The birth of algebra
Year of birth: 780 death year: 850 Know little news from the life of Al-Khwarizmi. An unfortunate effect of this lack of knowledge seems to be the temptation to invent facts about little evidence based. The name Al-Khwarizmi could indicate its origin from South of Khwarizm in Central Asia. Abu Ja ʿ far Muhammad ibn Musa was born in Baghdad in about 780 Khwarezm or Khwārizmī and lived to about 850 per year. Harun al-Rashid became the fifth Caliph of the Abbasid dynasty on 14 September 786, at about the same time as al-Khwarizmi. Harun commanded, from his court in the capital city of Baghdad, the Islamic Empire that stretched from the Mediterranean to India. He brought the culture in his court and tried to establish intellectual disciplines which at that time were not flourishing in the Arab world. He had two sons, the eldest was al-Amin and the youngest was al-Mamun. Harun died in 809 and there was an armed conflict between the two brothers. Al-Mamun won the battle and al-Amin was defeated and killed in 813. As a result, al-Mamun became Caliph and commanded the Empire from Baghdad. He continued the patronage of knowledge started by his father and founded an Academy called the House of Wisdom where the Greek scientific and philosophical works were translated. He also build a library of manuscripts, the first library to be built from Alexandria, who used to collect important works of the Byzantines. In addition to the House of Wisdom, al-Mamun had built observatories in which Muslim astronomers could study the knowledge acquired by earlier peoples. Al-Khwarismi and his colleagues were schoolboys at the House of Wisdom in Baghdad. Their duties there included the translation of Greek scientific manuscripts and also studied algebra, geometry and astronomy. Certainly al-Khwarizmi worked under the protection of al-Mamun and devoted two of his texts to the Caliph. These were his treatise on algebra and astronomy. Treatise on algebra Hisab al-Jabr w'al-Muqabala was the most famous and important of all works by al-Khwarizmi. The title of this text that gives us the word algebra is, in a sense that we will investigate later, the first book on algebra. The aim of the work was that al-Khwarizmi was intended to teach "what is easier and more useful in arithmetic, as what men constantly require in cases of inheritance, legality, causes, processes, is in all their comments with another, or requiring the land measures, dredging of canals and geometric calculations, and other subjects of various sorts and kind". Actually only the first part of the book is a discussion of what we today would recognise as algebra. However it is important to understand that the book was judged as very practical and that algebra was introduced to solve real life problems that were part of everyday life in the Islamic Empire at that time. At the beginning of the book al-Khwarizmi describes the natural numbers in terms that are nearly as fun for us who are so familiar to the system, but it is important to understand the new depth of abstraction and of knowledge: "when I consider what people want to calculate, I find that it is always a number. I also observed that each number is composed of units, and that every number can be divided into units. Also, I found that every number that can be expressed from one to ten, surpasses the previous one by one: then the TENs are duplicate or triplicate as before they were units so you get to twenty, thirty, up to one hundred: then the hundred is duplicated and tripled in the same way the tens, units and up to 1,000; so to the extreme limit"-numbering. Introducing the natural numbers, al-Khwarizmi introduces the main topic of this first section of his book, the solution of equations. His equations are linear or quadratic and consist of units, roots and squares. For example, to al-Khwarizmi a unit was a number, a root was x, and a square was x ^ 2. However, although we will use in this article the familiar algebraic notation to help readers understand the basics, the mathematics of al-Khwarizmi is made entirely of words without the use of symbols. Its geometrical proofs are a topic of discussion among the experts. The question, which doesn't seem to have an easy answer, is whether al-Khwarismi knew Euclid's elements. We know that he could meet them, perhaps we should say it should have been. In the Kingdom of al-Rashid, while al-Khwarizmi was still young, al-Hajjaj translated Euclid's elements into Arabic and al-Hajjaj was one of al-khwarizmi's colleagues in the House of Wisdom. It is thought that it is clear that if al-Khwarizmi has studied the work of Euclid, was influenced by other jobs. Al-khwarizmi continues his study of geometry in the Hisab al-Jabr w'al-Muqabala examining how the laws of arithmetic extends to an algebraic arithmetic for its arguments. For example he shows how to multiply an expression (a + bx) (c + dx) Although we must stress the fact that al-Khwarizmi uses just words to describe his expressions and no symbols. Al-Khwarizmi could be considered the greatest mathematician of the time, and if you take into account the circumstances concerning him, one of the greatest of all time. He also wrote a treatise on Arabic numbers-Indians. The Arabic text was lost but a Latin translation, Algoritmi de numero Indorum in English al-Khwarizmi on the Indian art of computing give rise to the word algorithm deriving from the name of the title. Unfortunately the Latin translation is known to be quite different from the original text (which even the title is unknown). The work describes the Indian value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The first use of the 0 key notation of the positions was probably due to this work. Arithmetic calculation methods are given, and provides a method to find the square roots is known to have been in the original Arabic, although he lost in the Latin version. 7 treaties were discussed in Latin of the 12th century Arabic treatise on arithmetic based on that which was lost. Another important work of al-Khwarizmi was his work on astronomy Sindhind Zij. The work is based on the Indian Astronomical works. The Indian text on which he based his treatise is one of those who had taken by the Court of Baghdad around 770 as a gift of a mission Indian politics. There are two versions of this work that he wrote in Arabic, but both are lost. In the 10th century al-Majriti made a critical review of the shorter version and this was translated into Latin by Abelard. There is also a Latin version of the longer version and both of these Latin works have survived. The main topics dealt with by al-Khwarizmi are calendars; the calculation of the true position of the Sun, Moon and planets, breast plates and tangents; the spherical astronomy; astrological Parallax calculations and tables of the Eclipse; the visibility of the moon. Although his astronomical work is based on that of the Indians and many of the values with which he built his boards come Indian astronomers, he was also influenced by the work of Ptolemy. He wrote an important work on the geography that gives the latitudes and longitudes of 2402 locations as bases of a world map. The work, which is based on the geography of Ptolemy, see latitudes and longitudes, cities, mountains, seas, Islands, regions and rivers. The manuscript includes maps which are more accurate than of Ptolemy. In particular it is clear that where were available more local knowledge, such as the region of Islam, Africa, the far East then his work is considerably more accurate than that of Ptolemy, but as far as Europe is al-Khwarizmi seems to have used the data of Ptolemy. A number of smaller works were written by al-Khwarizmi on topics such as the astrolabe, on which he wrote two operas and on the Jewish calendar. He also wrote political history containing horoscopes of important people. Citing the Shah of Iran Mohammad Khan: "the list of the greatest mathematicians of all times we find al-Khwarizmi. He wrote the oldest work on arithmetic and algebra. Were the main resources of mathematical knowledge for centuries to come from East to West. The work on arithmetic at first introduced Indian numerals to Europe, as we understand the algorithm name; and work on the algebra has given its name to this important branch of mathematics in the European world"