#### Brahmagupta

Brahmagupta was an Ancient Indian astronomer and mathematician, who lived from 597 AD to 668 AD.

He was born in the city of Bhinmal in Northwest India.

His father, whose name was Jisnugupta, was an astrologer.

One of the most significant input of Brahmagupta to mathematics was the introduction of ‘zero’ to the number system which stood for ‘nothing’.

His work the ‘Brahmasphutasiddhanta’ contained many mathematical findings written in verse form.

It had many rules of arithmetic which is part of the mathematical solutions now.

These are ‘A positive number multiplied by a positive number is positive.’, ‘A positive number multiplied by a negative number is negative’, ‘A negative number multiplied by a positive number is negative’ and ‘A negative number multiplied by a negative number is positive’.

The book also consisted of many geometrical theories like the ‘Pythagorean Theorem’ for a right angle triangle. Brahmagupta was the one to give the area of a triangle and the important rules of trigonometry such as values of the sin function.

He introduced the formula for cyclic quadrilaterals. Brahmagupta argued that the Earth and the universe are round and not flat.

He was the first to use mathematics to predict the positions of the planets, the timings of the lunar and solar eclipses.

Though all this seems like obvious and simple solutions it was a major improvement in science at that time.

He also calculated the length of the solar year which was 365 days, 5 minutes and 19 seconds which is quite accurate based on today’s calculation of 365 days, 5 hours and 19 seconds.

In addition to expounding on traditional Indian astronomy in his books, Brahmagupta devoted several chapters of Brahma-sphuta-siddhanta to mathematics.

In chapters 12 and 18 in particular, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations), which roughly correspond to arithmetic (including mensuration) and algebra, respectively.

Chapter 12 is simply named “Mathematics,” probably because the “basic operations,” such as arithmetic operations and proportions, and the “practical mathematics,” such as mixture and series, treated there occupied the major part of the mathematics of Brahmagupta’s milieu.

He stressed the importance of these topics as a qualification for a mathematician, or calculator (ganaka).

Chapter 18, “Pulverizer,” is named after the first topic of the chapter, probably because no particular name for this area (algebra) existed yet.

Brahmagupta’s view of numbers as abstract entities, rather than just for counting and measuring, allowed him to make yet another huge conceptual leap which would have profound consequence for future mathematics.

Previously, the sum 3 – 4, for example, was considered to be either meaningless or, at best, just zero.

Brahmagupta, however, realized that there could be such a thing as a negative number, which he referred to as “debt” as a opposed to “property”.

He expounded on the rules for dealing with negative numbers (e.g. a negative time, a negative is a positive, a negative time, a positive is a negative, etc).