On The Conceptions Of Mathematics In Ancient Greek-Taking Opinions Of Pythagoreans, Plato, And Aristotle As Examples

The study of this dissertation approaches the mathematical conceptions of early ancient Greeks. It is a fundamental research in history of scientific ideas. The meaning of this study is that this research tries to reconstruct the evolution of mathematical conceptions of early ancient Greeks, which also could be a foundation and sample of further study to civil research. The target of paper is to find out the evolution of mathematical conceptions of early ancient Greeks through trying to figure out and compare the different mathematical conceptions during that time. Concretely, this paper works out from three samples, namely mathematical conceptions of Pythagoreans, Plato, and Aristotle. During the process of research, the writer used many methods, such as method of analysis of materials; method of disassembling conceptions, and method of sample. With the application of all these approaching methods, the characteristics of the evolution of mathematical conceptions have been depicted quiet clearly. As a conclusion of this study, writer thinks that the mode of evolution of mathematical evolution in early ancient Greeks is gradually progressing. However, during some steps in the process, they are very radical, such as the progress in mathematical methods.The creation of this dissertation is mainly in the methods that this study used and in the arrangements of outline of this paper. Taking the sample of approaching methods, the sample method abstracts the history of mathematical conceptions easily; the disassembling of conceptions makes the comparing process to be carried out very simply. For instance, the conception of mathematics has been measured in five parts, namely the definition and contents of mathematics; the evaluation of mathematics; the objects of mathematics; the attributes of objects of mathematics, and the mathematical methods. Therefore, the foundation of analysis and comparison of mathematical conceptions has been laid firmly. Additionally, the arrangement of this writing can help the readers find out the process of analysis and the conclusion very simply, since every chapter has been summarized briefly.