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Teaching the Mathematical Sciences in Islamic Societies Eighth–Seventeenth Centuries

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Abstract

This chapter surveys important aspects of teaching the mathematical sciences in different Islamic societies between the eighth and seventeenth centuries. It explains the historical concept and classification of the mathematical sciences that were valid in the previous epochs but are yet different from current understanding. Following the historical sequence of institutions, this chapter at first focuses on teaching activities at courts and later on madrasas and similar institutions, using the lens of biographical dictionaries, teacher registers, and educational literature. A third focus of this chapter is how scholars in different periods represented their mathematics education in autobiographies. Further themes outlined are ideas about how one could become a productive mathematician, which mathematical discipline was considered legitimate for earning a living, and which textbooks became bestsellers of mathematics education. The conclusions raise historiographical questions about the possibility or impossibility of constructing one single history of mathematics education for all Islamic societies and the adequate evaluation of an increasing number of elementary mathematical texts in postclassical Islamic societies; this suggests that the so-far dominant macro-historical and long-term approach to the history of mathematical societies should be replaced by medio- and microscale studies.

The research for this paper was sponsored partly by ARG-ERC KOHEPOCU (Maribel Fierro, CSIC, Madrid) as well as by FFI2009-10224 (Spanish Ministry of Science) (José Ferreirós, Universidad de Sevilla, Seville)

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Notes

  1. 1.

    See also below Sect. 5.

  2. 2.

    See Sect. 2.

  3. 3.

    It is not clear which Sanskrit sources with arithmetical chapters were translated, and none of the Arabic translations are extant. But the Latin texts derived from Muḥammad b. Mūsā al-Khwārizmī’s work/s on Indian arithmetic, as well as the clear labeling of this kind of notation and the procedures related to them as Indian in Arabic sources since the ninth century, leave no doubt that mathematical knowledge from India and, in all likelihood, texts written in Sanskrit about this knowledge provided the basis for the decimal positional system and its fundamental rules of calculation, as described in extant texts of the tenth century by authors like Kūshyār b. Labbān from Gilan or al-Uqlīdisī from Damascus.

  4. 4.

    In the Maghrib and al-Andalus, this process took place later, perhaps during the thirteenth century.

  5. 5.

    In the thirteenth century, adherents of the legal doctrines as taught on the basis of Anas b. Mālik’s (fl. between 612–712) works and that of his early followers and interpreters also founded madrasas in Egypt and Syria.

  6. 6.

    These are the only three copies of the ninth-century translation into Arabic that are extant. Other copies are extant from Naṣīr al-Dīn al-Ṭūsī’s edition made in the thirteenth century.

  7. 7.

    The revised and enlarged English translation of this work, which unfortunately contains many typing as well as other errors, is Rosenfeld and Ihsanoğlu 2003. Other additions can be found in Rosenfeld 2004, 2006.

  8. 8.

    J.L. Berggren, Patronage of the Mathematical Sciences in the Buyid Courts, unpublished manuscript. I thank Lennart Berggren for allowing me to use his text.

  9. 9.

    This text has different titles in different manuscripts (Djebbar and Aballagh 2001, pp. 105–107).

  10. 10.

    It has not been studied when, where, and in which fields of knowledge this trend started. According to the sources I am familiar with, it was well on its way in the fourteenth century in Mamluk Egypt and Syria.

  11. 11.

    Among the additional works of Ibn al-Bannāʾ that al-Qalaṣādī studied in Tlemcen were his Raf‘ al-ḥijāb and his work on algebra (Aballagh 1988; Djebbar 1990). I thank Mohamed Aballagh for his generous help in verifying the details of al-Qalaṣādī’s education and later teaching positions.

  12. 12.

    This is the usual title given to this text. The manuscript Tunis, Bibliothèque nationale, 8275, however, gives the following title: al-Tabṣira al-wāḍiḥa fī masāʾil al-a‘dād al-lāʾiha. I thank the anonymous francophone reviewer for this information. Each Arabic letter carries a numerical value and served as a numeral.

  13. 13.

    I thank Mohamed Aballagh for this information taken from Aḥmad Bābā al-Ṭinbuqtī’s (1564–1627); al-Ṭinbuktī, Aḥmad Bābā. 1398/1989; biographical dictionary.

