BRAHMAGUPTABrahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta, written in 628 in Bhinmal. Brahmagupta is believed to have been born in 598 AD. He likely lived most of his life in Bhinmal in Rajasthan, during the reign and possibly under the patronage of King Vyaghramukha.Brahmagupta was the first to use zero as a number. He gave rules to compute with zero. Negative numbers did not appear in Brahmasputa siddhanta.  It is composed in elliptic verse, as was common practice in Indian mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta's mathematics was derived.Brahmagupta gave the solution of the general linear equation. He further gave two equivalent solutions to the general quadratic equation.

Which are, respectively, solutions equivalent to,

and

Many cultures knew four fundamental operations. The way we do now based on Hindu Arabic number system first appeared in his book. Contrary to popular opinion that they were already known by the Sumerians in 2500 BC.

He gave rules for dealing with five types of combinations of fractions,  ,  , 

,  , and  .Brahmagupta is considered as the man who found zero. Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals.

So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area

is  while, letting  , the exact area is

In verse 40 of his book, he gives values of π…

He used 3 as the “practical” value of π and    as an “accurate” value of π. He even contributed alot to Trigonometry, but all of that was to complicated to talk about. The main work of Brahmagupta , Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma"), written c.628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series ,Brahmagupta's identity, and the Brahmagupta’s theorem. The book was written completely in verse.

Brhmasphuta-siddhanta is one of the first mathematical books to provide concrete

ideas on positive numbers, negative numbers, and zero. He wrote the following rules:

The sum of two positive quantities is positive

The sum of two negative quantities is negative

The sum of zero and a negative number is negative

The sum of zero and a positive number is positive

The sum of zero and zero is zero.

The sum of a positive and a negative is their difference; or, if they are equal, zero

In subtraction, the less is to be taken from the greater, positive from positive

In subtraction, the less is to be taken from the greater, negative from negative

When the greater however, is subtracted from the less, the difference is reversed

When positive is to be subtracted from negative, and negative from positive, they

must be added together

The product of a negative quantity and a positive quantity is negative

The product of a negative quantity and a negative quantity is positive

The product of two positive, is positive.

Positive divided by positive or negative by negative is positive

Positive divided by negative is negative. Negative divided by positive is negative

A positive or negative number when divided by zero is a fraction with the zero as

denominator

Zero divided by a negative or positive number is either zero or is expressed as a

fraction with zero as numerator and the finite quantity as denominator

Zero divided by zero is zero

The last of these rules is not correct as division by zero is undefined for a Field; however

it is notable that it was the earliest attempt to define division by 0.