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Mathematical Treasure: 13th Century Manual of Inheritance Law

Frank J. Swetz (The Pennsylvania State University)

Writing in the 13th century, Shams al-dīn Maḥmūd ibn Abī Bakr al-Bukhārī al-Kalabādhī compiled the manual, Kitāb ḍawʼ al-sirāj li-l-shaykh al-‘allāmah al-ḥāsib (Book of the Glow of the Lamp for the Master of Legal Reckoning). The author's name reflects family origins in Bukhara, an important city in what is now Uzbekistan. The first page of the manual is shown below. The large writing at the top reads, “In the name of God, the merciful, the beneficent,” the standard phrase opening an Islamic text.

Islam guided many areas of social interaction and a manual such as the one featured here would have included a discussion of inheritance law. In the event of the death of the major income earner, the estate had to be divided to insure the status of the widow (or widower) and remaining children. A special area of reckoning concerned the proper distribution of estates according to religious rules. For example:

A woman dies, leaving her husband, son and three daughters,
but she also bequeaths to a stranger 1/8 + 1/7 of her estate.
Calculate the shares of each.

Here several conditions must be met: a legacy cannot exceed 1/3 of an estate unless all heirs agree, a husband receives ¼, and a son is to receive twice as much as a daughter. A judge or reckoner must make the necessary calculations.

Charts were used to demonstrate distribution patterns, as illustrated above.

Tables were also important aids in determining estate shares, as shown above.

The images above were obtained from the Digital Collection of the University of Pennsylvania (Lawrence J. Schoenberg Collection). The complete work is available for viewing via its reference number, LJS 436.


We thank Randy K. Schwartz of Schoolcraft College for his contributions to this article.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: 13th Century Manual of Inheritance Law," Convergence (January 2016)