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algebra was first invented along with the way we do arithmetic by a guy in Baghdad around 800 AD or so
The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.
you can tell it is arabic in origin because of the "al" in front. it is true that the babylonians knew how to solve stuff, but they did not have variables, so you cannot really call their work "algebra"
The word algebra comes from the Arabic language (al-jabr, الجبر literally, restoration) and much of its methods from Arabic/Islamic mathematics, its roots can be traced to earlier traditions, which had a direct influence on Muhammad ibn Mūsā al-Khwārizmī (c. 780–850). He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic. http://knol.google.com/k/the-father-of-algebra-muhammad-ibn-m%C5%ABs%C4%81-al-khw%C4%81rizm%C4%AB#
you can look here http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB to see also. form his name we also get the word "algorithm"
at the time he worked the roman empire was gone and most of the center of science was in Bagdhad.
the word Algebra is derived form the aeabis 'Al Jabr' which means' the working out'
http://en.wikipedia.org/wiki/History_of_Algebra (Same comment as other one)
should humble us a little because most of our american ancestors were living in europe in abject poverty and ignorance under Charlemagne's rule