A Research On The Probability Thought Of The Petersburg Mathematical School

The Petersburg Mathematical School (abbreviated as PMS below) was a research association of the Russian mathematicians which was found by P.L.Chebyshev. It was the first and the strongest mathematical association in Russia with the most important affect. It inherited and developed the essence of classical probability theory. Mathematicians in this school posed a series of methods and led the probability research into a new era.The thoughts of PMS are not studied systematically in Chinese and western works until now. Some correlative contexts often appear in the comprehensive books only, most of which are brief introductions. It is difficult to understand its essence for the reader. In view of the important status of PMS in the development of probability, this article has carried on a more exhaustive analysis and research on its development of probability thought. The main achievements are as follows:(1) The primary factors why the probability theory of PMS arose are revealed by the methods of the comparative research and the historical data analysis. The development of the probability theory of PMS depended on the influence of advanced mathematical culture of Western Europe, the good mathematical culture of Russia, the correct outlook and the methodology, the extraordinary influence of Chebyshev, the cooperation of its members and the community competition as well as the inherent contradictions of probability theory.(2) The contribution to probability and its development vein of probability thought are discussed from both of the exterior and interior historical aspects. The theorem of large and the related theory were strictly proved by PMS, the theory system of the classical central limit theorem was consummated, the model and the theory of Markov chain were established, and the axioms of probability theory was proposed for the first time. The essence of its probability thought was the precise estimate of experimental deviation under a limit condition.(3) Great attention is paid to discussing the relationship between correlative probability thought and the philosophy. The three essential factors of philosophy (opposition and unification, quantitative change and qualitative change, accident and inevitability) all contain the stochastic mathematical thought. This article discusses the influence and the enlightenment of philosophy to the probability thought of PMS from the view of scientific philosophy.(4) The far-reaching influence of the probability thought of PMS is elaborated through original literature. It was because of the influence of probability thought of PMS that Russia gradually became the center of the probability theory and led the research it of in the world. Its leading the role continued even to the middle of 20th century. (5) Based on the predecessor's achievements, the dissemination of probability theory in China is investigated. Careful research is made on the book Jue Yi Shu Xue which was the first probability work spreaded into China and the pioneers in probability and mathematical statistic domain as well as the study tendency of the domestic probability scholar.