Creator of Algebra Abu Ja'far Ibn Musa Al-Khwarizmi

My report is on Abu Ja'far Muhammad Ibn Musa Al-Khwarizmi. He was born around 780 BC in Baghdad. (Now in Iraq). There is little known about his life. The name al-Khwarizmi may indicate that he was from south of the Aral Sea in central Asia. He constructed some of the oldest works on arithmetic and algebra. His works was a significant source for mathematical insight for centuries to come in both the east and west.

Al-Khwarizmi and his colleagues, the Banu Musa, were scholars at The House of Wisdom in Baghdad. Their task there included the translation of Greek scientific manuscripts. In addition, they worked on algebra, geometry, and astronomy. Under the patronage of Al-Mamum, he dedicated two of his texts to the Caliph- his treatise on algebra and on astronomy. The algebra treatise- Hiss al-jabr w'al-muqabala, was his most known and significant of all of his works. It is this text that gives us the word "algebra" and is the first known book written on algebra. Here is a translation of al-Khwarizmi's own words telling his purpose on writing the book:

Ð'...what is easiest and most useful, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, other of various sorts and kinds are concerned.

The first section of the book is merely a discussion of what we perceive as algebra today. The book was highly practical and algebra was introduced to solve everyday problems in the Islam Empire at the time. Here is another quote describing his formula of new depth and abstraction:

When I consider what people generally want in calculating, I found that it is always a number. I also observed that any number composed of units and that any number may be divided into units. Moreover, I found that every number may be expressed from one to ten, surpasses the proceeding by one unit: the ten is doubled or tripled just as before the units were: thus arises twenty, thirty etc. Until a thousand; so forth to the utmost limit of numeration.

The main topic for the first section of his book is mainly the solution of equations. His equations are linear or quadratic and are composed of units, roots, and squares. Al-Khwarizmi's geometrical proofs are a matter of disagreement with experts. It is hard to determine if whether or not al-Khwarizmi was familiar with Euclid's Elements.

The next part of al-Khwarizmi's algebra includes applications and examples. He then to describe rules for finding the areas of figures like a circle and also finding the volume of solids such as spheres, cones, and pyramids. This section of the text has a lot more in common with Hindu and Hebrew texts than