Explanations:Al-Beruni, whose full name was Abu Rayhan Muhammad ibn Ahmad al-Biruni, was a Persian polymath who made significant contributions to various fields, including astronomy, mathematics, and geography. He was born in 973 CE in Kath, which is now part of Uzbekistan, and lived during the time of the Ghaznavid Empire, which was ruled by Mahmud of Ghazni.
Mahmud of Ghazni, who reigned from 997 to 1030 CE, was a powerful ruler known for his military conquests and his patronage of scholars and artists. He recognized the value of intellectual pursuits and supported many scholars during his reign. Al-Beruni was one of the most notable scholars patronized by Mahmud of Ghazni. Al-Beruni's contributions to astronomy and mathematics were particularly significant, and he is known for his accurate calculations and observations.
Al-Beruni's work in astronomy included the calculation of the Earth's circumference, which he determined with remarkable accuracy. He also made significant contributions to the field of mathematics, including the development of trigonometric tables and the study of algebra. His work in these fields was highly regarded and influenced later scholars and scientists.
It is important to distinguish Al-Beruni from other notable figures of the same period, such as Firdausi, who was a poet and the author of the epic poem "Shahnameh." Firdausi's contributions were in the field of literature, and he was not an astronomer or mathematician. Therefore, the correct answer to the question is Al-Beruni, who was indeed the patronized astronomer and mathematician of Mahmud of Ghazni.