The History Of Transmission Of Galois And His Theory

Galois Theory is the crowning achievement of the (algebraic) theory of equations, and the most important thing is that Galois Theory has opened another new and wide world for mathematics while it closed the door of the (algebraic) theory of equations. In the history of mathematics, Galois Theory and its founder Galois are always the main topics of study for mathematicians and historians. From 1832 to now, about 174 years have passed, although some questions remain in dark, we have known a lot. The purpose of this dissertation is to probe and to analyze systematically the transmission of Galois and his theory on the basis of reading original sources and of investigating previous researches on this subject. The major contributions made in the dissertation are as follows.Firstly, Galois and his mathematical works are discussed. Special attentions are paid to two questions. One is what had made Galois walk on the mathematical road and the other is what experiences and lessons we should learn from the death of Galois. The work that Galois' little brother Alfred Galois and Galois' friend Auguste Chevalier had done for Galois is systematically discussed. Proper mathematical places are given to every man who had made the main acts in the course of understanding and transmitting Galois and his theory.Secondly, Liouville and his publication of the works of Galois are discussed deeply. What were the contents in Liouville's publication? Why Liouville had attempted to excuse and justify those who had never recognized Galois while he was alive? How did Liouville obtain the works of Galois? Why Liouville decided to study the Galois' works which had ever been considered unclear in station by other mathematicians? How much dad Liouville understood Galois' works? Why Liouville had postponed his publication and never published his comments?Thirdly, on the basis of the late study, the thesis clarifies the event that Cauchy had lost Galois' important paper. By the analysis of Cauchy's life in France in 19 century, the reasons why Cauchy had not noticed Galois' works are discussed. On the dialectic point of view, the influences of Cauchy's systematical study on the theory of permutation to understanding Galois Theory to mathematicians in France are appraised.Fourthly, by all-sided use of comparative approach, the major contribution from the most representative authors in different periods of the Western history of Galois theory are evaluated as objectively as possible. The first man who had followed the thought of Galois and who had understood the thought of group in the Galois Theory was discussed. Why there was never no the reaction of Jacobi who had ever been asked by Galois? The first man who used the terminology "group" that Galois had used to memory Galois is discussed. The work of Serret and Jordan is mainly discussed in France.Fifthly, almost all of the studies on Galois and his theory that have been done in past 174 years are discussed systematically by the time order. These studies are very extensive including Galois' mathematical work, the life of Galois and Galois' methodology, language and pedagogy. Most interesting thing is that Films and dramas also appear. By analyzing these studies, the transmission in international is discussed.Finally, the process of introduction of Galois and his theory to china is briefly explored.