Scholar of mathematics. (B. 850?, *Al Hasib* (one who calculates) or *el-Mısrî*. Although there is not detailed information about his
life, it is known that he is originally from

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 2^{nd} 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 2^{nd} 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 2^{nd} 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 2^{nd} 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 1^{st}
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*.