William Dalrymple writes:

In 628 AD, an Indian sage living on a mountain in Rajasthan made one of the world’s most important mathematical discoveries. The great mathematician Brahmagupta (598–670) explored Indian philosophical ideas about nothingness and the void, and came up with the treatise that more or less invented – and certainly defined – the concept of zero.

Brahmagupta was born near the Rajasthan hill station of Mount Abu. When he was 30 years old, he wrote a 25-chapter treatise on mathematics that was immediately recognised as a work of extraordinary subtlety and genius.

He was the first mathematician to treat the circular zero symbol – originally just a dot – as a number just like the others, rather than merely as an absence, and this meant developing rules for doing arithmetic using this additional symbol along with the other nine.

These basic rules of mathematics for the first time allowed any number up to infinity to be expressed with just 10 distinct symbols: the nine Indian number symbols devised by earlier generations of Indian mathematicians, plus zero.These rules are still taught in classrooms around the world today.

Brahmagupta also wrote down in Sanskrit verse a set of arithmetic rules for handling positive and negative numbers, another of his innovations. In other writings, he seems to have been the first to describe gravity as an attractive force a full millennium before Isaac Newton.

But Brahmagupta was not alone, and he viewed himself as standing on the shoulders of an earlier Indian genius, Aryabhata (476–550). The latter’s work contains a very close approximation of the value of pi – 3.1416 – and deals in detail with spherical trigonometry. The ease of making calculations using his system had direct implications for astronomy and allowed him to calculate the movements of the planet, eclipses, the size of the Earth and, astonishingly, the exact length of the solar year toan accuracy of seven decimal points. [Continue reading…]