by 2000 bc
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Geometry did not originate in India.
Muhammad ibn Musa al-Khwarizmi
The word "algebra" came from the Arabic "al-jabr," meaning restoration. But algebra itself came earlier from India, the ancient Babylonians, Greeks, Chinese, and Egyptians.
Arabic, from al-jabr (الجبر) literally meaning restoration.
The first systematic book on algebra was written in Baghdad, Iraq. However, algebraic methods were also used in China, India, Egypt and Greece long before that.