18. Al-Karkhi
(Died between 410-420H/1019-1029AD) 

Al-Karkhi was one of the eminent Muslim mathematicians(104), and "one of the greatest mathematicians who had a real influence on the progress of mathematical sciences"(105). But only few information are available about him.

He is Abu Bakr Muhammad Ibn al-Hassan (or Hussain) al-Hassib al-Karkhi (after Karakh, a township in Baghdad suburbs. He lived in Baghdad at the time of the Vizir Abu Ghalib Muhammad Ibn Khalf Fakhr al-Malik, the Minister of Baha'u Dawla al-Bouwayhi.

Scientific Contributions

Al-Karkhi's books contained for the first time in the history of Arabs,  solutions of indeterminate equations as any other equations, using the methods adopted by De Fuentes(106).

Al-Karkhi also came up with various solutions to equations of second order and presented researches on approximate roots of numbers and proofs of the finding of total of squares and cubes of the natural numerals he enumerated(107).

Major Works

-"Al-Fakhri fi al-Jabr". This book was called al-Fakhri under Fakhr al-Mulk and was compiled between 401 and 407.

Smith says in his book entitled "History of Mathematics" that Kitab al-Fakhri is a valuable heritage in algebra(108). A translation was undertaken in 1853 by the French orientalist  Franz Woepcke.

- Al-Kafi fi al-Hissab (Basics of Calculus). This book was published between 401 and 407 and was given as a gift to Fakhr al-Mulk. It deals with the principles of calculus known at the time as well as some innovated rules and calculation methods to facilitate some operations. The author did not use Indian numerals in his book and instead wrote them in letter. The book was translated in German by Hocheim and was edited in three volumes between 1878 and 1880.

- Kitab "Al-Badi'a fi al-Hissab.