Islamic inheritance jurisprudence
Islamic Inheritance jurisprudence is a field of Islamic Jurisprudence (Arabic: fiqh) that deals with inheritance, a topic that is prominently dealt with in the Qur'an. It is often called Mīrāth, and its branch of Islamic law is technically known as ʿulm al-farāʾiḍ (Arabic: علم الفرائض, "the science of the ordained quotas"). All Muslims are expected to follow and implement the rules of Islamic inheritance.
Historical background 
Prior to Islam, and within the Arabian Peninsula, the system of inheritance was confined to male descendants. Women not only did not have any share of inheritance, but they themselves were inheritable too. Siblings from the mother's side, like half-brothers or half-sisters, were completely excluded. Other Semitic cultures also practiced primogeniture, under which all property went to the eldest male child.
Inheritance and the Qur'an 
The Qur'an introduced a number of different rights and restrictions on matters of inheritance, including general improvements to the treatment of women and family life. The Qur'an also presented efforts to fix the laws of inheritance, and thus forming a complete legal system. This development was in contrast to pre-Islamic societies where rules of inheritance varied considerably. Furthermore, the Qur'an introduced additional heirs that were not entitled inheritance in pre-Islamic times, mentioning nine relatives specifically of which six were female and three were male. The laws of inheritance in the Qur'an also included other male relatives, like the husband and half-brothers from the mother’s side, which were excluded from inheritance in old customs. The heirs mentioned in the Qur'an are the mother, father, husband, wife, daughter, uterine brother, full sister, uterine sister, and consanguine sister.
In general, the Qur'an improved the status of women by identifying their share of inheritance in clear terms. It also completely forbade the practice of inheriting widows.[4:19] Orientalist Joseph Schacht states that "this is not meant as a regular legal ordinance, but is part of the Qur'anic endeavor to improve the position of women." The Qur'an does not explicitly mention the shares of male relatives, such as the decedent's son, but provides the rule that the son's share must be twice that of the daughter's. Muslim theologians explain this aspect of inheritance by looking at Islamic law in its entirety, which bestows the responsibility and accountability on men to provide safety, protection and sustenance to women.[Qur'an 4:34]
In addition to the above changes, the Qur'an grants testamentary powers to Muslims in disposing their property.[Qur'an, 2:180-182, 2:240, 4:33, 5:106-107] In their will, called waṣeyya, Muslims are allowed to give out a maximum of one third of their property. Muslims are also encouraged to give money to the orphans and poor if they are present during the division of property.
Later development 
The Qur'an contains only three verses [4:11, 4:12 and 4:176] which give specific details of inheritance and shares, in addition to few verses dealing with testamentary power. It has also been reported in Hadith that Muhammad allotted great importance to the laws of inheritance and ordered his followers to learn and teach them. Muslim jurists used these verses as a starting point to expound the laws of inheritance even further using Hadith, as well as methods of juristic reasoning, like Qiyas. In later periods, large volumes of work have been written on the subject.
This amalgamation of old agnatic customs and Islamic law led to a number of problems and controversies that Muslim jurists have solved with great ingenuity. Through the use of deductive reasoning (Qiyas), Muslim jurists added three additional heirs: the paternal grandfather, maternal grandmother, and agnatic granddaughter. These heirs, if entitled to inherit, are given their fixed shares and the remaining estate is inherited by the residuaries (ʿaṣaba). In some cases, they have also upheld the rule of men having twice the share of women in circumstances not readily mentioned in the Qur'an, and tried to deal with complex cases in a variety of different contexts. This led to some minor differences between jurisprudence schools of the Sunni maddhabs. Also, the laws of inheritance for Twelver Shia, despite being based on the same principles, differ in a number of features due to the rejection of certain accounts of Hadith and based on their understanding of certain events in early Islam. On the other hand, the system of inheritance of the Kharajite Ibadis and Zaidis closely resemble that of the Sunni system. In modern Muslim countries, usually a mixture of different schools of jurisprudence (including Shia) is in effect, in addition to a number of important reforms to the traditional system. The main achievements of such modern systems was the codification of inheritance laws.
