Al-Kashi

Ghiyath al-Din Jamshid Mas'ud al-Kashi (c. 1380–1429) was one of the most accomplished mathematicians and astronomers of the medieval Islamic world. He was born in Kashan, a city in central Persia, around 1380 — the year is a traditional estimate, since no source records it directly. The first firmly dated event of his life is his observation of a lunar eclipse at Kashan in June 1406. He worked there in difficult, reportedly impoverished conditions, producing his early astronomical treatise Sullam al-sama' ("The Stairway of Heaven," 1407) and later the Khaqani Zij, a large set of astronomical tables.

Around 1420 al-Kashi was invited by the Timurid prince Ulugh Beg — himself a serious astronomer — to join the new madrasa (college) and observatory at Samarqand, in Transoxiana. There he became the institution's foremost mathematician and astronomer. In a treatise of 1424 he calculated 2π to nine sexagesimal (base-60) places, equivalent to sixteen decimal places — a precision unsurpassed for roughly 180 years. His Miftah al-Hisab ("Key to Arithmetic," 1427) is a landmark on decimal fractions and computational methods; a trigonometric relation he used is still called "al-Kashi's theorem" in France.

He died at Samarqand on 22 June 1429. Sources disagree on the cause: some later reports claim he was murdered, possibly on Ulugh Beg's orders, while others hold he died naturally. Ulugh Beg is reported to have praised him as a remarkable scientist who could solve the most difficult problems.