The First Algebra Book in the Ottoman Empire: An Analysis of Khayr Al-dın Khalil B. Ibrahim’s Mushkilkusha-yi Hussab Wa Mu‘dilnuma-yi Kuttab

Khayr al-dīn Khalil b. Ibrahim was a 15th-century Ottoman mathematician known for his works in Persian. Some sources suggest he might be the same as Khodja Khayreddin, the tutor of Sultan Mehmed II, though this remains uncertain. His most notable works are Miftāḥ-i Kunūz-i Erbāb al-Kalam ve Misbāḥ-i Rumūz-i Ashāb al-Raḳam and Mushkilkushā-yı Ḥussāb wa Muʿḍılnumā-yı Kuttāb, the latter being an advanced algebra book dedicated to Sultan Bayezid II.

Miftāḥ-i Kunūz was a foundational arithmetic book used by Ottoman accountants, covering topics such as fractions, divisibility, proportional numbers, multiplication, division, debt calculation, and root extraction. It was later translated into Turkish by his student Pīr Maḥmud Ṣıdkī Edirnevī. Mushkilkushā-yı Ḥussāb is a six-chapter algebra book that includes definitions, methods, and advanced problem-solving techniques. It covers quadratic, cubic, and higher-degree equations, including unique methods not commonly found in classical algebra texts. The manuscript in the Ayasofya Collection suggests it was copied for a royal audience.

This study aims to analyze the introduction and first chapter of Mushkilkushā-yı Ḥussāb by examining its manuscripts from the Ayasofya and Şehid Ali Paşa collections. The research explores the mathematical content, methodology, and instructional approach of the book, highlighting its significance as the earliest known algebra text written in the Ottoman Empire. By investigating the problem-solving techniques presented in the work, this study sheds light on the advanced mathematical training required for Ottoman accountants and scribes.

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