Abū Kāmil Shujā ibn Aslam

Abū Kāmil
Born	c. 850
Died	c. 930
Residence	Egypt
Other names	al-ḥāsib al-miṣrī
Academic background
Influences	Al-Khwarizmi
Academic work
Era	Islamic Golden Age
Main interests	Algebra, geometry
Notable works	The Book of Algebra
Notable ideas	Use of irrational numbers as solutions and coefficients to equations
Influenced	Al-Karaji, Fibonacci

Abū Kāmil, Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (Latinized as Auoquamel,Arabic: ابو كامل‎‎, also known as al-ḥāsib al-miṣrī—lit. "the Egyptian reckoner") (c. 850 – c. 930) was an Egyptian Muslim mathematician during the Islamic Golden Age. He is considered the first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations. His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important part in introducing algebra to Europe.

Abu Kamil made important contributions to algebra and geometry. He was the first Islamic mathematician to work easily with algebraic equations with powers higher than ${\displaystyle x^{2}}$ (up to ${\displaystyle x^{8}}$), and solved sets of non-linear simultaneous equations with three unknown variables. He wrote all problems rhetorically, and some of his books lacked any mathematical notation beside those of integers. For example, he uses the Arabic expression "māl māl shayʾ" ("square-square-thing") for ${\displaystyle x^{5}}$ (i.e., ${\displaystyle x^{2}\cdot x^{2}\cdot x}$).

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