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Did the Indians invent algebra which was taken by Arabs and introduced by them to Europe as their own invention?

Or did the Arabs invent algebra?

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    $\begingroup$ Algebra is a large body of technique that was invented over a very long period of time by many peoples, starting at least 2,800 years ago in Egypt. It was not an invention of one place or time. $\endgroup$ – MJD Mar 24 '14 at 15:05
  • $\begingroup$ More accurate to say the history of algebra begins with the French around the time of Descartes. Everything beforehand is the pre-history of algebra. $\endgroup$ – David H Mar 24 '14 at 15:25
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    $\begingroup$ In fact, it was not an invention at all, more like a discovery :) We don't invent math, we discover. It is all out there. We try to reach for it.... (+1) $\endgroup$ – imranfat Mar 24 '14 at 15:26
  • $\begingroup$ @DavidH Well, I tend to disagree with that quite a bit. Cardano was a generation before Descartes and boy, did he and his contemporaries do a lot of algebra...The formula to solve a cubic can me from Tartaglia and that derivation survived and can now be found in some algebra textbooks. $\endgroup$ – imranfat Mar 24 '14 at 15:29
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According to the relevant Wikipedia aritcle

The roots of algebra can be traced to the ancient Babylonians

whereas the word "Algebra" that is used today to describe this branch of mathematics originates from the arabic language

Algebra (from Arabic al-jebr meaning "reunion of broken parts")

As it stated in the article, other civilizations of the time (like Greeks, Egyptians and Chinese), used geometric method to solve equations, in contrast to the arithmetic methods ob the Babylonians that led to the subsequent development of this branch.

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    $\begingroup$ There is also a separate article on the History of Algebra. It is also worth pointing out that the name “algebra” comes not from al-jebr in general, but from its specific use in the title of al-Khwarismi's influential book Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala. Al-Khwarismi was himself probably not an Arab; he was most likely Persian or Uzbek. $\endgroup$ – MJD Mar 24 '14 at 15:07
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At the cost of risking adventurous eurocentrism, I would point out that the meaning of the term "algebra" is ambiguous but if it refers to symbolic notation used in mathematics then its creator is certainly Vieta (1540-1603) of France.

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