'Abd al-Hamīd ibn Turk

ʿAbd al-Hamīd ibn Turk (fl. 830), known also as ʿAbd al-Hamīd ibn Wase ibn Turk Jili (Arabic: ابومحمد عبدالحمید بن واسع بن ترک الجیلی‎‎) was a ninth-century Muslim mathematician. Not much is known about his biography. The two records of him, one by Ibn Nadim and the other by al-Qifti are not identical. Al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili. Jili means from Gilan. On the other hand, Ibn Nadim mentions his nisbah as khuttali (ختلی), which is a region located in north of the Oxus and west of Badakhshan. In one of the two remaining manuscripts of his al-jabr wa al-muqabila, the recording of his nisbah is closer to al-Jili.

He wrote a work on algebra of which only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived.

He authored a manuscript entitled Logical Necessities in Mixed Equations, which is very similar to al-Khwarzimi's Al-Jabr and was published at around the same time as, or even possibly earlier than, Al-Jabr. The manuscript gives exactly the same geometric demonstration as is found in Al-Jabr, and in one case the same example as found in Al-Jabr, and even goes beyond Al-Jabr by giving a geometric proof that if the discriminant is negative then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.

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