Who Taught Allah Math?
March 14, 2007
By Ali Sina
One of the most obvious mathematical mistakes of the Quran can be found in the division of the inheritance.
The laws of inheritance are spread out in several Suras. One can find references to them in Al-Baqarah(2), Al-Maidah(5) and Al-Anfal(8). But the details of these laws are spelled out in the Surah Nisa (4).
“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 (‘s) after the payment of legacies and debts…”
Q. 4: 12
“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 it is a man that dies, leaving a sister but no child, she shall have half the inheritance: If (such a deceased was) a woman, who left no child, Her brother takes her inheritance: If there are two sisters, they shall have two-thirds of the inheritance (between them): if there are brothers and sisters, (they share), the male having twice the share of the female. Thus doth Allah make clear to you (His law), lest ye err. And Allah hath knowledge of all things.”
Despite the fact that it says “Allah made them clear”, these laws are far from clear.
Verse 4:11 says that if a man has only one daughter, she gets half of the inheritance irrespective of other heirs. But since the same verse says that the portion of the male is twice that of the female, her brother is supposed to get all the inheritance. Isn’t this a discrepancy? Certainly there is an error in how this law is written. Yet the problem is aggravated further when the share of other heirs like parents and wives are taken into consideration.
There are cases when the total of the shares assigned to the heirs exceeds the patrimony. Take for example the following.
According to the above verses, if a man dies leaving behind a wife, three daughters and his two parents,
His wife’s share of his inheritance is 1/8. (In what ye leave, their share is a fourth, if ye leave no child; but if ye leave a child, they get an eighth)
His daughters would receive 2/3 (if only daughters, two or more, their share is two-thirds of the inheritance;)
and his parents each will get 1/6 of his inheritance. (For parents, a sixth share of the inheritance to each, if the deceased left children;)
When you add all these fractions the sum is more than the total of inheritance.
Wife1/8 = 3/24
Daughters 2/3 = 16/24
Father 1/6 = 4/24
Mother1/6 = 4/24
Total = 27/24
Now take another example. Say a man is survived by his wife, his mother and his sisters.
The wife receives 1/4 of the inheritance, (In what ye leave, their share is a fourth, if ye leave no child;)
the mother 1/3 (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 heirs, the mother has a third;)
and the sisters 2/3. (If there are two sisters, they shall have two-thirds of the inheritance (between them)
When we add up these fractions they too are more than the total.
Wife1/4 = 3/12
Mother 1/3 = 4/12
Sisters 2/3 = 8/12
Total = 15/12
In the above examples, the shares apportioned to the heirs exceed the total of the inheritance. In both cases the total of the inheritance sums to exactly one BEFORE taking into account the wife’s share.
What should be done if a man has two wives, one with children and the other without children? Does the one with children receive 1/8 and the one without children 1/4? And is this justice?
Now suppose a woman dies leaving a husband and a brother:
Husband receives half (In what your wives leave, your share is a half, if they leave no child.)
Brother receives everything (If (such a deceased was) a woman, who left no child, Her brother takes her inheritance.)
Does this mean that the parents, sisters and husband do not get anything? In that case where is the justice and if they do how can the brother get everything?
Husband, (1/2) = 1/2
Brother (everything) = 2/2
Total = 3/2
This verse does not specify that the brother gets everything only when there are no other heirs. It just says when there are no children he gets everything. In the same verse it says that if a man dies leaving a sister, she gets half. What will happen to the other half?
Here is another example: A woman leaves behind a husband, a sister and a mother.
Husband, (1/2) = 3/6
Sister (1/2) = 3/6
Mother (1/3) = 2/6
Total = 8/6
We can conclude that the Quran in matters of inheritance is very obtuse. It is so obtuse that Shiites and Sunnis practice this law differently. For example:
If a man leaves a wife and the two parents, the Shiits will give the wife 1/4 and then distribute the remainder as 1/3 for the mother and 2/3 for the father, i.e. they will receive 1/4 and 1/2 of the original estate (see #2741). Sunnis give the wife 1/4, the mother 1/3 and the father as the nearest male relative the rest, i.e. 5/12. As one can witness, the Quran is anything but clear.
In order to solve these problems the Islamic doctors of law have devised a complex “science” called “Al-Fara’id”. It contains rules of “Awl” and “Usbah,” and the laws of “Usool” of the Fara’id, the laws of “Hajb wa Hirman,” and many other issues relating to this matter.
The laws of “Awl” (accommodation) deals with cases when the inheritor’s shares exceed or “overshoot” the sum of the total inheritance. In such case the shares are adjusted to accommodate everyone. This is how it works:
Wife1/8 = 3/24 is changed to 3/27
Daughters 2/3 = 16/24 is changed to 16/27
Father 1/6 = 4/24 is changed to 4/27
Mother1/6 = 4/24 is changed to 4/27
Total = 27/24 27/27
and for the second case,
Wife1/4 = 3/12 is changed to 3/15
Mother 1/3 = 4/12 is changed to 4/15
Sisters 2/3 = 8/12 is changed to 8/15
Total = 15/12 15/15
Thus the problem is solved thanks to human ingenuity but the portions are not the same as indicated in the Quran. Each party has to waive part of his or her share in order to make this law work. This is a clear case in which the words of Allah needed human intervention in order to become applicable.
