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Teaching the Mathematical Sciences in Islamic Societies Eighth–Seventeenth Centuries


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.


  • Mathematical Education
  • Mathematical Knowledge
  • Mathematical Science
  • Thirteenth Century
  • Mathematical Text

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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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  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.


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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.

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