When was algebra first developed?
History of algebra
Mathematical historians[77] generally agree that the use of x in algebra was introduced by René Descartes and was first published in his treatise La Géométrie (1637).[78][79] In that work, he used letters from the beginning of the alphabet (a, b, c,...) for known quantities, and letters from the end of the alphabet (z, y, x,...) for unknowns.[80] It has been suggested that he later settled on x (in place of z) for the first unknown because of its relatively greater abundance in the French and Latin typographical fonts of the time.[81]
Computer algebra
At the beginning of computer algebra, circa 1970, when the long-known algorithms were first put on computers, they turned out to be highly inefficient. Therefore, a large part of the work of the researchers in the field consisted in revisiting classical algebra in order to make it effective and to discover efficient algorithms to implement this effectiveness. A typical example of this kind of work is the computation of polynomial greatest common divisors, which is required to simplify fractions. Surprisingly, the classical Euclid's algorithm turned out to be inefficient for polynomials over infinite fields, and thus new algorithms needed to be developed. The same was also true for the classical algorithms from linear algebra.For a detailed definition of the subject: 
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