Credited to Iraq. Scholars disagree on how original the work was. Rashed stresses the originality of its conception, while Crossley and Toomer rate it lower, and its geometry may draw on earlier sources.
How it began
Muhammad ibn Musa al-Khwarizmi worked around 820 at the House of Wisdom in Baghdad, capital of the Abbasid Caliphate, in present-day Iraq, under the patronage of Caliph al-Mamun. His treatise on al-jabr and al-muqabala, compiled between 813 and 833, gives the word algebra and, in the words of the MacTutor archive, can be considered the first book written on algebra. Few details of his life are known. He may have been born near Baghdad.
How it works
The book reduces problems to six standard types of equation, such as squares equal to roots, or squares and roots equal to numbers. Al-jabr, completion, is the removal of negative terms from an equation. Al-muqabala, balancing, is the reduction of positive terms of the same power on both sides. Al-Khwarizmi solved the equations by rule and proved the methods geometrically, for example by completing the square. The mathematics is written entirely in words, with no symbols.
How it spread
Al-Khwarizmi's works were widely influential on later authors in the Islamic world and in Europe. Robert of Chester translated the algebra into Latin, and his mathematics spread in Europe in the 12th century. The title word al-jabr became algebra, and the Latin form of the author's name gave the word algorithm.
Who pushed back
Historians differ on the book's originality. Roshdi Rashed stresses the originality of its conception and style. John Crossley writes that al-Khwarizmi may not have been very original, and G. J. Toomer judges his scientific achievements at best mediocre. Experts also disagree on whether the geometric treatment was inspired by Euclid's Elements or owes more to practical texts such as the Hebrew Mishnat ha Middot.
What changed first
Al-Khwarizmi wrote that he meant to teach what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits and trade, and in measuring lands and digging canals. The book was a practical manual for the legal and commercial life of the caliphate as much as a work of theory.
