In his book “A History of Mathematics”, Carl Boyer mentions that both AlKhwarizmi and Abd ElHamid Ibn Turk wrote their books on Algebra (“Aljabr w Almuqabla” and “Logical Necessities” respectively) at nearly the same time. He also states that they use the same methodology and even an example used for demonstration is exactly the same in both books. He then concludes that this indicates that these books weren't the first on the subject as it's widely believed and that Algebra was already mature enough at that time for them to share the same methodology.
Quoting from the book:
The Algebra of al-Khwarizmi is usually regarded as the first work on the subject, but a publication in Turkey raises some question about this. A manuscript of a work by ‘Abd-al-Hamid ibn-Turk, titled “Logical Necessities in Mixed Equations,” was part of a book on Al-jabr wa’l muqabalah, which was evidently very much the same as that by al-Khwarizmi and was published at about the same time— possibly even earlier. The surviving chapters on “Logical Necessities” give precisely the same type of geometric demonstration as al- Khwarizmi’s Algebra and in one case the same illustrative example, $x^2+21=10x$. In one respect, ‘Abd al-Hamid’s exposition is more thorough than that of al-Khwarizmi for he gives geometric figures to prove that if the discriminant is negative, a quadratic equation has no solution. Similarities in the work of the two men and the systematic organization found in them seem to indicate that algebra in their day was not so recent a development as has usually been assumed. When textbooks with a conventional and well-ordered exposition appear simultaneously, a subject is likely to be considerably beyond the formative stage. Successors of al-Khwarizmi were able to say, once a problem had been reduced to the form of an equation, “Operate according to the rules of algebra and almucabala.” In any case, the survival of al-Khwarizmi’s Algebra can be taken to indicate that it was one of the better textbooks typical of Arabic algebra of the time. It was to algebra what Euclid’s Elements was to geometry—the best elementary exposition available until modern times—
Did any further investigation go into this and try to trace the steps that led to this claimed maturity?