  14. 14.

    Be aware, however, of the misleading modernization of terms like ‘ilm al-nujūm, ‘ilm al-athqāl, and ‘ilm al-ḥiyal by Zonta replaced here by my own translations.

  15. 15.

    The name of the city is barely legible.

  16. 16.

    Chavalan or Jabalan was, according to Dekhoda’s Lughat-nāma, a fortress in Yemen. I thank Nasrollah Pourjavady for this information.

  17. 17.

    This understanding of a surd fraction was already present in the first chapter on number theory in the Rasāʼil Ikhwān al-Ṣafāʼ in the late tenth or early eleventh century (Brentjes 1984, pp. 181–274).

  18. 18.

    The work of Ibn al-Bannāʼ extracted by the students is the Mukhtaṣar fī l-misāḥa (Souissi 1984, pp. 491–520).

  19. 19.

    Maribel Fierro, Madrid. Oral communication. I thank Maribel for sharing her insights into Almohad cultural policies with me.

  20. 20.

    Lamrabet and Djebbar, for instance, reject this attribution to Ibn al-Yāsamīn (Lamrabet 1994, pp. 66–67; Djebbar 2005, pp. 97–132).

  21. 21.

    Each line of the poem consists of two verses, which are separated physically on paper by an empty space.

  22. 22.

    All that al-Ṭūsī could access in the middle of the thirteenth century were manuscripts ascribed to either of the two main textual traditions of al-Ḥajjāj b. Yūsuf b. Maṭar (tradition 1) and Isḥāq b. Ḥunayn, edited by Thābit b. Qurra (tradition 2). As we know today, the texts found in all extant manuscripts contain mostly variants of the first tradition, although a good number of these manuscripts are ascribed to the second tradition. It took us more than 100 years of research to discover this mixture of the two traditions. Al-Ṭūsī, having no concept of critical source analysis, could not find out whether an ascribed text did indeed belong to the tradition to which it was attributed.

  23. 23.

    The two textual versions described by al-Ṭūsī are in the extant manuscripts for Books III-IX, variants of tradition 1 only, although they possess the features ascribed by al-Ṭūsī to tradition 2. This suggests that al-Ṭūsī worked, not surprisingly, with similarly mixed texts ascribed to tradition 2 as those that are extant today.

  24. 24.

    These more advanced works are in particular the following: ʿImād al-Dīn ʿAbdallāh b. Muḥāmmad al-Khuddāmī (1245–1325), Fawāʾid al-Bahāʾiyyya fī l-qawāʾid al-ḥisābiyya (The Advantages of Arithmetical Rules); Niẓām al-Dīn Nīsābūrī, al-Risāla al-shamsiyya fī l-ḥisāb; Jamshīd al-Kāshī, Miftāḥ al-ḥisāb (Key to Arithmetic); and its Talkhīṣ (Epitome) Examples can be found in MS Berlin 1733. Information on the study of Ibn al-Bannā’ can be found, according to Aballagh, in al-Tinbuktī, Aḥmad Bābā. 1398/1989.

References

  • Aballagh, Mohamed. 1988. Le Rafʿ al-Hijab d’Ibn al-Bannā’ [Le lever du voile sur <les différents> aspects des procédés du calcul]. Thèse de Doctorat, Université de Paris I, Panthéon-Sorbonne.

    Google Scholar 

  • Abdeljouad, Mahdi. 2004. The eight hundredth anniversary of the death of Ibn al-Yāsamīn: Bilaterality as part of his thinking and practice. http://abdeljaouad.atsm-mahdia.net/dar/histoire/yasamin.pdf. Accessed 6 Aug 2011.

  • al-Majārī, Abū ʿAbdallāh Muḥammad. 1982. Barnāmij al-Majārī. Taḥqīq Muḥammad Abū al-Ajfān. Bayrūt: Dār al-gharb al-islāmī.

    Google Scholar 

  • al-Muḥibbī, Muḥammad Amīn b. Faḍlallāḥ n.d. Khulāṣat al-āthār fī aʿyān al-qarn al-ḥādī ʿashar. Beirūt, 4 volumes in 2 books.

