One of the characteristics of modem mathematics is to use algebra in every fields of mathematics. But we don't have the exact definition of algebra, and we can't clearly define algebraic thinking. In order to solve this problem, this paper investigate the history of algebra. First, we describe some of the features of proportional Babylonian thinking by analysing some problems. In chapter 4, we consider Greek's analytical method and proportional theory. And in chapter 5, we deal with Diophantus' algebraic method by giving an overview of Arithmetica. Finally we investigate Viete's thinking of algebra through his ‘the analytical art’. By investigating these history of algebra, we reach the following conclusions. 1. The origin of algebra comes from problem solving(various equations). 2. The origin of algebraic thinking is the proportional thinking and the analytical thinking. 3. The thing that plays an important role in transition from arithmetical thinking to algebraic thinking is Babylonian ‘the false value’ idea and Diophantus’ ‘arithmos’ concept.