The Gupta Empire was an ancient Indian empire existing from the midto- late 3rd century CE to 543 CE. Brahmagupta (born c. 598 CE, died c. 668 CE) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the
Br?hmasphu?asiddh?nta, a theoretical treatise, and the Kha??akh?dyaka Brahmagupta were the first to give rules to compute with zero. The texts composed by Brahmagupta were in elliptic verse [clarification needed] in Sanskrit, as was common practice in Indian mathematics.
As no proofs are given, it is not known how Brahmagupta’s results were derived. Bh?skaracharya made a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddh?nta Shiromani is divided into four parts called Lil?vat?, B?jaga?ita, Grahaga?ita, and Gol?dhy?ya, which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Kara?aa Kaut?hala.