Details of inheritance in Islamic Law 
Inheritance is considered as an integral part of Shariah Law and its application in Islamic society is a mandatory. Muslims inherit from one another as stated in the Qur'an.[Qur'an 4:7] Hence, there is a legal share for relatives of the decedent in his estate and property. The major rules of inheritance are detailed in Qur'an, Hadith and Fiqh.
When a Muslim dies there are four duties which need to be performed. They are:
- Pay funeral and burial expenses.
- Pay debts.
- Execute the testamentary will of the deceased (which can only be a maximum of one third of the property).
- Distribute the remainder of estate and property to the relatives of the deceased according to Shariah Law.
Therefore, it is necessary to determine the relatives of the deceased who are entitled to inherit, and their shares.
These laws take greater prominence in Islam because of the restriction placed on the testator (a person who makes a will). Islamic law places two restrictions on the testator:
- To whom he or she can bequeath his or her wealth.
- The amount that he or she can bequeath (which must not exceed one third of the overall wealth).
Different types of heirs 
Heirs referred to as primary heirs are always entitled to a share of the inheritance, they are never totally excluded. These primary heirs consist of the spouse relict, both parents, the son and the daughter. All remaining heirs can be totally excluded by the presence of other heirs. But under certain circumstances, other heirs can also inherit as residuaries, namely the father, paternal grandfather, daughter, agnatic granddaughter, full sister, consanguine sister and mother. Those who inherit are usually confined to three groups:
- Quota-heirs (dhawu al-farāʾḍ), usually include daughters, parents, grandparents, husband and wife/ wives, brothers and sisters, and others. This group usually take a designated share or quota of the estates.
- Members of the ʿaṣaba (residuaries), usually a combination of male (and sometimes female) relatives that inherit as residuaries after the shares of the Quota-heirs is distributed.
- In case a person leaves no direct relatives and there is no ʿuṣaba, his property goes to the state treasury, Bayt al-mal.
Rules of Inclusion and Exclusion 
In Islamic law, only relatives with a legitimate blood relationship to the deceased are entitled to inherit. Thus, illegitimate children and adopted children have no shares in inheritance. In general, a full brother will exclude a consanguine brother, but not uterine brother. In case where a deceased man leaves a pregnant woman, the unborn child's share will be reserved. Also a woman during the time of waiting (ʿidda) after divorce is considered as a wife of the deceased for purposes of inheritance.
There are even further rules of exclusion and inclusion of different relatives. The only "practical situations" which may cause disqualification are differences of religion and homicide. But schools of Islamic jurisprudence differed whether a Muslim can inherit from a non-Muslim or not. All the jurists agree that intentional or unjustifiable killing would exclude a person form inheritance.
Women and inheritance 
In Islam, women are entitled the right of inheritance. In general circumstances, though not all, Islam allots women half the share of inheritance available to men who have the same degree of relation to the decedent. For example, where the decedent has both male and female children, a son's share is double that of a daughter's. Additionally, the sister of a childless man inherits half of his property upon his death, while a brother of a childless woman inherits all of her property. However, this principle is not universally applicable, and there are other circumstances where women might receive equal shares to men. For example, the share of the mother and father of a childless decedent.. Also the share of a uterine brother is equal to the share of a uterine sister, as do the shares of their descendants.
Some times woman gets double share then share of man, for example if there are only parents and husband, husband will receive half, father gets 1/6 and mother gets 2/6. This is according to Ibne Abbas's interpretation of verses 11, 12 of sorat an nisa. [Quran 4:11,12] Also the Qur'an does not discriminate between men and women in cases of kalalah relation. Kalalah describes a person who leaves behind neither parents nor children; it also means all the relatives of a deceased except his parents and children, and it also denotes the relationships which are not through [the deceased’s] parents or children. Islamic scholars hold that the original reason for these difference is the responsibilities allotted to spouses. A husband in Islam must use his inheritance to support his family while a wife has no support obligations. Additionally, Arab society traditionally practiced the custom of bride price or dower rather than dowry; i.e., the man paid a gift to his wife or her family upon marriage, rather than the opposite, placing a financial burden on men where none existed on women. This custom received Islamic sanction.
