【作者】 徐传胜；

【导师】 曲安京；

【作者基本信息】 西北大学 ， 科学技术史， 2007， 博士

【摘要】 彼得堡数学学派系彼得堡科学院院士切比雪夫所创立的俄罗斯数学家研究团体，是俄罗斯在数学领域创建最早、实力最强、影响最大的学派。彼得堡数学学派继承和发展了古典概率论之精华，拯救了濒临危机的概率论；变革和制定了一系列研究方法，振兴了概率论学科；提出和创立了概率论新思想，开拓了概率论新领域。资料的限制、语言的困难和文化的差异使得国内外系统研究彼得堡数学学派概率思想者还甚少，有关资料相当匮乏，一些相关论述大都出现在综合性的书籍中，倾向于按照现代数学的习惯给出一般性的解释，且多为简要性介绍，读者难以了解其精髓所在。鉴于彼得堡数学学派在概率论发展史上的重要地位，本文以概率论思想为主线，对其概率思想的发展进行了系统而全面的分析和研究。主要成果为：(1)以“为什么数学”为切入点，用比较研究和史料分析的方法揭示出彼得堡数学学派振兴概率论学科的主要因素。彼得堡数学学派对概率论的发展赖于西欧尤其是法国先进的数学文化影响、俄罗斯良好的数学文化背景、彼得堡数学学派正确的世界观和方法论、切比雪夫超凡的影响力、学派成员间的互相合作和群体竞争以及概率论的内在矛盾等。(2)运用内史和外史相结合、学派整体和数学家相结合、概率思想和文化背景相结合等研究方法探讨了彼得堡数学学派的学术范式及其概率思想的演化过程；论证了彼得堡数学学派概率思想之精髓为精确估计在极限状态下的试验偏差。在其概率思想指导下，彼得堡数学学派严格论证了大数定理理论、完善了古典中心极限定理的理论体系、创立了马尔可夫链模型、发展了数理统计理论、首次提出概率论的公理化体系等。(3)注重学科间的交叉融合，讨论了相关概率思想与哲学、社会、宗教及相关学科的联系。试图从概率论哲学视角揭示彼得堡数学学派成员概率思想的轨迹，展示概率论与其它学科相结合的理论意义。(4)通过对英、俄和法文等重要经典原始文献的研读和分析，论述了彼得堡数学学派概率思想的深远影响。正是在彼得堡数学学派概率思想的影响下，俄罗斯逐步成为世界概率论研究中心，引领概率论的研究方向。这种领先地位一直保持到20世纪中叶乃至现在。(5)在前人研究的基础上，考察了概率论在中国的传播和发展。就传入中国的第一部概率论著作《决疑数学》、开创我国概率论与数理统计领域的先驱以及当今国内概率学者研究动态等均作了较细致的论述和分析。更多还原

【Abstract】 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.更多还原