In 628, Brahmagupta wrote the first rules for calculating with zero
Babylonians used zero as a placeholder and Romans as a sign of absence, but a 30-year-old Indian astronomer was the first to treat it as a number you can add, subtract and multiply. Brahmagupta's rules for zero and negative numbers are nearly modern. He stumbled only on dividing by zero.
Brahmagupta was born in 598 in Bhillamāla, modern Bhinmal in Rajasthan, capital of the western Indian kingdom of Gurjaradesa and a centre for mathematics and astronomy. A Shaivite Hindu, he belonged to the Brahmapaksha school of astronomy. In 628 he completed the Brāhmasphuṭasiddhānta, a revision of his school's standard treatise into which he poured a great deal of original material: 24 chapters in 1,008 verses. Late in life, at 67, he wrote a practical astronomy manual for students, the Khandakhadyaka, after moving to the astronomical centre of Ujjain, where he is presumed to have died around 668.
His treatment of zero is the headline. His book is the earliest known to handle zero as a number in its own right and to lay down rules for negatives: a positive plus a negative gives their difference, two negatives multiplied give a positive, anything times zero is zero. He declared that zero divided by zero equals zero and gave no clear answer for other numbers divided by zero; modern mathematics leaves both undefined.
The same work contains the first clear statement of the quadratic formula, solutions to linear equations and a method called the pulverizer for equations with several unknowns. He gave formulas for the sums of squares and cubes of the first n whole numbers and four methods of multiplication, one of them close to the technique taught today. His algebra was syncopated, using abbreviations: a dot over a number marked subtraction, and a divisor was written below the dividend without a bar.
His influence travelled west. After Sindh fell to the Arab Caliphate in 712, an embassy to Caliph al-Mansur's court brought astronomical texts including his, which al-Fazārī translated into Arabic. They helped spread the decimal system, feeding into al-Khwarizmi's work on Indian arithmetic, known in medieval Europe as the method of the Indians. The historian George Sarton called him the greatest scientist of his time.
Source: Brahmagupta