    Google Scholar 

  • al-Nuʿaymī, ʿAbd al-Qādir. 1990. Al-Dāris fī tārīkh al-madāris. Taḥqīq Jaʿfar al-Ḥasanī. 2 vols. Beirūt: Dār al-Kutub al-‘ilmiyya.

    Google Scholar 

  • al-Sakhāwī, Shams al-Dīn. n.d. al-ḍawʾ al-lāmiʿ li’ahl al-qarn al-tāsiʿ, 4 vols. Beirūt: Manshūrāt Dār Maktabat al-ḥayāt.

    Google Scholar 

  • Al-Sijzī’s treatise on geometrical problem solving, a fourth/tenth century text on problem-solving strategies in geometry. 1996. Translated and annotated by Jan P. Hogendijk. Tihrān: Fatemi Publishing House.

    Google Scholar 

  • al-Ṭinbuktī, Aḥmad Bābā. 1398/1989. Nayl al-ibtihāj bi-taṭrīz al-dībāj, Taḥqīq ʿAbd al-Hāmid ʿAbdallāh al-Ḥarama. Tripoli: Manshūrat Kulliyyat al-daʿwa ‘l-Islāmiyya.

    Google Scholar 

  • As-Suyuti’s who’s who in the fifteenth century Nazm ul-Iʻqyān fi A’yān-il-A’yān being a biographical dictionary of notable men and women in Egypt, Syria and the Muslim world, based on two manuscripts, one in Cairo and the other in Leiden, ed. Philip Hitti. 1927. New York: Syrian-American Press.

    Google Scholar 

  • az-Zarnūjī. 1991. Instrucción del estudiante; El método de aprender, (Ta’lim al-muta’allim; Tariq at-ta’llum), Traducción, estudio preliminar y notas de la Dra. Olga Kattan. Madrid: Ediciones Hiperión.

    Google Scholar 

  • Belon du Mans, Pierre. 1553. Les observations de plusieurs singularitez et choses memorables trovvees en Grece, Asie, Iudée, Egypte, Arabie et autres pays estranges. Paris: G. Corrozet.

    Google Scholar 

  • Berggren, J.L. 2003. Tenth-century mathematics through the eyes of Abū Sahl al-Kūhī. In The enterprise of science in Islam: New perspectives, ed. Jan P. Hogendijk and Abdelhamid I. Sabra, 177–196. Cambridge: MIT Press.

    Google Scholar 

  • Bouwman Oriental Books. n.d. Category: Islam. http://www.bouwmanbooks.com/browse_cat_items.php?id=4&row=480. Accessed 6 Aug 2011.

  • Brentjes, Sonja. 1984. Die erste Risāla der Rasā’il iḫwān aṣ-ṣafā’ über elementare Zahlentheorie – ihr mathematischer Gehalt and ihre Beziehungen zu spätantiken arithmetischen Schriften. Janus LXXI: 181–274.

    MathSciNet  Google Scholar 

  • Brentjes, Sonja. 2008a. The study of geometry according to al-Sakhāwī (Cairo, 15th c) and al-Muḥibbī (Damascus, 17th c). In Mathematics celestial and terrestrial, Festschrift for Menso Folkerts zum 65. Geburtstag. Acta Historica Leopoldina, vol. 54, ed. Joseph W. Dauben, Stefan Kirschner, Andreas Kühne, Paul Kunitzsch, and Richard Lorch, 323–341. Halle (Saale): Deutsche Akademie der Naturforscher Leopoldina.

    Google Scholar 

  • Brentjes, Sonja. 2008b. Courtly patronage of the ancient sciences in post-classical Islamic societies. Al-Qanṭara XXIX: 403–436.

    Article  Google Scholar 

  • Brentjes, Sonja. 2008c. Shams al-Dīn al-Sakhāwī on Muwaqqits, Mu’adhdhins, and the teachers of various astronomical disciplines in Mamluk cities in the fifteenth century. In A shared legacy, Islamic science east and west, Homage to professor J.M. Millás Vallicrosa, ed. Emilia Calvo, Mercè Comes, Roser Puig, and Mònica Rius, 129–150. Barcelona: Universitat de Barcelona, Publicacions i Edicions.

