The early Arab mathematician and astronomer al-Khwarizmi has been considered by some to be the founder of algebra, a branch of mathematics dealing with equations containing unknown quantities and variables. While this has been disputed, it is certain that his publications on the subject were among the earliest available to the Arab world, and were highly influential among later audiences. (Sen, 2)
One of the most well-known early Arab scientists, he wrote his famous treatise, "The Compendious Book on Calculation by Completion and Balancing," by the year 830. Later, this work had a great impact on Western mathematics and science; Latin translations of his work were quite important to scholars and businesspeople during the Middle Ages. Al-Khwarizmi is also known for bringing the Hindu system of fixed numerals to international attention. He wrote an Arab-language text that explained Hindu methods of calculation, which depended upon written numerals rather than the more primitive counting techniques that were widely used at the time.
The 'publication' of the book of al-Khwarizmi at the beginning of the ninth century-between 813 and 833 -is an outstanding event in the history of mathematics. For the first time, one could see the term algebra appearing in a title to designate a distinct mathematical discipline, equipped with a proper technical vocabulary. Muhammad ibn Miss al-Khwarizmi, mathematician, astronomer and distinguished member of the 'House of Wisdom' of Baghdad, had compiled, he wrote, 'a book on algebra and al-muqbala, a concise book recording that which is subtle and important in calculation' (Gandz, 263-277). The event was crucial, and was recognized as such by both ancient and modern historians. Its importance did not escape the mathematical community of the epoch, nor that of the following centuries. This book of al-Khwarizmi did not cease being a source of inspiration and the subject of commentaries by mathematicians, not only in Arabic and Persian, but also in Latin and in the languages of Western Europe until the eighteenth century. But the event appeared paradoxical: to the novelty of the conception, of the vocabulary and of the organization of the book of al-Khwarizmi was contrasted the simplicity of the mathematical techniques described, if one compares them with the techniques in the celebrated mathematical compositions, of Euclid or Diophantus, for example. But this technical simplicity stems precisely from the new mathematical conception of al-Khwarizmi. Whilst one of the elements of his project was found twenty-five centuries before him with the Babylonians, another in the Elements of Euclid, a third in the Arithmetica of Diophantus, no earlier writer had recompiled these elements, and in this manner. But which are these elements, and what is this organization
The goal of al-Khwarizmi is clear, never conceived of before: to elaborate a theory of equations solvable through radicals, which can be applied to whatever arithmetical and geometrical problems, and which can help in calculation, commercial transactions, inheritance, the surveying of land etc.
Al-Khwarizmi begins by defining the basic terms of this theory which, because of the requirement of resolution by radicals and because of his know-how in this area, was only concerned with equations of the first