While Arabic mathematicians may have refined and furthered the study of algebra (the name "algebra" is derived from the Arabic "al-jabr"), they can not be credited with inventing it. The following is a concise history of the development of algebra:
Algebra has been studied for many centuries. Babylonian, and ancient Chinese and Egyptian mathematicians proposed and solved problems in words, that is, using "rhetorical algebra".
However, it was not until the 3rd century that algebraic problems began to be considered in a form similar to those studied today.
In the 3rd century, the Greek mathematician Diophantus of Alexandria wrote his book Arithmetica. Of the 13 parts originally written, only six still survive, but they provide the earliest record of an attempt to use symbols to represent unknown quantities. Diophantus did not consider general methods in Arithmetica, but instead solved a large number of practical problems.
Several Indian mathematicians carried out important work in the field of algebra in the 6th and 7th centuries. These include Aryabhatta, whose book entitled Aryabhatta included work on linear and quadratic equations, and Brahmagupta, who presented a general solution for a quadratic equation.
The next major development in the history of algebra was the book al-Kitab al-muhtasar fi hisab al-jabr wa'l-muqabala ("Compendium on calculation by completion and balancing"), written by the Arabic mathematician Al-Khwarizmi in the 9th century. The word algebra is derived from al-jabr, or "completion". This book developed methods for solving six different types of quadratic equations, and contained the first systematic consideration of the subject separately from number theory.
In about 1100, the Persian mathematician Omar Khayyam wrote a treatise on algebra based on Euclid's methods. In it he identified 25 types of equations and made the first formal distinction between arithmetic and algebra.
Some time later during the 12th century, Al-Khwarizmi's works were translated and became available to Western scholars. In the 13th century Leonardo Fibonacci wrote some important and influential books on algebra. Other highly influential works were those of the Italian mathematician Luca Pacioli (1445-1517), and of the English mathematician Robert Recorde (1510-1558).
Rules for solving cubic equations were discovered about 1515 by Scipione del Ferro (c. 1465-1526), and for the quartic equation by Ludovico Ferrari (1522-1565) about 1545. In 1824 Niels Henrik Abel (1802-1829) finally proved that, in general, it is not possible to give general rules of this kind for solving equations of the fifth degree or higher.
Further contributions to the symbols used in algebra were made in the late 16th century and the 17th century by François Viète (1540-1603) and René Descartes, among others.
Complex and negative roots were a later discovery, and took some time to become accepted. In 1799, Karl Friedrich Gauss proved the fundamental theorem of algebra, which had been proposed as early as 1629.
In the 19th and 20th centuries algebra has become much more abstract and has grown to include much more than the theory of equations. Modern developments in algebra include group theory and the study of matrices.
Thanks Cliff