    Google Scholar 

  • Brentjes, Sonja. 2010. The mathematical sciences in the Safavid empire: Questions and perspectives. In Muslim cultures in the Indo-Iranian world during the early-modern and modern periods, ed. D. Hermann and F. Speziale, 325–402. Berlin/Tehran: Klaus Schwarz Verlag/Institut Français de Recherche en Iran.

    Google Scholar 

  • Chamberlain, M. 1994. Knowledge and social practice in medieval Damascus, 1190–1350. Princeton: Princeton University Press.

    Google Scholar 

  • Charette, François. 2007. Ibn al-Majdī: Shihāb al-Dīn Abū al-ʿAbbās Aḥmad ibn Rajab ibn Ṭaybughā al-Majdī al-Shāfiʿī’. In The biographical encyclopedia of astronomers, Springer reference, ed. Thomas Hockey et al., 561–562. New York: Springer.

    Google Scholar 

  • Djebbar, Ahmed. 1990. Le livre d’algèbre d’Ibn al-Banna, analyse mathématiques, traduction française et édition critique. In Mathématiques et Mathématiciens dans le Maghrib médiéval (IXe – XVIe s.) Contribution à l’étude des activités scientifiques de l’Occident Musulman. Thèse de Doctorat, Université de Nantes.

    Google Scholar 

  • Djebbar, Ahmed. 2005. Les mathématiques dans le Maghrib impérial (XIIe-XIIIe s.). Actes du 7e Colloque maghrébin sur l’histoire des mathématiques arabes (Marrakech, 30 mai-2 juin 2002). Marrakech: al-Wataniya.

    Google Scholar 

  • Djebbar, Ahmed, and M. Aballagḥ 2001. Ḥayāt wa muʾallafāt Ibn al-Bannāʾ al-Murrākushī [sic]. Rabat: Publications de la Faculté de Lettres et Sciences Humaines.

    Google Scholar 

  • Djebbar, Ahmed, and M. Moyon. 2011. Les sciences arabes en Afrique, astronomie et mathématiques (IXe-XIXe siècles). Paris: Grandvaux-Vecmas.

    Google Scholar 

  • Dodge, Bayard (ed. and trans.). 1970. The Fihrist of al-Nadīm, a tenth-century survey of Muslim culture, 2 vols. New York: Columbia University Press.

    Google Scholar 

  • Dold-Samplonius, Yvonne. 2008. A Qubba in Morocco. In Mathematics celestial and terrestrial, Festschrift für Menso Folkerts zum 65. Geburtstag, Acta Historica Leopoldina, 54, ed. Joseph W. Dauben, Stefan Kirschner, Andreas Kühne, Paul Kunitzsch, and Richard P. Lorch, 379–384. Halle (Saale): Deutsche Akademie der Naturforscher Leopoldina.

    Google Scholar 

  • Gutas, Dimitri. 1988. Avicenna and the Aristotelian tradition. Introduction to reading Avicenna’s philosophical world. Leiden: E.J. Brill.

    Google Scholar 

  • Heath, Peter. 1992. Allegory and philosophy in Avicenna (Ibn Sînâ): With a translation of the book of the Prophet Muḥammad's ascent to heaven. Philadelphia: University of Pennsylvania Press.

    Google Scholar 

  • Ibn al-‘Ibrī, Abū l-Faraj. 1997. Ta’rīkh mukhtaṣar al-duwal. Beirut: Dār al-Kutub al-‘ilmiyya.

    Google Scholar 

  • King, David A. 1996. On the role of the muezzin and the muwaqqit in medieval Islamic society. In Tradition, transmission, transformation: Proceedings of two conferences on pre-modern science held at the University of Oklahoma, ed. F. Jamil Ragep and Sally P. Ragep with Steven Livesey, 285–346. Leiden: Brill.

    Google Scholar 

  • King, David A. 2004. In synchrony with the heavens: Studies in astronomical timekeeping and instrumentation in medieval Islamic civilization, The call of the Muezzin, vol. 1. Leiden: Brill (edited reprint of King, “On the role of the Muezzin and the Muwaqqit in medieval Islamic Society.” see fn 88).

