"Funny Math" in the Qur'an
Some Things About Inheritance Laws Just Don't Add Up

When one considers the Muslim claim that the Qur'an is a perfect, inerrant, and God given book, one must then examine this claim rather than blindly accepting it. When this process is undertaken, however, one begins to find that the Muslim claim quickly falls under the weight of some rather obvious errors in Islam's holy book. One of these concerns the inheritance laws laid out by Mohammed in Surah 4 (An-Nisaa). Let us begin by looking at the pertinent verses, from the Yusuf Ali translation:

"Allah (thus) directs you as regards your children's (inheritance): to the male, a portion equal to that of two females: if only daughters, two or more, their share is two-thirds of the inheritance; if only one, her share is a half. For parents, a sixth share of the inheritance to each, if the deceased left children; if no children, and the parents are the (only) heirs, the mother has a third; if the deceased left brothers (or sisters) the mother has a sixth. (The distribution in all cases is) after the payment of legacies and debts. Ye know not whether your parents or your children are nearest to you in benefit. These are settled portions ordained by Allah: and Allah is All-Knowing, All-wise." (4:11)

"In what your wives leave, your share is a half, if they leave no child; but if they leave a child, ye get a fourth; after payment of legacies and debts. In what ye leave, their share is a fourth, if ye leave no child; but if ye leave a child, they get an eighth; after payment of legacies and debts. If the man or woman whose inheritance is in question, has left neither ascendants nor descendants, but has left a brother or a sister, each one of the two gets a sixth; but if more than two, they share in a third; after payment of legacies and debts; so that no loss is caused (to any one). Thus is it ordained by Allah; and Allah is All- Knowing, Most Forbearing." (4:12)

These two passages lay out many of the rules for inheritance which Allah supposedly revealed to Mohammed. The problem is that when one begins to actually plug in a man's surviving relatives into these convoluted equations, some funny results appear.

For example, let us propose that a man dies, and leaves behind him two daughters, his wife, and his widowed mother. The shares of the inheritance then are divided as such: Two daughters get 2/3 (4:11), his wife gets 1/8 (4:12), and the widowed mother gets 1/6 (4:11). Adding the fractions, 16/24 + 3/24 + 4/24 = 23/24. The inheritance laws provides no further information which suggests where the final 1/24 of the inheritance goes.

Even more amusingly, however, is when we take an example involving the death of a man who leaves four daughters, both parents, and his wife. The shares divvied up become: Daughters get 2/3 (4:11), his parents get 1/3 total (4:11), and his wife gets 1/8. This adds up to 9/8 of the inheritance being distributed! Let's hope the IRS doesn't find out about this!

These demonstrate a serious mathematical problem in the Qur'an, which calls into question the divine nature of the Quranic revelation. It seems that these passages are of human origin, and demonstrate the fallability of this book on what is really an issue of basic fractional mathematics.

When confronted with this information, Muslim apologists will typically attempt to circumvent the Quranic aspect of the argument, and try to make an argument from later Islamic jurisprudence, known as fiqh. This word refers to the body of later Muslim interpretation of the Qur'an and the ahadith, which is presented as legalistic interpretation (or rationalisation) of the initial Quranic and hadithic precepts. Yusuf Ali presents a typical demonstration of this argument,

"The principles of inheritance law are laid down in broad outline in the Qur'an; the precise details have been worked out on the basis of the Prophet's practice and that of his Companions, and by interpretation and analogy."1

With reference to the extra 1/24 of a man's inheritance (which comes up fairly often, apparently), the apologist will argue from later fiqh, pointing out that Islamic law makes a provision for the distribution of the remaining inheritance, and thus, there is not an error in the Qur'an. Of course, this answer is nonsense, as the apologist is pointing to what is essentially later and lesser addenda to the Qur'an, which was added centuries after the Qur'an was compiled and standardised. The argument is anachronistic, attempting to correct the prior literature with later interpretation, and then claiming that this corrects the problem present in the original work.

In the case of excessive inheritance division (such as the 9/8 from the example above), both Shi'a and Sunni Muslims have worked out different ways to solve this problem. The Shi'a, typically, will grant to the widow her full share of the inheritance first, and then distribute the rest from unity according to the Quranic precept, keeping the ratios the same with a proportional lowering of the total absolute share. The Sunni follow the principle of "proportional distribution", whereby every inheritor receives a proportionally lower share to keep the inheritance ratio the same, but based on unity, without the surplus. Again, though, this is based upon later Islamic legal tradition, and not on the Qur'an itself. The supposedly infallible Qur'an has to be corrected by human jurisprudence for it to be fully applicable.

End Notes

(1) - 'Abdullah Yusuf Ali, The Meaning of the Holy Qur'an, p. 186, Note #516, on Surah 4:11