Algebra is a branch of mathematics in which all the arithmetical operations and formal manipulations are applied in maths to abstract the symbols rather than specific numbers. The notion that these calculations exists such a distinct

sub discipline of the mathematics, as well as the term algebra is used to denote it. It is resulted from a very slow historical development. This article mainly presents that history and tracing the evolution in the famous mathematician countries like India and China involving concept of the equation, symbols for conveying and manipulating mathematical statements, number systems, and the modern abstract and structural view of the algebra.

**The equation of Algebra in India and China**

Many famous Indian mathematicians, such as the Brahmagupta (AD 598–670) and the Bhaskara II (AD 1114–1185), developed

the non symbolic. It is yet very very precise involving procedures that are used for solving first and second degree equations and the type of equations with more than one variable. However, the main fundamental contribution of the Indian mathematicians was the invention of the decimal and positional numeral system. A full-fledged decimal and positional system certainly existed long time in India by the ending of 9th century. Yet most of its central ideas

had been very well transmitted well before that time to the China and the historical Islamic world. The Indian arithmetic and moreover it has developed consistent and correct rules for the operating with the positive and the negative numbers and especially for treating the zero like any other type of number. Several hundred years passed before the European mathematicians fully integrated such type of ideas into the developing discipline of the algebra.

Many Chinese mathematicians during the time period parallel to the European Middle Ages developed their own kind of methods for classifying and solving the quadratic equations by the radicals — a type of solutions that contain only those combinations of the most used tractable operations such as the – addition, multiplication, subtraction, division, and for taking roots. They were very unsuccessful, however, in their most of the attempts to obtain

the exact solutions to very higher-degree equations. Instead, they had developed approximation methods of very high accuracy, such as those described in the Yang Hui’s- Yang Hui suanfa (1275; “Yang Hui’s type of Mathematical Methods”). These type of calculation advantages afforded by their most expertise with the abacus may help them explain why Chinese mathematicians gravitated to the numeric analysis methods.