THE TEACHING OF ARITHMETIC AND ALGEBRA AT THE OTTOMAN MEDRESES

Cevat İzgi

Arithmetic had been one of the sciences taught at the Ottoman medreses since their foundation. In some of the arithmetic books, the students could also gain some knowledge of algebra as these books contained chapters on algebra in addition to arithmetic. Though not mentioned as a seperate course like geometry and astronomy in Fatih's Kanunname on education, arithmetic existed in the curriculum.

Kevakib-i Seb'a (1155/1745) states that the science of arithmetic was not taught as an independent course like geometry. According to this source, arithmetic was taught when passages on mathematical sciences such as astronomy and geometry in the Islamic theology books were studied. On the other hand, it is understood from the autobiographies that arithmetic books were generally read after Philosophy and Islamic theology, before the Hadith and the Quranic commentary.

There are records proving that arithmetic was also taught in "tekke"s and "zaviye"s. Arithmetic certificates, though very few, were given in the medreses. It is observed that Ottoman scholars of the nineteenth century learned also arithmetic and algebra from the specialists as well as in the preparatory and high schools (Idadis and Rüşdiyes). Cevdet Pasha, one of the nineteenth century Ottoman scholars who learned arithmetic both in the old and modern tradition, was one of them.

Ottoman scholars used mostly the arithmetic books written by the mathematicians of Islam. But in the Ottoman medreses, mainly the Hulasatu'l-Hisab of Bahauddin el-Amili and the el-Muhammediyye fi'l Hisab of Ali Kuşçu were used as text books. Hulasatu'l-Hisab was translated into Turkish by Kuyucakli-/Ade Muhammed Atıf in 1242/1826 during the reign of Sultan Mahmud the Second. The fact that this book was published three times in Istanbul in the following years proves that it preserved its importance in education.

In the teaching of arithmetic, many tools such as sand, wood, iron bars, paper and pen-cases were also used besides text books. The arithmetic books were cojftd in the "Ellili medrese" in Istanbul and Anatolia. Some of these were read by way s of examination (by methods of bahs, tedkik, fehm, tahkik) and dictation.

Ottomans started wri??? arithmetic books from the beginning of the 15th century onwards. Arithmetical texts were translated into Turkish later than astronomical texts, but earlier than geometrical texts. Miftâhu'1-Hisab (anonymous), Risale fi İlm-i Hisab (anonymous) and Miftahu'l-Muşkilat (Muhammed Musa-i Vafi) are examples. Arithmetic books that were prepared by the "muha-sips" (book-keepers) and "divan katipleri" (secretaries of the Council of State) were usually written in Turkish. Mecmau'l-Kavaid (889/1484) by Hacı Atmaca is an example. The greatest work among Turkish books of arithmetic, that was written in the classical tradition, was Ali b. Veli b. el Cezairi el-Mağribi's (d. 1022/1614) Tuhfetu'l A'dad which was presented to Sultan Murad the Third (d.1595).

Independent books on algebra were also written besides the many arithmetic books which had chapters on algebra. In Ottoman medreses, algebra went hand in hand with arithmetic. Both arithmetic and algebra were present in the curriculum ot "Darulhilafeti'1-Aliyye" (est. 1914). Thus, we can conclude that mathematics maintained its place within the medrese education, and the scholars of medrese continued to produce works on mathematics.