The date of the foundation of Fes is from the early 9th century. Fes soon after received an influx of diverse origins, Berbers, Jews, Arabs, including also Spanish Muslims from Cordoba. A strong scientific tradition was established in Fes, and many men of science lived there.

Fes is a symbol of Muslim excellence. Browsing through Burckhardt's work on the city[1] one is struck by the crucial element that has marked Muslim civilisation in its glory days: the search for perfection; a search which marked all Muslim sciences, artistic and literary achievements. Many such accomplishments have disappeared with time, yet the traces can be still seen in Fes. Somehow, the city is a depository of the might of Muslim achievements, and much of such might can be seen in the photos of buildings and treasures of the city.

The date of the foundation of Fes is from the early 9^{th} century, the work of the Idrisids.[2] Fes soon after received an influx of diverse origins, Berbers, Jews, Arabs, including also Spanish Muslims from Cordoba who had just been severely repressed by the ruler Al-Hakem I.[3] The city grew sizeably and in cultural importance. Available information shows that a strong scientific tradition was established in Fes, and many men of science lived there.[4]

The city's greatest symbol of culture and science is the Qarrawwiyin mosque university. Al-Qarrawwiyin was first built in 859 CE, and was for some time one of the three or four schools of the city, before becoming the principal centre of higher learning in Morocco.[5] At the Qarrawwiyin, there were courses on grammar, rhetoric, logic, elements of mathematics, astronomy,[6] and possibly history, geography along with elements of chemistry.[7] The Qarawiyyin had three separate libraries, the most prestigious of which being the Abu Inan Library, also known as the Ilmyia library, whose original building is still standing.[8] Founded by the Merinid Sultan, al-Mutawakkil Abu Inan, the library opened its doors to students and the general public in 750H/1349 CE. The Sultan was an avid reader and collector. In his newly founded library, deposited books included various subjects that included religion, science, intellect and language. He also appointed a librarian to take charge of the affairs of the library.[9] The university itself was endowed principally by royal families and received students from diverse origins, near and distant, from the Maghreb, the Sahara and also Europe.[10] Students lived in residential quadrangles, which contained two and three storey buildings, accommodating between sixty to a hundred and fifty students. What is more, all received a minimal assistance for food and accommodation.[11] Fes also had a number of madrassas (schools) built by the Merenids, thus helping secure regular and universal education in the city.[12]

However, it was during the rule of the Almohads, in the 12^{th} century, that Fes witnessed its cultural, literary and commercial apogee. In the reign of al-Mansur and his followers there were in Fes seven hundred and eighty five mosques and zawiyas (Sufi retreats) . There are about 250 today; 240 places of convenience and purification, and 80 public fountains, which were all fed with water from springs and brooks. There were 93 public baths and 472 mills within and alongside the walls, not counting those outside the city. The same chronicler goes on to mention 89036 dwelling houses, 19041 warehouses, 467 founduks (hotels) for the convenience of merchants, travellers, and the homeless; 9082 shops, two commercial districts, one in the Andalusian district, near the river Masmuda, and the other in the Kairaounese district; 3064 workshops, 117 public wash-houses; 86 tanneries; 116 dye works; 12 copper smiths; 136 bread ovens; and 1170 other ovens. In Fes, there were also notably 400 paper making shops,[13] which gives an idea of the scope of the intellectual life of the city.

Learning and scholarship in Fes is symbolised by the Qarrawwiyin mosque. Al-Qarrawwiyin Mosque University had a great impact on learning both around the Mediterranean and Europe. From the beginning of the 12th century until our time, it is held that 'the glory' of the Qarrawwiyin was its body of scholars (ulamas).'[14] Among the scholars who studied and taught there were Ibn Khaldun, Ibn al-Khatib, al-Bitruji, Ibn Harazim, Ibn Maymoun, and Ibn Wazzan, and possibly even the future Pope Gerbert (d.1003), who later became Pope Sylvester II, who introduced the Arabic numerals into Europe.[15] The most prominent of these figures later on exerted their skills in other places. But the scholar to identify most with Fes, and whose scientific accomplishments out-lasted the centuries is the mathematician Ibn al-Banna.

Ibn al-Banna, also known as Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi, was born in 1256 in the city of Marrakesh, the son of an architect.[16] Ibn al-Banna studied geometry, fractional numbers and learnt much of the impressive contributions that the Muslims had made to mathematics over the preceding 400 years.[17] At the university in Fes Al-Banna taught all branches of mathematics, which at this time included arithmetic, algebra, geometry and astronomy. Many students studied under al-Banna in a thriving academic community.[18]

Al-Banna wrote a large number of works, between 51 and 74 works, most of them on mathematics and astronomy.[19] Based on the inventory that was made, at the time, by Ibn Hayder, Ibn al-Banna seems to be in fact the author of more than 100 titles, of which 32 concern Mathematics and Astronomy, the others being dedicated to disciplines very distant from each other, like Linguistics, Rhetoric, Astrology, Grammatics and Logic.[20] The eminent position Al-Banna occupied in the court helped him solve the problems that preoccupied his contemporaries, one work in particular, which addressed a whole new form of mathematical problems and questions.[21] This work is *Tanbih al-albab 'ala masa'il al-hisab *(Warnings to the Intelligent Regarding Matters of Calculation), the first part of which contains the precise mathematical answers to domains of everyday life, like the composition of medicaments, the calculation of the drop of irrigation canals, the arithmetical explanation of a verse of the Qu'ran concerning inheritance, the determination of the hour of the third daily prayer, the explanation of frauds linked to instruments of measurement, the enumeration of delayed prayers which have to be said in a precise order, the exact calculation of legal tax in the case of a delayed payment, etc.[22] The second part, which belongs to the already ancient tradition of judicial and cultural mathematics, joins a collection of minor arithmetical problems presented in the form of poetical riddles.[23]

