Ghiyaseddin Jamsheed Kashani (1380 - 22 June 1429) was a Persian astronomer and mathematician. His name also appears as Al-Kashi. He was born in Kashan, Iran.
While Tamerlane was undertaking his military campaigns, conditions were very difficult with widespread poverty where Kashi grew up. And Kashi lived in poverty, like so many others, and devoted himself to science while moving from town to town. But conditions improved when Shahrokh took over after his father's death. He brought economic prosperity to the region, and strongly supported artistic and intellectual activity. With the changing atmosphere, Kashi's life also improved markedly.
Kashi's luck soon arrived at his doorstep, and Ulugh Beg invited Kashi to join him at his great school of learning in Samarkand, as well as around sixty other scientists. There is little doubt that Kashi became the leading astronomer and mathematician at Samarkand and he was called the second Ptolemy by a contemporary historian of his.
Kashi's compendium of the Science of Astronomy written in 1410-11 was dedicated to Ulugh Beg, who had been made ruler of Samarkand by his father Shahrokh. The compendium was based on the tables of the Persian scholar Nasir al-Din Tusi.
Letters which al-Kashi wrote in Persian to his father, who lived in Kashan, have survived. These were written from Samarkand and give a wonderful description of the scientific life there.
It is clear that Kashi was the best scientist and closest collaborator of Ulugh Beg at Samarkand and, despite Kashi's ignorance of proper court behaviour and lack of polished manners, he was highly respected by Ulugh Beg.
Kashi produced his treatise on the Circumference in July 1424, a work in which he calculated 2pi to nine sexagesimal places and translated this into sixteen decimal places. This was an achievement far beyond anything which had been obtained before by the Greeks, Chinese or Indians. It would be almost 200 years before van Ceulen would surpass Kashi's accuracy with 20 decimal places.
Al-Kashi's most impressive mathematical work was, however, The Key to Arithmetic which he completed on 2 March 1427. The work is a major text intended to be used in teaching students in Samarkand, in particular Kashi tries to give the necessary mathematics for those studying astronomy, surveying, architecture, accounting and trading.
In the Key to Arithmetic, Kashi, for the first time, along with Al-Samawal and some other's from al-Karaji's school, gives a description of decimal fractions.
Kashi also had an algorithm for calculating nth roots, which was a special case of the methods given many centuries later by Ruffini and Horner. But again, these methods were also present in the work of mathematicians of Karaji's school, in particular al-Samawal.
Kashi also computed sine values to the same accuracy as he had computed the pi in his earlier work. He also considered the equation associated with the problem of trisecting an angle, i.e. the cubic equation. He was not the first to look at approximate solutions to this equation since Biruni had worked on it earlier. However, his iterative method was unique.
All these works were long unknown in Europe and were studied later in the nineteenth and twentieth centuries by historians.
He died in Samarkand in 1429.