帕斯卡尔的早期数学观

On Pascal's Early Views on Mathematics

数学是社会思想和文化的产物,几乎每一位数学家的数学观都受到其所生活的时代和环境的智识氛围、思想思潮和所有社会资源的影响。在这方面,帕斯卡尔早期数学观的发展变化提供了一个典型的案例,其典型特征是他关于数学的观点与其宗教追求密切地联系在一起,主要体现在其数学研究的动机、目标以及他对数学之于信仰的价值等问题坚持不懈的追求和思考上。帕斯卡尔的早期数学观深受以梅森为代表的巴黎数学家团体的影响;他们对数学的神圣性、有效性和确定性深信不疑,数学研究是其信仰的一部分。这种认识奠定了帕斯卡尔数学生涯的基础,他的数学实践深深地打上这种宗教数学观的烙印,其关于算术三角形的工作即是这种特色的典型体现。但同时,随着帕斯卡尔交往圈子的扩大,詹森主义者对数学之于信仰的价值的质疑以及德·梅勒爵士对于数学的确定性以及应用的局限性的质问,促使帕斯卡尔对其早期数学观进行反思。

Mathematics is the product of social culture. Almost every mathematician＇s mathematical view was influ- enced by the intellectual atmosphere of his times and the environment, and all the social resources. In this respect, the de- velopment of Pascal＇s early mathematical concept provides a typical case, whose typical characteristic was that Pascal＇s views on mathematics were closely connected with his pursuit of religious spirit, his motivation of doing mathematics, the methods of mathematical research, and the perennial pursuit of the relations between mathematics and knowledge, tran- scendence and salvation. Pascal was influenced in his boyhood by Mersenne＇s cycle, which was a group of mathematicians in Paris. They thought of God as a supreme mathematician and mathematics as a Divine Science with certainty o{ supreme beauty, thus there is a clearly religious significance in the pursuit o{ the mathematical sciences. This faith laid a foundation for his mathematical career and spiritual life. Pascal＇s mathematical practice is deeply imprinted on this religious mathe- matical concept, and his work on arithmetic triangle is a typical manifestation of the characteristic. At the same time, Jansenist＇s questioning of the sufficiency of mathematical reasoning in faith and Chevalier de Mere＇s suggestions that mathematics was of dubious value awakened Pascal＇s reflection on the suitability and limitations of mathematics.