al-Karajī, also known as al-Karkhī, in full, Abū Bakr ibn Muḥammad ibn al-Ḥusayn al-Karajī (born c. 
al-Karajī, also known as al-Karkhī, in full, Abū Bakr ibn Muḥammad ibn al-Ḥusayn al-Karajī (born c. 980, most likely Karaj, Persia, rather than Karkh, near Baghdad, Iraq—died c. 1030), mathematician and engineer who held an official position in Baghdad (c. 1010–1015), perhaps culminating in the position of vizier, during which time he wrote his three main works, al-Fakhrī fīʾl-jabr wa’l-muqābala (“Glorious on algebra”), al-Badī‘ fī’l-hisāb (“Wonderful on calculation”), and al-Kāfī fī’l-hisāb (“Sufficient on calculation”). A now lost work of his contained the first description of what later became known as Pascal’s triangle (see binomial theorem).
Al-Karajī combined tradition and novelty in his mathematical exposition. Like his Arabic predecessors he did not use symbolism—even writing numbers as words rather t