Scholar of mathematics. (B. 850?,
Ebû Kamil Şuca drew attention with his success at mathematics and especially at algebra. He lived in the same period with the famous mathematician Harizmî. He widely benefited from Harizmî’s works and solved algebra equations of 2nd degree with his method. However he was not contented with it and brought some different explanations to these solution methods. He presented solution ways concerning linear (of first degree), quadratic (of second degree), levels above, unknown equations and whole number problems. For the first time in the history of algebra he enabled the solution of equations above the 2nd degree with a great accuracy. Therefore he was regarded as the second theoretician of algebra after Harizmî. He used this authority in algebra for the solution of feraiz (partition of the inheritance) calculations which make one of the most important issues of fiqh knowledge in Islam.
He established a connection between Harizmî, the founder of algebra, and Haracî and played a major role at the development of mathematics. It is also known that he contributed to the creation of Fibonacci's books and was a scholar who introduced mathematics to the West.
“Kitab-ül-Cebr vel-Mukabele” which was his most important work aimed to develop Harizmî’s algebra. In the introduction of the work he put his thanks to Harizmî into words and in the first chapter he summarized Harizmî’s algebra and explained it with supplements. He showed the solution of complicated 2nd degree equations whose coefficients were irrational (radix) numbers. Thus he refuted the false knowledge of Greeks on numbers.
In the second chapter of the work, he proved that the geometric problems which could hardly be solved by Greek and Islamic mathematicians who preceded him and even could not be solved by them, could easily be solved using the algebraic solution method which was his invention. The problems he solved in this chapter contain the numerical assignment of side lengths of an equilateral pentagon, decagon and quindecagon drawn in a circle. He calculated these side lengths using algebraic equations and applied the algebraic equations to Euclidean geometry.
He began the third chapter of the work with 2nd degree unknown equations and such equation systems. He said that some of these equations were new and a part of them was analyzed before. These second type equations prove that Ebû Kâmil did not stay under influence of Diophantos and Aritmetica. After these equations, he focused on entertaining (calming) mathematical problems which contain 1st degree equation systems. In the end of his work there is information on terms which give the sum of squares of numbers starting from a random number.
In his work titled Kitab-ut Taraif-fi’l-Hisab he explained the solution methods of equations with three, four and give unknowns with examples. He used letters as symbols instead of objects during the solution of algebraic problems.
He was followed by El-Kerhi and Ömer Hayyam. He adopted Leonardo Fibonacci, and Ebû Kâmil’s method from the Western World. Florian Cajori in his work about the history of mathematics states that Ebu Kamil’s works by the middle of XIII. Century was accepted as the only source books in the field of mathematical sciences in the Western Scientific World and Islamic Territory. In the Islamic World Abu Kamil Şuca produced the most important works of mathematical sciences after Harizmî. The Arabic edition of the book he wrote about algebra titled “Kitâb el Cebr ve’l Mukâbele” is registered with the number 19046 in Istanbul Beyazıt Library. Besides, there are manuscripts of Latin and Hebrew translations of this text. The Arabic text of the book is about two hundred pages.
Other interpretations were also done to the mentioned book of Ebû Kâmil by other scholars. The most famous ones among them are the interpretations of Ali İbn Ahmed el-Imrâni and el-Iştahri el-Hasib. These interpretations were mentioned in the sources; however we do not have the texts today.
Kitabu Kemal-il-Cebri ve Temamihi ve-Ziyadetihi fi Usulihi, Kitab-ut Taraif-fi’l-Hisab (A sample of this work is present in the library in Leiden city of Netherlands.), Kitab-üş-Şamil fil-Cebr vel Mukabele, Kitab-ül-Vesaya bil Cüzuri, Kitab-ul-Cem’ vet-Tefrik, Kitab-ül-Hataeyn, Kitab-ül-Kifaye, Kitab-ül-Mesaha vel Hendese, Kitabü’t-Tayr, Kitabul-Miftah-il-Felah, Risale fil-Muhammes vel-Mu’aşşar.