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{{Short description|Muslim mathematician (790–854)}}
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'''{{transliteration|ar|ALA|ʿAbd al-Hamīd ibn Turk|italics=no}}''' ([[floruit|fl.]] 830), known also as '''{{transliteration|ar|ALA|ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili|italics=no}}''' ({{langx|ar|ابومحمد عبدالحمید بن واسع بن ترک الجیلی}}) was a ninth-century [[Islamic mathematics|mathematician]]. Not much is known about his life. The two records of him, one by [[ibn al-Nadim|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'' ({{lang|ar|ختلی}}), which is a region located 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''.<ref name="cgie">[http://www.cgie.org.ir/fa/publication/entryview/1465 Ibn Turk] in ''Dāʾirat al-Maʿārif-i Buzurg-i Islāmī'', Vol. 3, no. 1001, Tehran. To be translated in [[Encyclopaedia Islamica|Encyclopædia Islamica]].</ref> [[David Pingree]] / ''[[Encyclopaedia Iranica]]'' states that he originally hailed from [[Khuttal]] or [[Gilan Province|Gilan]].{{sfn|Pingree|1982|page=111}}
He wrote a work on [[algebra]] 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''.<ref name="Boyer Ibn Turk">{{cite book|first=Carl B.|last=Boyer|authorlink=Carl Benjamin Boyer|title=A History of Mathematics|edition=Second|publisher=[[John Wiley & Sons, Inc.]]|year=1991|chapter=The Arabic Hegemony|isbn=0-471-54397-7|quote=The ''Algebra'' of [[al-Khwarizmi]] usually is regarded as the first work on the subject, but a recent publication in Turkey raises some questions about this. A manuscript of a work by 'Abd-al-Hamid ibn-Turk, entitled "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<sup>2</sup> + 21 = 10x. In one respect 'Abd-al-Hamad'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 works 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. ... Note the omission of [[Diophantus]] and [[Pappus of Alexandria|Pappus]], authors who evidently were not at first known in Arabia, although the Diophantine ''Arithmetica'' became familiar before the end of the tenth century.|page=[https://archive.org/details/historyofmathema00boye/page/234 234]|chapter-url-access=registration|chapter-url=https://archive.org/details/historyofmathema00boye/page/234}}</ref>  Only a chapter called "Logical Necessities in Mixed Equations", on the solution of [[quadratic equations]], has survived.  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.<ref name="Boyer Ibn Turk" /> 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.<ref name="Boyer Ibn Turk" />

== References ==
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== Further reading ==
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* {{cite journal |last=Høyrup |first=J. |title=Al-Khwarizmi, Ibn Turk and the Liber Mensurationum: On the Origins of Islamic Algebra |journal=Erdem |volume=5 |year=1986 |issue=5 |pages=445–484|doi=10.32704/erdem.1986.5.445 |s2cid=126060042 |url=https://dergipark.org.tr/tr/pub/erdem/issue/44571/553155 }}
* {{cite encyclopedia | article = ʿABD-AL-ḤAMĪD B. VĀSEʿ | last = Pingree | first = David | authorlink = David Pingree| url = http://www.iranicaonline.org/articles/abd-al-hamid-b-vase | editor-last = | editor-first =  | editor-link = | encyclopedia  = Encyclopaedia Iranica, Vol. I, Fasc. 1 | page = 111 | location = | publisher = | year = 1982 | isbn = }}
* {{cite book |last=Sayili |first=Aydin |authorlink=Aydin Sayili |title=Abdülhamit İbn Türk'ün Katışık Denklemlerde Mantıki Zaruretler Adlı Yazısı ve Zamanın Cebri. (Logical necessities in mixed equations by ʿAbd al Hamīd ibn Turk and the algebra of his time.) |location=Ankara |publisher=Türk Tarih Kurumu Basımevı |year=1962}} Rev. by Jean Itard in Revue Hist. Sci. Applic., 1965, I8:123-124.
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==External links==
* {{cite web|last1=Pingree|first1=David|authorlink=David Pingree|title=ʿABD-AL-ḤAMĪD B. VĀSEʿ|url=http://www.iranicaonline.org/articles/abd-al-hamid-b-vase|website=www.iranicaonline.org|publisher=Encyclopaedia Iranica|language=en}}

{{Islamic mathematics}}

{{Authority control}}

{{DEFAULTSORT:Turk, Abd Hamid}}
[[Category:Mathematicians of the medieval Islamic world]]
[[Category:Mathematicians from the Abbasid Caliphate]]
[[Category:9th-century mathematicians]]
[[Category:9th-century people from the Abbasid Caliphate]]
[[Category:Year of birth unknown]]
[[Category:Year of death unknown]]


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