioning of inheritance.

2.1. The Andalusian tradition

With regards to Muslim Spain, it seems that since the beginning of the 9^th century, the children of princes, of dignitaries or of well-to-do persons, have benefitted from scientific teaching using the first copies of translations of Greek and Indian works, made in the foyers of the centre of the empire, and maybe even copies of the first Arabic teaching books that started to appear in Baghdad, from the end of the 8^th century. This might have been the case of the children of the merchant and royal families, in particular those of ‘Abd ar-Rahmān II [Ibn Sa‘īd 1978: I, 45]. One knows also that the last one, after becoming caliph, participated in his turn in the support and the dynamisation of scientific activities by financing the establishment of an important library, and by providing it with books bought in the East. These caliphal initiatives, and probably other private initiatives, of which no precise testimonies have come to us, could only have favoured the quantitative and qualitative development of scientific activities in the principal cities of Muslim Spain. However that may be, it seems that it is in this period, that is around the middle of the 11^th century, that consequent scientific foyers started to exist on their own, in Cordoba and in other cities such as Toledo, Seville, Zaragoza and Valencia, which already knew relative economic prosperity [Sā‘id 1987: 122]. It is also in this period that one meets the first scholars whose names were transmitted by bio-bibliographers, together sometimes with some information on their profile or on their activities [Ibn Bushkuwāl 1966; Adhdhabbī 1884; Ibn Al-Abbār 1886].

During the last third of the 9^th century and throughout the 10^th, teaching and research, in the different fields of mathematics, were given greater importance due to the patronage of the two great Omeyyad caliphs of the 10^th century, ‘Abd ar-Rahmān III (912-961) and his son al-Hakam II (961-976). One sees thus a real research tradition being established around high level professors like Maslama al-Majrītī (d. 1007), who wrote works of mathematics and astronomy rivalling those that were produced in the East in the same epoch, and one sees a greater number of young researchers emerge, like Ibn as-Samh and az-Zahrāwī, who dominated the scientific activities of the first half of the 11^th century and whose books were an authority both in Spain and in the Maghrib [Sezgin 1974: 334-35, 355-56].

At the internal level of scientific tradition, one does not always have direct and precise testimonies on the nature and content of the exchanges that took place, during this period, between, on the one hand, the East and the West, and, on the other hand, between Muslim Spain and the Maghrib. But the analysis of the mathematical texts that came to us allows us to say that students, teachers and researchers had at their disposal initially translations of fundamental Greek texts, such as Euclid’s Elements, Ptolemy’s Almagest, Apollonius’ Conic Sections, and Archimedes’ On the Sphere and the Cylinder, and other works of less importance but essential to the training of a future mathematician or a future astronomer, such as Euclid’s Data, Archimedes’ Lemmas, and Menelaus’ Sphaerica. Later (or maybe simultaneously in the case of Algebra), one studied certain works of Arabic scholars from the East, like the Book on Indian Calculation and the Book of Algebra by al-Khwārizmī (d. 850), the Treatise of the Secant Figure and the Treatise on Amicable Numbers by Thābit Ibn Qurra (d. 901), the book of Banū Mūsā (9^th century) on The Measure of Plane and Spherical Figures, the Book of Algebra of the Egyptian Abū Kāmil (d. 930), as well as other writings of the same epoch, like the Epistle on Proportion and Proportionality and Epistle on Similar Arcs by Ahmad Ibn ad-Dāya (d. 944), another mathematician from Egypt [Sezgin 1974: 288-90].

2.2. The Maghribian tradition

Concerning the Maghrib we may say that the testimonies which have come to us on scientific activities between the 9^th and the 11^th century allow us to think that the beginning of mathematics, in this region of North Africa, took place in Ifriqiya and more precisely at Kairouan, from the end of the 8^th century and that these activities have remained confined within the limits of this region for a long time. Some names of scholars have come to us, like that of Yahyā al-Kharrāz [Ibn Tamīmī: 90-91] and that of his pupil Yahyā al-Kānūnī (828-901), author of the first Maghribian book of Hisba (which deals with the rules of commercial transactions at the market places) [Ibn al-Faradhī 1966: II, 183]. Maghribian sources cite also Shuqrūn Ibn ‘Alī who was a specialist in Calculation and in the Science of Inheritance and who is perhaps the first Maghribian to have written a book on the partitioning of successions [Makhlūf 1930: no. 31]. According to the testimony of Ibn Khayr (12^th century), the content of this book was still taught in the 12^th century, at Bougie, a scientific metropolis of the Central Maghrib [Zerrouki 1995: 15].

