• Etymology: Middle English, bone-setting, and Italian, algebra, both from Medieval Latin, from Arabic al-jabr (wa-l-muqbala), the restoration (and the compensation), addition (and subtraction) : al-, the + jabr, bone-setting, restoration (from jabara, to set (bones), force, restore; see gpr in Appendix II). (1)
• al’Khwarizmi, whose full name is Abu Abd-Allah ibn Musa al’Khwarizmi, was born about AD 790 near Baghdad, and died about 850. His most important contribution, written in 830, was Hisab al-jabr w’al-muqabala. From the al-jabr in the title we get algebra. The treatise develops a system for the solutions of quadratic expressions including geometric principles for completing the square.
Many say that the Babylonians first developed systems of quadratic equations. This calls for over simplification, because the Babylonians had no concept of an equation. Also, all solutions to Babylonian problems were positive because they were solutions to problems involving lengths. (2)
• Algebra was originally the name given to the study of equations. In the 9th century, the Arab mathematician Muhammad ibn-Musa al-Khwarizmi used the term al-jabr for the process of adding equal quantities to both sides of an equation. When his treatise was later translated into Latin, al-jabr became algebra and the word was adopted as the name for the whole subject.
The basics of algebra were familiar in ancient Babylonia (c. 18th century BC). Numerous tablets giving sets of problems and their answers, evidently classroom exercises, survive from that period. The subject was also considered by mathematicians in ancient Egypt, China, and India. A comprehensive treatise on the subject, entitled Arithmetica, was written in the 3rd century AD by Diophantus of Alexandria. In the 9th century, al-Khwarizmi drew on Diophantus' work and on Hindu sources to produce his influential work Hisab al-jabr wa'l-muqabalah (Calculation by Restoration and Reduction). (3)
• Diophantus is sometimes called "the father of Algebra," but this title more appropriately belongs to al-Khwarizmi. Al-Khwarizmi's work is on a more elementary and rhetorical level than that of Diophantus. Also, Arab scholars did not make any use of syncopation or of negative numbers. Al-jabr comes closer to elementary algebra of today than the works of either Diophantus or Brahmagupta, because the book is not concerned with difficult problems in indeterminant analysis but with a straight forward and elementary exposition of the solution of equations, especially that of second degree (Boyer, 228). (4)
• At the end of the classical period, Europe entered a mathematical and scientific dark age, lasting hundreds of years. During this time, science and mathematics were kept alive by Arab scholars, who assimilated the Greek and Hindu traditions. Baghdad was a major cultural centre and it was there that Mohammed ibn Musa al-Khowarizmi wrote a book about the Hindu numbers and gave instructions on how to use them. He also wrote ilm al-jabr w'al muquabalah or "the science of reduction and cancellation". We get our word algebra from the al-jabr in the title; we also get the word algorithm from the Latinised version of al-Khowarizmi (Algorismi or Alkarismi - spellings vary). The knowledge accumulated in the schools of Baghdad seeped slowly into Europe, brought by people such as Adelhard of Bath (who translated Euclid's Elements and some of al-Khowarizmi's tables) and Leonardo of Pisa. Leonardo was the son of Bonacci, a merchant and so is also known as Filius Bonacci or Fibonacci. Fibonacci is famous for his book Liber Abaci, 'The book of the Abacus' and for the Fibonnaci number sequence. (5)