The role of Islamic inheritance in the development of Islamic Mathematics 
The Islamic law of inheritance served as an impetus behind the development of algebra (derived from the Arabic al-jabr) by Muhammad ibn Mūsā al-Khwārizmī and other medieval Islamic mathematicians. Al-Khwārizmī's Hisab al-jabr w’al-muqabala, the foundational text of algebra, devoted its third and longest chapter to solving problems related to Islamic inheritance using algebra. He formulated the rules of inheritance as linear equations, hence his knowledge of quadratic equations was not required.
Al-Hassār, a mathematician from the Maghreb (North Africa) specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar. The "dust ciphers he used are also nearly identical to the digits used in the current Western Arabic numerals. These same digits and fractional notation appear soon after in the work of Fibonacci in the 13th century.
In the 15th century, Abū al-Hasan ibn Alī al-Qalasādī, a specialist in Islamic inheritance jurisprudence, used a mathematical notation for algebra which took "the first steps toward the introduction of algebraic symbolism." He represented mathematical symbols using characters from the Arabic alphabet.
See also 
- Schacht, Joseph (1991). "Mīrāth". Encyclopaedia of Islam 7 (2nd ed.). Brill Academic Publishers. pp. 106–113. ISBN 90-04-09419-9.
- Islamic Laws of Inheritance – Dr. Abid Hussain
- "From what is left by parents and those nearest related there is a share for men and a share for women, whether the property be small or large,-a determinate share."Sura 4:7 
- Qur'an, [Quran 4:11].
- Qur'an, [Quran 4:126]
- "If a man or a woman is made an heir on account of his [or her] kalalah relationship [with the deceased] and he [or she] has one brother or sister, then the brother or sister shall receive a sixth, and if they be more than this, then they shall be sharers in one-third, after payment of any legacies bequeathed and any [outstanding] debts – without harming anyone. This is a command from God, and God is Gracious and All-Knowing." Qur'an, [Quran 4:12].
- "People ask your pronouncement. Say: God enjoins you about your kalalah heirs that if a man dies childless and he has only a sister, then she shall inherit half of what he leaves and if a sister dies childless, then her brother shall be her heir; and if there are two sisters, then they shall inherit two-thirds of what he [or she] leaves. If there are many brothers and sisters, then the share of each male shall be that of two females. God expounds unto you that you err not and God has knowledge of all things." Qur'an, [Quran 4:176].
- Javed Ahmed Ghamidi, Mizan, The Islamic Law of Economics, Al-Mawrid
- Tafsir Nemooneh, Sura Nisa, v.12
- Gandz, Solomon (1938). "The Algebra of Inheritance: A Rehabilitation of Al-Khuwarizmi". Osiris (University of Chicago Press) 5: 319–91. doi:10.1086/368492.
- Høyrup, J. (2009). "Hesitating progress-the slow development toward algebraic symbolization in abbacus-and related manuscripts, c. 1300 to c. 1550: Contribution to the conference" Philosophical Aspects of Symbolic Reasoning in Early Modern Science and Mathematics", Ghent, 27–29 August 2009". Preprints 390. Berlin: Max Planck Institute for the History of Science. "Fibonacci uses ibn al-Yāsamin’s fraction notations to the full in the Liber abbaci [ed. Boncompagni 1857], writing composite fractions from right to left and mixed numbers with the fraction to the left – all in agreement with Arabic customs. Further, he often illustrates non-algebraic calculations in rectangular marginal frames suggesting a lawha."
- Fibonacci, Leonardo; Barnabas Hughes (2008). Fibonacci's De practica geometrie. Springer. p. 12. ISBN 978-0-387-72930-5. "At this point it would be well to make a few remarks about Fibonacci's fractions. The first thing to note is the format, 1/2 4, which means four and a half. The format is unique to Andalusia and the Maghrib and reflects the Arabic method of writing from right to left, something Fibonacci most probably learned as a student in a Moslem school in Bougie."
- Livio, Mario (2003). The Golden Ratio. New York: Broadway. p. 96. ISBN 0-7679-0816-3.
- O'Connor, John J.; Robertson, Edmund F., "Abu'l Hasan ibn Ali al Qalasadi", MacTutor History of Mathematics archive, University of St Andrews.