This article examines the evolution of mathematical sciences within the Ottoman State over a six-hundred-year period, specifically focusing on the conceptual and practical integration of mathematics into the Islamic intellectual and social framework. By analyzing the lives and contributions of key figures such as Qādīzāda al-Rūmī, Ali al-Qushjī, and Matrakçı Nasūh, the study demonstrates how the Ottomans harmonized the "rational sciences" (al-ulūm al-aqliyya) with the "religious sciences" (al-ulūm al-naqliyya). It argues that mathematics underwent a distinct process of institutionalization within the Madrasa system, where arithmetic (hisāb) was often categorized as a compulsory religious necessity for tasks such as calculating inheritance (farāʾiḍ), managing endowments (waqf), and determining prayer times. Through a survey of seminal textbooks and the establishment of institutions like the Sahn-i Sāmān, the article illustrates how mathematical inquiry was framed as a pursuit of wisdom (hikma) and a means to contemplate the order of creation. Furthermore, the transition from classical Arabic and Persian manuscripts to vernacular Turkish texts for state accountants reflects a unique synthesis of high-level scholarship with the pragmatic administrative needs of an Islamic caliphate, maintaining a coherent scientific identity even as it engaged with emerging Western technologies in the later centuries.
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