The rules of Islamic law governing inheritance have attracted mathematicians' attention for centuries.
One such mathematician was al-Khwārizmī (~780–~850), whose name gave rise to the term "algorithm." In the introduction to his algebra book, the first of its kind, he writes, "I wanted [this book] to encompass what is subtle in computation and what is most noble in it, which people necessarily require for their inheritances, their bequests and their divisions", thus linking the Islamic rules for dividing inheritances with mathematics.
Fractions and the Quran -----------------------------
These rules for dividing inheritances are based on a passage from the chapter of the Quran known as "Women." From this passage, Muslim jurists developed rules defining certain groups of heirs as entitled to a fraction of the estate. These groups are based on their family relationship to the deceased, and the presence of one group may exclude another from the inheritance or reduce its share. For example, the deceased man's wife is legally entitled to one-quarter of the estate. If she must share the inheritance with descendants of the deceased, however, her share is reduced to one-eighth. These "Quranic" heirs thus receive an initial portion of the estate, made up of the fractions described in the Quran. These fractions are known as "prescribed shares."
Once these have been distributed, the remainder passes to the male line: the sons, if there are any; otherwise the grandsons; otherwise the father or grandfather, brothers, uncles, and so on. Since the prescribed shares are distributed first, these heirs may in practice receive very little or even nothing. For example, if a woman dies leaving her husband, her sister and her uncle, the husband receives half the inheritance, as does the sister. Nothing therefore remains for the uncle, even though he is legally entitled to inherit the remainder! A complete list of the fractions required for every heir in every case would be too long, as the rules are complex, but some are summarized in the box opposite.