For the 9^th century, the name of only one mathematician has survived. It is that of Abū Sahl al-Qayrawānī, whose parents were natives of Baghdad. He is also the first known Maghribian mathematician of whom the title of one of his treatises has come to us. It is called Kitāb fī ‘l-hisāb al-hindī [Book on Indian calculation]. As its title clearly indicates, this book belongs to the new Arabic arithmetical tradition, of Indian origin, which started at the end of the 8^th or at the beginning of the 9^th century, in the handbooks of the mathematicians of the East.

It seems that it was the eminent role played by Kairouan in the theological debates, at the Aghlabid epoch (800-910) that attracted numerous intellectuals from the East to Ifriqiya, such as Abū Sahl and, among them, of men of science educated in arithmetical and geometrical techniques that could serve, in particular, to solve problems of land measurement or inheritance.

As in the other regions of the countries of Islam, the patronage in favour of scientific activities existed in the Maghrib between the 9^th and the 11^th century, and functioned in the image of that of the great metropolis of the East: buying of books, financing of copies of manuscripts, remuneration of scholars, construction of schools or institutions. This is not surprising if one knows the links which are woven between the caliphate of Baghdad and the Aghlabid dynasty that had governed Ifriqiya until the beginning of the 10^th century, and when one knows that the kings of this dynasty imitated both the model of government of the caliphs and their initiatives in favour of science and culture in general.

However the only information we have, with respect to this patronage, concerns the Bayt al-hikma [House of Wisdom] founded by Ibrāhīm II (875-902) and that bears indeed the same name as of that famous institution created by the Abbassid caliph Hārūn ar-Rashīd (r. 786-809) who played a great role in the translation of Greek and Indian scientific works [Abdalwahhab 1956: 253-72]. This institution, which survived its founder as a scientific centre until the arrival of the Fatimid dynasty, would have received mathematicians, astronomers and astrologers, such as at-Tallā‘ [Zubayd 1954: 164] and ‘Uthmān as-Sayqal [Abdalwahhab 1965-72: I, 249-50, 252-54].

There is very little known about the mathematical activities in the Maghrib during the 10^th century. It seems that the patronage started by the Aghlabids, in the 9^th century, was continued and profited Mathematics and Astronomy, in particular in the course of the first two decades of the government of the Fatimid caliph al-Mu‘izz (953-975) [Nu‘mān: 91]. However, nothing has come to us in the form of scientific documents which might inform us about the content of that what was produced or taught at that time. The biographers have only retained some names of persons who made themselves known by their activity in mathematics or by their interest in this discipline. As examples, one may cite al-‘Utaq al-Ifrīqī (d. 955) [Suter 1900: 70-71], Ya‘qūb Ibn Killīs (d. 990) and al-Huwārī (d. 1023) [Ziriklī 1980: VIII, 202-3, 158-59].

We are relatively better informed on the mathematical activities of the 11^th century. But our knowledge remains still very fragmentary. Certain scholars of this period are better known. This is the case of Ibn Abi r-Rijāl (d. 1034-35) who published works in Mathematics and Astronomy, which have not come down to us, and who was equally interested in Astrology. It is indeed due to this last discipline that he has been known in Europe since the 12^th century, as his book al-Bāri‘ fī ahkām an-nujūm [The brilliant book on the judgments of the stars] was translated by Constantin the African [Bouyahya 1972: 83-88]. This is also the case of Abū s-Salt (d. 1134), a native Spanish scholar, who spent most of his life in Egypt and then in Ifriqiya, and who published works concerning Geometry, Astronomy and Logic [Djebbar 1988b: 61-66]. Other mathematicians are less well known, such as ‘Abd al-Mun‘im al-Kindī (d. 1043-44) and Ibn ‘Atiya al-Kātib (c.a. 1016) [Dabbagh 1902: III, 228; Bouyahya 1972: 146]. We know that they occupied themselves with Geometry and Arithmetic, but we are still ignorant of their links with the different scientific foyers of their epoch and, in particular, about the circulation and the impact of their mathematical writings in the cities of the Maghrib.

By Professor Ahmed Djebbar, to be continued…