Islamic Culture

An understanding the medieval Muslim mathematicians requires an understanding of the Arab and Islamic culture in which they lived and worked. Though an accurate and thorough study of a civilization cannot, of course, be completed in a few paragraphs, this page will share a bit of the civilization so Islamic mathematics can be better understood.


Muhammad was born in Mecca around 570 CE. His father died a few months before his birth, and his mother passed away when he was six years old. Muhammad became a merchant for a wealthy widow Khadijah, who promoted him to the position of managing her trading caravans. Khadijah later proposed to Muhammad, who accepted. Muhammad remained in a monogamous relationship until after Khadijah's death, and often spoke of his great love for her and her support of him. Khadijah was also the first contemporary Muslim, converting after Muhammad's first revelation. She is given credit for reassuring Muhammad of his role as a Prophet of God.

Muhammad began preaching Islam, which means "submission" [to God]. His main message was one of monotheism, though the Qur'an provided guidelines for worship of God in all areas of life. Islam is the completion of Christianity and Judaism, and Muhammad is the final and universal Prophet sent by God to all peoples (the Seal of the Prophets). Mecca, Muhammad's home town where he began preaching Islam, had an economy greatly based on the pilgrims who visited the Kaba, which held hundreds of statues of local gods and goddesses. His message of monotheism, then, was seen as dangerous to the economy. Muhammad and his followers were forced to flee to Medina, who had offered him a job as a city mediator. This flight is called the hijra.

In Medina, Muhammad set up an Islamic city, where laws conformed to the regulations set forth in the Qu'ran. He and his followers also conquered Mecca a few years after the hijra; the capture of Mecca was a blood-less battle, though both Meccans and Medinians suffered heavy losses in battles before this final capture. Shortly after returning to Mecca, Muhammad passed away. He had not designated anyone to succeed him, which resulted in crisis and opposition political camps.

The Abbasid Caliphate

The Abbasid empire focused on an international identity. The capital was moved to Baghdad, which became the center for learning in the Muslim empire. Scholars from Syria, Iran, and Mesopotamia were brought to Baghdad in the late 8th century, which included Jewish and Christian scholars. The Caliph al-Mansur (r. 775-785 CE) began funding the study and translation of mathematical texts. It was in 766 CE that the Sinhind, the first mathematical treatise from India, was brought to Baghdad. This work is called the Sinhind in Arabic, but may refer to the Brahmasphuta Siddhanta, which was influential in the development of Algebra. This text was translated in 775 CE. Ptolemy's astrological Tetrabiblos was translated from Greek into Arabic in 780 CE. The Abbasid Caliph Harun Al-Rashid (r. 786-809 CE) began a more rigorous translation of classical mathematics in Greek and Sanskrit to Arabic, and it was during his reign that a very few parts of Euclid's Elements were translated into Arabic. Al-Rashid also established the Bayt al-Hikma, or the House of Wisdom, in Baghdad. The Abassid Caliphate reigned until 1258 CE, when it was destroyed by the invading Mongols.

The House of Wisdom

The House of Wisdom flourished under the reign of Al-Rashid's son, al-Ma'mun. The House of Wisdom was primarily involved with the translation of philosophical and scientific works from Greek originals; Caliph al-Ma'mun is said to have had a dream in which Aristotle appeared to him, after which al-Ma'mun resolved to have Arabic translations of all the Greek works he could acquire. It is during this period that Ptolemy's Almagest and a complete version of Euclid's Elements were translated into Arabic. According to tradition, Greek originals were brought to Baghdad by a delegation sent by Caliph al-Ma'mun to the country of Rome, referring to the Byzantine Empire. (The capital of the Byzantine Empire, Constantinople, was known as "Second-Rome.") Greek manuscripts were obtained through treaties with the Byzantine Empire, with which the Islamic Empire had an uneasy peace. Among the famous mathematicians employed at the House of Wisdom was al-Khwarizmi. In addition to "compiling the oldest astronomical tables, al-Khwarizmi composed the oldest work on arithmetic and the oldest work on algebra. These were translated into Latin [in the 12th century] and used until the sixteenth century as the principal mathematical textbooks by European universities" (Al-Daffa 23-4). His work also introduced algebra, both the mathematical subject and the word, and Arabic-Indian numerals to Europeans.

Mathematics and Culture

The mathematics which was absorbed by Muslim scholars came from three primary traditions: Greek mathematics, Hindu mathematics, and practitioner mathematics. Greek mathematics includes the geometrical classics of Euclid, Apollonius, and Archimedes, as well as the numerical solutions of indeterminate problems in Diophantus' Arithmetica. It also includes the practical manuals of Heron. The second tradition, Hindu mathematics, includes their arithmetic system based on nine signs and a dot for an empty space, as well as their algebraic methods, an emerging trigonometry, methods in solid geometry, and solutions of problems in astronomy. The third tradition, "mathematics of practitioners," includes the practical mathematics of surveyors, builders, artisans in geometrical design, merchants, and tax and treasury officials. This mathematics was part of an oral tradition which "transcended ethnic divisions and was a common heritage of many of the lands incorporated into the Islamic world" (Boyer 516).

Medieval Islamic mathematics not only reflected these three sources but also gave a primary importance to the Muslim society that sustained it. This can be seen in al-Khwarizmi's application of his algebra to the Islamic inheritance laws (Boyer 518). Islamic mathematics in the eighth through the thirteenth centuries was marked with a steady development in conic theory in geometry, methods and theories of solving general geometrical problems, treatment and definitions of irrational magnitudes, trigonometry, algebra, and the geometrical analysis of algebra. One important aspect of Islamic mathematics, in contrast to Greek mathematics, is the close relationship between theory and practice. For example, mathematical works discuss solutions to problems which arise when creating modules for use in Islamic tessellations, relating to the Islamic architectural decorative designs (Boyer 519). Mathematicians took into account the objections of artisans to their theoretical methods, and artisans also learned to understand the differences between exact and approximate methods.

Another example is the mathematical instrument, the astrolabe. It used "the circle-preserving property of stereographic projection to create an analog computer to solve problems of spherical astronomy and trigonometry" (Boyer 519). This is a good example of the intersections of mathematical traditions and Islamic culture, as the astrolabe was a Greek invention but Muslims added circles indicating azimuths on the horizon, which proved useful in determining the direction of Mecca. However, the construction of these circles was not just for religious purposes, but instead stimulated geometrical investigations. Mathematics blended together with Islamic culture in a way that is quite distinct from any of the three mathematical traditions from which Muslim mathematicians acquired their knowledge.

Please see the "Paper" section for further information on the culture of the medieval Islamic Empire.