From Bija to Algebra: The Arabic Transmission

How Indian algebra traveled to become 'al-jabr'

Trace how Indian algebraic methods were transmitted to the Arab world and eventually to Europe, becoming 'algebra' in the process.

A Persian at the House of Wisdom

In or around the year 820 CE, in a courtyard at the Bayt al-Ḥikma, the House of Wisdom, in the new Abbasid capital of Baghdad on the banks of the Tigris, a Persian mathematician named Muḥammad ibn Mūsā al-Khwārizmī sets down his pen and looks at what he has just finished writing.

The book is short. Its title is Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wa-l-Muqābala, the Compendious Book on Calculation by Restoration and Balancing. Five centuries from now, in a Latin translation prepared at Toledo, this title will give the European languages the word algebra. The room around al-Khwārizmī smells of lamp oil and paper. (Baghdad has paper now. The technology came through Samarkand from China seventy years earlier, and the city's scribes have stopped using parchment.) Through the courtyard window the Tigris moves past in the dusk.

Al-Khwārizmī is not inventing the methods in the book he has just finished. He says so himself. In the preface to his companion treatise on arithmetic, Kitāb al-Jamʿ wa-l-Tafrīq bi-Ḥisāb al-Hind, On Addition and Subtraction After the Method of the Indians, he names his sources directly. The methods come from al-Hind, India. They were carried to Baghdad two generations earlier by an Indian embassy that arrived at the court of Caliph al-Manṣūr in 771 CE, and they have been circulating in Arabic ever since. What al-Khwārizmī has done is package them as a clear, teachable Arabic discipline.

He is honest about the lineage. The Arab scholars who follow him will be honest in turn. The break in attribution will not happen in Baghdad. It will happen later, in Latin Europe, where the Arab citations to India will be quietly dropped. By the time the chain reaches the modern textbook, only the most recent links will have names attached.