Abu Kamil

Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (Latinized as Auoquamel, Arabic: أبو كامل شجاع بن أسلم بن محمد بن شجاع, also known as Al-ḥāsib al-miṣrī—lit. "The Egyptian Calculator") (c. 850 – c. 930) was a prominent Egyptian 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 illustrated the rules of signs for expanding the multiplication ${\displaystyle (a\pm b)(c\pm d)}$. 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 ${\displaystyle x^{5}}$ (as ${\displaystyle x^{5}=x^{2}\cdot x^{2}\cdot x}$). One notable feature of his works was enumerating all the possible solutions to a given equation.

The Muslim encyclopedist Ibn Khaldūn classified Abū Kāmil as the second greatest algebraist chronologically after al-Khwarizmi.