There are yet cases when the shares of the inheritors do not sum to a whole 100% and there is a surplus left.
Take for example a man who dies and leaves his wife and his parents.
Parents 1/3 = 4/12
Wife 1/4 = 3/12
Total = 7/12
Who will receive the balance 5/12 of the inheritance?
The following are other cases that after the distribution, there is a surplus of Inheritance::
scenario fund distributed surplus
Only a wife: = 1/4 3/4
Only a mother: = 1/3 2/3
Only a daughter = 1/2 1/2
Two daughters = 2/3 1/3
Only a Sister = 1/2 1/2
A mother and a sister = 1/3 + 1/2 = 5/6 1/6
A wife and a mother = 1/4 + 1/3 = 5/12 7/12
A sister and a wife = 1/2 + 1/4 = 3/4 1/4
In all these cases and many other combinations there is a surplus. What will happen to this surplus? Who will inherit it?
To deal with this problem the law of “Usbah” comes to effect. This law is to regulate the unclaimed shares, which have no corresponding people to receive them. Of course if the Quran was clear with no errors, there would have been no need for all these “sciences” and amendments.
The law of Usbah is based on the following Hadith.
Sahih Bukhari 8. 80. 724
Narrated Ibn ‘Abbas:
The Prophet said, “Give the Fara’id (the shares of the inheritance that are prescribed in the Qur’an) to those who are entitled to receive it. Then whatever remains, should be given to the closest male relative of the deceased.”
According to this law, a man who dies and is survived by only his daughter with no other close male relative except a second cousin, his daughter will receive half of his inheritance and the other half will go to the man’s second cousin. This seems quite unfair to the daughter, but it would be especially unfair if the man had a needy aunt or a female first cousin that would receive nothing because they are of the wrong gender.
Now suppose that a man has no other heir except his wife and a distant male relative. The wife will receive 1/4 and the distant male relative gets the balance, i.e. three times the inheritance that his widowed wife gets. Is this justice?
What if the deceased has no male relative at all? What will happen to the rest of his inheritance? What happens in the reverse case when a wife has no relatives? The husband will receive half of her inheritance; who will get the other half?
Note that in the Quran there is no priority for the distribution of the inheritance. In nowhere it says “first give to these and from what is left, give to those”. Even if we had to reinterpret these laws and prioritize them in the order that they are mentioned, it still does not work because in that case, each subsequent inheritor will have his or her share shrunk. Also in most cases the total inheritance will never be used up.
This is the fallacy in which Mr. Sami Zaatari engages. In an attempt to refute this article Mr. Zaatari wrote: “If A [ the deceased] left a widow or widower, the widow’s or widower’s share would first be calculated as in the first half of verse 4:1”
Mr. Zaatari must show us this instruction in the Quran. There is no provision in the Quran to pay certain inheritors first and divide the rest among other heirs. The fact remains that the Quran in matters of the division of the inheritance is wrong mathematically.
The obtuseness of these laws of inheritance is further emphasized in the following example. Consider the case of a man with only one daughter and 10 sons. According to the Quran, the daughter receives half while all the sons must share among themselves the other half. So each will receive not more than 1/20 of the inheritance. But this would contradict the other ruling that a male is to receive twice the share of the female.
Of course for 1400 years Muslims have practiced Islam and somehow they managed to make these confusing laws work. How they did it? They reinterpreted, adjusted and compromised to make sense of these nonsense laws. They put all the inheritance in a pool and gave to each male child twice the share of their female siblings. This solution, though satisfies one of the ruling of the Quran about the inheritance, it contradicts the other.
Despite all these incongruencies and errors the real problem with these laws is not the fact that they do not add up. The problem is in the inherent injustice that they embody. A fair minded person cannot avoid but to question, why daughters should receive half of what the sons receive? Why sisters receive less than brothers? And why a widower is entitled to double the share than a widow? Why the Quran states “to the male, a portion equal to that of two females”? (4:11). Think of a man with four wives. All the wives have to share the ¼ of his wealth, if he has no children and 1/8 if he has. In the first case each wife will receive 1/16 of the inheritance and in the second case 1/32. How a woman who may not be young enough to remarry can survive with such meager share in a male dominated society as Islamic countries? On the other hand a man who loses all his four wives will inherit half to ¼ of every wife’s wealth. Isn’t this the formula to enrich the men and impoverish the women? It is easier to forget the mathematical errors of the Quran than forgive its injustice.
The verse (4:175) claims that “Thus doth Allah make clear to you (His law), lest ye err. And Allah hath knowledge of all things.” As we saw, the above laws are anything but clear. They do not add up, the portions are not clearly defined, and the shares are distributed unfairly. It is up to Muslims to decide whether Allah, does not have the “knowledge of all things”, cannot add simple fractions, is confused and unfair or that the Quran is mistaken, and Muhammad was not a prophet of God. It is one or the other. You decide.