The relationship between fiqh and mathematics: The case of inheritance (Farāʾiḍ) calculations

The science of fiqh, which serves as a guide for the practical life of Muslims, encompasses a comprehensive scope due to its rulings that pertain to all areas of life. This extensive scope necessitates the development of fiqh in interaction with other sciences. Indeed, the accurate judgment of Islamic law on matters depends on a thorough understanding of the nature of those matters, which in turn requires proficiency in the relevant disciplines. One of the sciences with which fiqh engages in a two-way dialectical relationship is mathematics. This study aims to explore the theoretical interaction between fiqh and mathematics, specifically through the lens of Islamic inheritance law, also known as the science of farāʾiḍ in traditional literature. The thesis consists of an introduction, three main chapters and a conclusion. The introduction provides a preamble on the general interaction of fiqh with other sciences, particularly mathematics. In the first chapter, the use of mathematics in fiqh works is examined, and the nature of mathematics employed in classical sources is specified, followed by a classification of calculations found in fiqh texts. The second chapter addresses the science of farāʾiḍ in relation to mathematics, while the third chapter, which constitutes the focal point of the thesis, explores the farāʾiḍ sections within Islamic mathematical works. It is observed that in certain Islamic mathematical works, the practical aspect of this science is demonstrated through inheritance calculations following the theoretical explanations of mathematics. Based on this observation, a sample of Islamic mathematical works is selected, and the problems in these works are classified from a fiqh perspective, thereby revealing how fiqh is utilized within mathematics. Through this approach, the contribution of farāʾiḍ specifically, and fiqh more generally, to the theoretical and practical development of mathematics is evaluated.