    Google Scholar 

  • Lamrabet, Driss. 1994. Introduction à l’histoire des mathématiques maghrébines. Rabat: Imprimerie al-Ma‘ārif al-jadīda.

    Google Scholar 

  • Makdisi, George. 1981. Rise of colleges: Institutions of learning in Islam and the West. Edinburgh: University Press.

    Google Scholar 

  • Marín, Manuela. 2004. The making of a mathematician: al-Qalaṣādī and his Riḥla. Suhayl 4: 295–310.

    MATH  MathSciNet  Google Scholar 

  • Matvievskaya, Galina P. and Boris A. Rozenfel’d. 1983. Matematiki i astronomy musul’manskogo srednevekov’ya i ich trudy (VIII–XVII vv), 3 vols. Moscow: Nauka.

    Google Scholar 

  • Osmanlı Astronomi Literatürü Tarihi (History of astronomy literature during the Ottoman period). 1997. 2 vols., ed. E. Ihsanoğlu. Istanbul: IRCICA.

    Google Scholar 

  • Osmanlı Matematik Literatürü Tarihi (History of mathematical literature during the Ottoman period). 1997. 2 vols., ed, E. Ihsanoğlu. Istanbul: IRCICA.

    Google Scholar 

  • Ragep, F. Jamil. 1993. Naṣīr al-Dīn al-ṭūsī’s memoir on astronomy (al-Tadhkira fī ʿilm al-hayʾa), 2 vols. New York: Springer-Verlag.

    Google Scholar 

  • Rosenfeld, Boris A. 2004. A supplement to mathematicians, astronomers and other scholars of Islamic civilisation and their works (7th-19th cc). Suhayl 4: 87–139.

    MATH  MathSciNet  Google Scholar 

  • Rosenfeld, Boris A. 2006. A second supplement to mathematicians, astronomers and other scholars of Islamic civilisation and their works (7th-19th cc). Suhayl 6: 9–79.

    MATH  MathSciNet  Google Scholar 

  • Rosenfeld, Boris A., and E. Ihsanoğlu. 2003. Mathematicians, astronomers and other scholars of Islamic civilisation and their works (7th-19th cc). Istanbul: IRCICA.

    Google Scholar 

  • Souissi, M. 1984. al-Ashkāl al-misāḥiyya li Abī l-‘Abbās Aḥmad Ibn al-Bannāʼ al-Murrākushī [sic]. Majallat Ma‘had al-makhṭūṭāt al-‘arabiyya 28(2): 491–520.

    Google Scholar 

  • Theodosius’ Sphaerica. 2010. Arabic and Latin translations. In ed. Paul Kunitzsch and Richard Lorcḥ Stuttgart: Franz Steiner Verlag.

    Google Scholar 

  • Witkam, Januarius Justus. 1989. De Egyptische Arts Ibn al-Akfānī (gest. 749/1348) En Zijn Indeling Van De Wetenschapen. Proefschrift. Leiden: Ter Lugt Pers.

    Google Scholar 

  • Zonta, Mauro. 1992. La ‘Classificazione delle scienze’ di al-Fārābī nella tradizione ebraica. Edizione critica e traduzione annotata della versione ebraica di Qalonymos ben Qalonymos ben Me’ir. EURASIATICA 29.

    Google Scholar 

Manuscripts

  • MS Berlin, Preußischer Kulturbesitz, Staatsbibliothek, We 1733.

    Google Scholar 

  • MS Berlin, Preußischer Kulturbesitz, Staatsbibliothek, or. Quarto 728.

    Google Scholar 

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Authors and Affiliations

  1. Max Planck Institute for the History of Science, Berlin, Germany

    Sonja Brentjes

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  1. Sonja Brentjes
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Editors and Affiliations

  1. Teachers College, Columbia University, New York, New York, USA

    Alexander Karp

  2. Universität Bielefeld Institut für Didaktik der Mathematik, Bielefeld, Germany

    Gert Schubring

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Brentjes, S. (2014). Teaching the Mathematical Sciences in Islamic Societies Eighth–Seventeenth Centuries. In: Karp, A., Schubring, G. (eds) Handbook on the History of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9155-2_5

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