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I have been told by a computer scientist that most people in that field believe that algebra was invented (along with algorithms) by the 9th century mathematician Muhammad ibn Musa al-Khwarizmi. (I have no idea what most mathematicians believe about this, if anything.) Yet, the Indian mathematician Brahmagupta gave a clear statement of the quadratic formula over a century before al-Khwarizmi was active. Also, Euclid presents algebra in geometric form in his Elements, and the Babylonians knew how to solve some quadratic equations.

According to the Wikipedia article on Algebra, some have argued that Diophantus is the "father of algebra". (Is that the same as "inventing" it?)

If you google "inventor of algebra", you are told in no uncertain terms that it was al-Khwarizmi. Undoubtedly his book played a crucial role in organizing algebra into a subject (as did Euclid's Elements in geometry), and in bringing these ideas to Europe. But it seems to me that this is far from "inventing" algebra, especially given the previous work of Brahmagupta and others. It is apparently clear that al-Khwarizmi knew of some of Brahmagupta's work, which seems to have reached Baghdad before he was born, but it is not clear if he knew of Brahmagupta's algebra.

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    $\begingroup$ There is no single inventor in science but it always a gradual build-up of great ideas. As Newton said, "standing on the shoulder of giants" and Nersnt added "to see a little further than anybody else before". The problem with history is that it can always be re-written and it depends on a who is writing it. Wikipedia is another nuisance in this regard, because anyone can edit it. There is a recent wave of this Indian nationalism in which everything is credited to some ancient Indian scholar. contd... $\endgroup$ – M. Farooq Oct 18 '19 at 13:05
  • $\begingroup$ One may accept these Wikipedia stories, we need to see their original work in some form. Sadly it does not exist, if it did, it never reached the West. One can trace the original works of Khwarizmi in Latin translations but where is the Brahmagupta's original work? $\endgroup$ – M. Farooq Oct 18 '19 at 13:07
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    $\begingroup$ We are told many things by google, in no uncertain terms. Historians do not operate in such simplistic terms whether it comes to algebra, or anything else. Al-Khwarizmi invented algebra no more than Euclid invented geometry, but guess what google has to say about that. Google also tells us about Pythagoreans discovering irrational numbers, Euclid doing "geometric algebra", and many other pop-cultural gems. By the way, why does solving quadratic equations serve as the rite of passage for "algebra", what is wrong with linear equations? $\endgroup$ – Conifold Oct 18 '19 at 14:28
  • $\begingroup$ This discussion is also relevant hsm.stackexchange.com/questions/8062/… $\endgroup$ – M. Farooq Oct 18 '19 at 19:47
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There most certainly were multiple 'inventors' -- or 'discoverers,' depending on your phiilosophy, of basic algebra. Even today, there are youngsters who develop algebra independently.
As to who should get credit for bringing a given chunk of math to the world, that's not really an answerable question. The growth of knowledge is nonmonotonic; civilizations grow and die, and much of their knowledge can be lost until the next civilization comes along.

Further, take a look at Edison and Jobs (or Gates if you prefer). They are credited with major technological revolutions but in fact they were in the right place at the right time and managed to beat out rivals who may or may not have preceded them in a given discovery or invention.

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