Algebra in the Golden Age

This week’s That’s Maths column in The Irish Times (TM054, or search for “thatsmaths” at is about the emergence of algebra in the Golden Age of Islam. The Chester Beatty Library in Dublin has several thousand Arabic manuscripts, many on mathematics and science.

Left: Societ stamp commemorating al-Khwārizmī's 1200th birthday. RIght: A page from al-Khwārizmī's Al-Jebr.

Left: Soviet Union postage stamp (1983) commemorating al-Khwārizmī’s 1200th birthday. RIght: A page from al-Khwārizmī’s Al-Jebr.

“The ink of a scholar is holier than the blood of a martyr.”

Some years ago a book was published with the title How the Irish Saved Civilisation. It told of how, by copying ancient manuscripts, Irish monks preserved the knowledge of ancient times through the Dark Ages, when Europe was plunged into ignorance and turmoil. Far to the East, a more extensive rescue operation was under way.

Evidence of Arabic science, the science practiced by the scholars of the Islamic Empire, is all around us. For example, most of the stars in the sky have Arabic names. We owe a huge debt to the achievements of the scholars of the Arabic world. The scientific revolution in sixteenth and seventeenth century Europe depended greatly on the advances made in mathematics, physics, chemistry, medicine and philosophy in the medieval Islamic world.

Following the arrival of Islam in the early seventh century, an empire with a flourishing civilization emerged, the Islamic Golden Age. During this period, Arabic was the language of international science and mathematics over a region stretching from India to Spain.

After the foundation of Baghdad in 762AD, a massive programme of translation was started, in which the great works of India, Persia and Greece were translated into Arabic. Baghdad became a centre of enlightenment, culture and learning, with the House of Wisdom, established by Caliph al-Ma’mun, playing a role similar to the earlier Library of Alexandria.

Al-Khwarizmi’s Al-Jebr

One of the greatest scholars of the Golden Age was the Persian mathematician Muhammad ibn-Musa al-Khwarizmi. He worked in the House of Wisdom around 820AD, where he wrote several astronomical and mathematical texts. One of his works, giving an account of the decimal system of numbers, is based on the earlier work of the Indian mathematician Brahmagupta. After al-Khwarizmi’s book was translated into Latin, the decimal system of numbers was popularised in Europe by Leonardo of Pisa, also known as Fibonacci, in his Liber Abaci.

Al-Khwarizmi’s greatest work was Kitab Al-Jebr, translated as The Compendious Book on Calculation by Completion and Balancing. In this book, quadratic equations are solved by the process of completing squares, the method taught in schools to this day. The term “al-jebr” in the title gives us the word algebra. The text played for algebra a role analogous to that played by Euclid’s Elements for geometry: it was the best text available on the subject until modern times and it gave a new direction to the development of mathematics.

There were good reasons for developing new mathematical methods, which, according to Al-Khwarizmi, “men constantly require in cases of inheritance, legacies, partition, lawsuits and trade”. He also considered practical problems such as measuring land and digging canals.

Had it not been for the translation programme during the Golden Age of Islam, we would not have access today to many mathematical texts of the Greeks. Moreover, the knowledge transferred to Europe in the Renaissance was richer in many ways than that inherited by the Arabs from Greece, Persia and India.

Ishaq ibn Hunayn's Arabic Translation of Euclid's Elements, AD 1270. CBL Ar 3035, ff.105b-106a © The Trustees of the Chester Beatty Library.

Ishaq ibn Hunayn’s Arabic Translation of Euclid’s Elements, AD 1270. CBL Ar 3035, ff.105b-106a © The Trustees of the Chester Beatty Library.

A-to-Z Exhibition

The unique collection of the Chester Beatty Library includes some 2650 Arabic manuscripts. They cover religion, geography, medicine, astrology, mathematics and more, with original works and translations from ancient Greek. A complete history of Arabic mathematics is not yet possible, as many manuscripts remain unstudied. The current A-to-Z exhibition at the Library features works on optics and astronomy.


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