Al-Banna's other most famous work is *Talkhis amal al-hisab* (Summary of the operations of calculation) and the *Raf al-Hijab *(Lifting of the veil) which is al-Banna's own commentary on the *Talkhis*. The Talkhis contains many new features, including improved treatment of fractions; sums of squares and cubes; casting out of nines, eights, and sevens; rules of double false position.[24] It is in this work that al-Banna introduces some mathematical notation which has led certain authors to believe that algebraic symbolism was first developed in Muslim civilisation by ibn al-Banna and al-Qalasadi.[25] The Talkhis was very popular, its success lasting for over two centuries as a manual of mathematical scholarship.[26] There are also many interesting mathematical ideas and results which appear in the *Raf al-Hijab*, such as continued fractions used to compute approximate square roots.[27]

Al-Banna also seems to have been the first to consider a fraction as a ratio between two numbers and in his *Kitab al-Manakh* (hence the word, almanac), which includes data on astronomy and meteorology, he seems to be the first to use the world manakh in this sense.[28]

And finally, it is worth concluding that Ibn al-Banna was the teacher of Ibn Brahim al-Abbali (d.1368) who in his turn was Ibn Khaldun's teacher.

**Bibliography**

-T.Burckhardt:* Fez City of Islam;* The Islamic Text Society; Cambridge; 1992.

-A Djebbar: Mathematics in medieval Maghreb;* AMUCHMA-Newsletter *15; Universidade Pedagogica (UP), Maputo (Mozambique), 15.9.1995.

-Bayard Dodge: *Muslim Education in Medieval Times*; The Middle East Institute, Washington D.C, 1962.

-J J O'Connor and E F Robertson: Arabic mathematics, a forgotten brilliance at:

__http://www-history.mcs.st-andrews.ac.uk/history/index.html__

-Levi Provencal, Evariste, Comp. *Nukhab Tarikhiya Jamia li Akhbar al-Maghrib al-Aqsa*, Paris: La Rose, 1948.

-E. Levi Provencal: La Fondation de Fes; in *Islam d'Occident*; Librairie Orientale et Americaine; Paris; 1948; pp. 1-32.

-E,L. Provencal: entry: Al-Maghrib; in *Encyclopaedia of Islam*; New edition; Vol 5; 1986; pp 1208-9.

-G. Sarton: *Introduction to the History of Science*; The Carnegie Institution; Washington; 1927; vol 2; p. 998.

-M. Sibai: *Mosque Libraries**: An Historical Study*: Mansell Publishing Limited: London and New York: 1987.

-R. Le Tourneau: *Fes in the age of the Merinids*, trsl from French by B.A. Clement, University of Oklahoma Press, 1961.

[1] T.Burckhardt:* Fez City of Islam;* The Islamic Text Society; Cambridge; 1992.p.73

[2] E.Levi Provencal: La Fondation de Fes; in *Islam d'Occident*; Librairie Orientale et Americaine; Paris; 1948; pp. 1-32. pp.3-4.

[3] E.L. Provencal: La Fondation; pp. 6-7.

[4]A Djebbar: Mathematics in medieval Maghreb;* AMUCHMA-Newsletter *15; Universidade Pedagogica (UP), Maputo (Mozambique), 15.9.1995.

[5] Bayard Dodge: *Muslim Education in Medieval Times*; The Middle East Institute, Washington D.C, 1962.

[6] R. Le Tourneau: *Fes in the age of the Merinids*, trsl from French by B.A. Clement, University of Oklahoma Press, 1961, p. 122.

[7] Ibid.

[8]M. Sibai: *Mosque Libraries**: An Historical Study*: Mansell Publishing Limited: London and New York: 1987. p 55.

[9] Levi Provencal, Evariste, Comp. *Nukhab Tarikhiya Jamia li Akhbar al-Maghrib al-Aqsa*, Paris: La Rose, 1948: pp 67-68.

[10] E.L. Provencal: entry: Al-Maghrib; in *Encyclopaedia of Islam*; New edition; Vol 5; 1986; pp 1208-9.

[11] B. Dodge: Muslim Education, op cit, p 27.

[12] E,L. Provencal: entry: Al-Maghrib; in *Encyclopaedia of Islam*; New edition; Vol 5; 1986; pp 1208-9.

[13](Rawd al-Qirtas) in T.Burckhardt: *Fez City of Islam*; op cit; .p.73

[14] *Encyclopedia of Islam:* Vol IV, p 633.

[15] Rom Landau, The karaouine at Fes,* The Muslim World* 48 (April 1958): pp. 104-12; at p. 105.

[16] G. Sarton: Introduction to the History of Science; The Carnegie Institution; Washington; 1927; vol 2; p. 998.

[17] J J O'Connor and E F Robertson: Arabic mathematics, a forgotten brilliance at:

__http://www-history.mcs.st-andrews.ac.uk/history/index.html__

[18] J J O'Connor and E F Robertson

[19] G. Sarton: Introduction to the History of Science; op cit; p. 998.

[20]Al-Balagh and Djebbar, 1995b, in A Djebbar: Mathematics; op cit;.

[21] A. Djebbar: Mathematics.

[22]Al-Ballagh; Djebbar, 1995, b, in A Djebbar: Mathematics.

[23]A Djebbar: Mathematics;.

[24] G. Sarton: Introduction to the History of science; op cit; pp. 998-9.

[25] J J O'Connor and E F Robertson: Arabic mathematics; op cit.

[26]G. Sarton: Introduction; op cit; p. 999.

[27] J J O'Connor and E F Robertson

[28]G. Sarton: Introduction; op cit; p. 999.