A thread on the Hindu origins of the works of the medieval Persian mathematician Al-Kḥwārizmī (Ibn Musa) (خوارزمی) who lived from 780-850 CE.
First, let us understand that Al-Kḥwārizmī did not invent a new science or discover it. So what is Algebra then? Kḥwārizmī’s chief treatise was named “Hisab Al-Jabr va Al-Muqabla”(Al-Jabr) meant the restoration of an equation by eliminating negative terms. Or multiplying both sides of the equation to remove fractions. While, Al-Muqabla meant subtracting negatives from both sides of eqn. So this is merely basic mathematical operation. But was Kḥwārizmī the first to do this? or write a treatise on equations?
The Ottoman Turkish biographer Ḥājjī Khalīfa says he was only the “first Mohammedan” to write about the solution of problems by rules of reduction. This is confirmed by an anonymous Arabic writer whose quotation was preserved by the scholar Michael Casiri in his encylopedic work (Bibliotheca Arabico-Hispana). So according to Islamic tradition itself - Musa was just the first Muslim to write a treatise on this.
Leave aside Muslim tradition, we already know such a claim (of Ibn Musa writing the first treatise on Algebra) is patently false considering Diophantus, the Hellenic mathematician wrote a treatise on algebraic equations centuries before. The name “Algebra” isn’t the science!
Indian science had already been transmitted to the Abbasid court (where Kḥwārizmī would later find work) during the reign of Al-Mansur. In 773 AD, an Indian scholar, as part of an embassy, had given a Sanskrit astronomical treatise called the Mahāsiddhānta to the Arabs. This Sanskrit work was translated into Arabic by Muhammad Al-Fazari & rendered as “Sindhind Al-Kabīr” This fact is also mentioned by the astronomer Ibn Al Adami. Now, Kḥwārizmi would later work at the Abbasid court & under the reign of Al-Mansur write his first book.
The Hindu book was used to compile an astronomical table called the “Zij al-Sindhind”. Later on, Kḥwārizmī himself wrote a revised “Zij al Sindhind” based on the Sanskrit text containing 37 chapters of calendrical, astronomical calculations & a table of sine values.
Ibn Al-Qifti says Khwarizmi used the tables of the mean motions of the Sindhind (as well as Ptolemy’s table). The values in Khwarizmi’s book are actually all taken from the Brahmasphutasiddhānta of Brahmagupta (6th century). There is direct evidence of course, as Al-Kḥwārizmī wrote a treatise “Book of Hindu Computation” (kitāb al-ḥisāb al-hindī) which only survives today in a 12th century Latin translation (Algoritmi de numero indorum).
However, some of the evidence isn’t direct… For example, Khwarizmi gives a method which gives the value of pi as 3.1416~ But his method is exactly (verbatim) taken from Aryābhaṭa-s treatise (Chapter II, 28).
Now, Khwarizmi says “the mathematicians” say this and the “astronomers among them” - but who is “them” ? The “mathematicians” here are the Hindu mathematicians and the astronomers are the astronomers amongst this group of Hindus. This is clear from the language used (ahl al-hindisah). This is confirmed by the fact that both the formulas being discussed here (p = √10d^2) and p = d * 62832 / 20,000 occur nearly verbatim in the bIjaganita and the second in Bhāskara’s Līlāvati. (p is periphery of circle, d is the diameter)
To conclude, Al-Kḥwārizmī (Ibn Musa) was following an established Arab (and Persian) tradition of translating Indian or Greek mathematical & astronomical works & writing their own treatises based on the knowledge in them. This is how Hindu numbers were transmitted! When Kḥwārizmī wrote his text, both Greek and Hindu algebra had advanced well beyond the elementary stage of his work.