Brahmagupta

As the top math-guru of his era, Brahmagupta journeyed into astronomy and trigonometry: trying to evaluate the periodic positions of heavenly bodies. He was a pacesetter too: introducing some of the earliest known symbolical expressions in his treatises on Geometry, Arithmetic and Algebra (similar to what Diophantus did three centuries prior). Most of his works did not survive, but those that did showed that he was obsessed with quadrilaterals. This explains why some contemporary theorems (such as the formula for the area of a cyclic quad), are named after him. But even more noteworthy is that Brahmagupta is credited (alongside: Liu Hui, Zhang Cang, etc.) with depicting decimals, zero and negative numbers as useful mathematical entities. These are evidenced in his book, titled: Brahmasphutasiddhanta. And a century after his demise, the astronomer, Muhammad Al-Fazari, safeguarded this work by translating it into Arabic. It was a copy of this translation that Muhammad Al-Khwarizmi used to learn the decimals. He then used the acquired knowledge to publish his Al-Jam wal-tafriq bi hisal-al-Hind (which means: Addition and Subtraction based on Indian Arithmetic). This book by Al-Khwarizmi was later translated into Latin (as Algorithmi de numero Indorum), and was sold throughout Europe. Thus, Brahmagupta taught Europeans (and the wider world) the decimal system. His reputation as a mathematician is such that few people realized how profoundly versed he was in astronomy. I am impressed by how his exegesis, Khandakhadyaka, beautifully and eloquently augmented Aryabhata’s Ardharatrikapaksa. Several concepts and theorems are named after Brahmagupta.