In Surah An-Nisa (4:11-12), the Quran establishes a detailed system of inheritance division based on precise proportions: the male receives a share equal to that of two females, two or more daughters receive two-thirds, a single daughter receives half, each parent receives one-sixth or one-third depending on the case, etc.
"يُوصِيكُمُ اللَّهُ فِي أَوْلَادِكُمْ ۖ لِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ" — "Allah instructs you concerning your children: for the male, what is equal to the share of two females." (4:11)
This system of fractions posed a major mathematical challenge: how to divide an inheritance among several heirs when the sum of the prescribed fractions may exceed or fall short of unity?
Muslim jurists developed sophisticated methods to solve these problems, notably the technique of "awl" (proportional reduction) when the shares exceed unity, and "radd" (return) when shares remain available.
These methods stimulated the development of algebra. The Persian mathematician Al-Khwarizmi (780-850), in his treatise "Kitab al-Jabr wa-l-Muqabala," devoted an entire section to the calculation of inheritance shares, thus contributing to the birth of modern algebra.
The Quranic inheritance system is remarkable for its internal coherence: it covers all possible combinations of heirs and provides precise rules for each case. Jurists have identified dozens of different scenarios, each with its exact mathematical solution.
This systematic approach to proportions, revealed in the 7th century, laid the foundations of a mathematical tradition that profoundly influenced the development of algebra and arithmetic throughout the world.