Al-Khwarizmi's Debt: How 'Algorithm' Got Its Name

The Persian mathematician who acknowledged learning from India

Learn how Al-Khwarizmi's treatise on 'Hindu computation' spread Indian numerals to the Islamic world and gave the world the words 'algorithm' and 'algebra.'

The Man Whose Name Became a Method

In the early 820s CE, a scholar named Muhammad ibn Musa al-Khwarizmi arrived at the Bayt al-Hikma, the House of Wisdom, in Baghdad. The building stood on the west bank of the Tigris, its shelves holding manuscripts in Arabic, Greek, Persian, and Syriac. Among the recent acquisitions was an Arabic translation of Brahmagupta's Brahmasphutasiddhanta, a Sanskrit astronomical treatise from 628 CE, carried to Baghdad in the 770s CE and known there as the Sindhind. Al-Khwarizmi read it carefully. He had come from Khwarezm, south of the Aral Sea, to work under Caliph al-Ma'mun. His task was to make mathematics usable in Arabic. What Brahmagupta had written down nearly two centuries earlier was the most powerful arithmetic system any civilization had produced. Al-Khwarizmi decided to teach it.

The two books he wrote gave the modern world the words algorithm and algebra. Both carry inside them this man's quiet insistence that the method was not his own. He had learned it from the Indians. This is the story of that honesty and what it cost him in attribution.

820 CE: The House of Wisdom

By the time al-Khwarizmi arrived in Baghdad, the city was sixty years old and already the intellectual capital of the Islamic world. Caliph al-Ma'mun, who came to the Abbasid throne in 813 CE, expanded his father Harun al-Rashid's library into a formal institution known as the Bayt al-Hikma, the House of Wisdom. Scholars there were translating Greek, Persian, Syriac, and Sanskrit texts into Arabic at a pace unmatched anywhere in the medieval world. Among the Sanskrit manuscripts in the Bayt al-Hikma's holdings was the Sindhind, the Arabic name for Brahmagupta's Brahmasphutasiddhanta, which had arrived with Kankah's 773 CE delegation and been translated a generation earlier.

Al-Khwarizmi was one of al-Ma'mun's scholars. He was born in Khwarezm, a region south of the Aral Sea in what is now Uzbekistan, and he carried the name of his homeland with him as his nisba, his locational surname. Under al-Ma'mun's patronage he produced four major works. The two that matter most for this lesson are his book on Indian arithmetic and his book on equations.