Brahmagupta

Brahmagupta (c. 598–668 CE) was an Indian mathematician and astronomer from the Gupta period. He was born in Bhinmal, in present-day Rajasthan, and worked at royal courts in northern India. His mathematics and astronomy influenced later scholars in India and beyond, including Islamic scholars who transmitted Indian ideas to the medieval world.

His most influential work is the Brahmasphutasiddhanta (The Opening of the Universe), completed in 628 CE. It is among the earliest treatises to treat zero as a number in its own right and to present rules for arithmetic with zero and negative numbers. The text also provides methods for solving linear and quadratic equations and includes astronomical procedures.

In geometry and algebra, Brahmagupta introduced results that became foundational. He formulated Brahmagupta's formula for the area of a cyclic quadrilateral: area = sqrt((s − a)(s − b)(s − c)(s − d)), where s is the semiperimeter. The Brahmagupta–Fibonacci identity, relating products of sums of two squares, is attributed to him as well. He also offered methods for solving certain Diophantine equations and contributed to the development of algebraic reasoning in Indian mathematics.

In astronomy, he wrote the Khandakhadyaka (c. 665 CE) and improved computational methods for predicting planetary positions and celestial events such as eclipses. His work employed trigonometric calculations and sine tables, helping to lay groundwork for later Indian and Islamic astronomy.

Brahmagupta's writings were translated into Arabic and influenced medieval Islamic mathematicians, aiding the transmission of Indian mathematical ideas to later Europe. His emphasis on zero, algebraic rules, and geometric formulas marks him as a pivotal figure in the history of mathematics.