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A Blatant Mathematical Error in the Quran

In Surah 4, Muhammad gives three lengthy verses governing how a person's wealth should be distributed when they die.

These inheritance laws are:

Surah 4:11-12, 176

11 Allah commands you regarding your children: the share of the male will be twice that of the female. If you leave only two ˹or more˺ females, their share is two-thirds of the estate. But if there is only one female, her share will be one-half. Each parent is entitled to one-sixth if you leave offspring. But if you are childless and your parents are the only heirs, then your mother will receive one-third. But if you leave siblings, then your mother will receive one-sixth - after the fulfilment of bequests and debts. ˹Be fair to˺ your parents and children, as you do not ˹fully˺ know who is more beneficial to you. ˹This is˺ an obligation from Allah. Surely Allah is All-Knowing, All-Wise.

12 You will inherit half of what your wives leave if they are childless. But if they have children, then ˹your share is˺ one-fourth of the estate - after the fulfilment of bequests and debts. And your wives will inherit one-fourth of what you leave if you are childless. But if you have children, then your wives will receive one-eighth of your estate - after the fulfilment of bequests and debts. And if a man or a woman leaves neither parents nor children but only a brother or a sister ˹from their mother’s side˺, they will each inherit one-sixth, but if they are more than one, they ˹all˺ will share one-third of the estate - after the fulfilment of bequests and debts without harm ˹to the heirs˺. ˹This is˺ a commandment from Allah. And Allah is All-Knowing, Most Forbearing.

176 They ask you ˹for a ruling, O Prophet˺. Say, “Allah gives you a ruling regarding those who die without children or parents.” If a man dies childless and leaves behind a sister, she will inherit one-half of his estate, whereas her brother will inherit all of her estate if she dies childless. If this person leaves behind two sisters, they together will inherit two-thirds of the estate. But if the deceased leaves male and female siblings, a male’s share will be equal to that of two females. Allah makes ˹this˺ clear to you so you do not go astray. And Allah has ˹perfect˺ knowledge of all things.

Though these are supposedly divine formulas given by Allah, there are examples in which the above formulas simply do not work:

  • 1 widow, 3 daughters, 2 parents
    • 1/8 + 2/3 + 1/3 = 112.5%
  • 1 widow, 2 full sisters, 3 half-sisters from mother's side
    • 1/4 + 2/3 + 1/3 = 125%

It also has no provision that applies to many circumstances, such as:

  • 2 parents, 2 daughters, 1 widow, 2 siblings
  • 2 parents, 2 daughters, 1 widow, 3 siblings
  • 2 parents, 2 daughters, 1 widow, 4 siblings
  • 2 parents, 2 daughters, 1 widow, 5 siblings
  • 2 parents, 2 daughters, 2 widows, 2 siblings

There are literally an infinite number of cases which these formulas do not cover, and the same goes for the cases in which the total sums to over 100%, because you can always add one to one of the factors, and get a new combination.

Muslim Solution

The only way that the mathematical problem where fractions sum to over 100% of the estate is solved is by giving priority to certain groups, and then distributing further from what remains, until everyone is accounted for. The problem with that is, nowhere in these passages is priority mentioned. That's an ad-hoc, extra-Quranic practice, which only needed to be introduced because the false prophet Muhammad had no idea what he was talking about.

This pseudo-solution also rapidly diminishes each successive person's inheritance. For instance, if I have 1/3 coming to me, but someone before me had 1/2, I would now be getting 16.7% of the original amount instead of 33.3%. In most cases, it also guarantees a larger remainder, because smaller and smaller pieces are being taken from the whole with each successive person.

Conclusion

This isn't divine at all. It's a formula that barely works in a few circumstances, almost always leaves a remainder, and has to be deviated from when a case isn't covered, or substantially modified to avoid producing mathematical impossibilities.

When fixing this error of their false prophet, Muslims have to add to their fake scripture - which they otherwise profess to believe are the "words of God", and "fully explained" (Surah 6:114, 15:1, etc.) - and introduce a concept stated nowhere in the text, which itself has a host of bizarre consequences for how the estate is divided up.