人文数学的文化意蕴及价值意义——兼论数学文化的三元结构

The Cultural Connotation and Value of Humanistic Mathematics:A Tripartite Structure of the Mathematical Culture

一个时代的特征,在很大程度上与这个时代的数学活动密切相关。本文提出人文数学的概念,试图建立一个以数学、哲学、艺术为内核,以其他人文社会科学为亚内核,以系统学科、科学技术、生态学、统计学等为外延的有限域的人文数学体系架构。这一架构突出彰显人文数学的基础意义、工具意义、模型意义、方法意义和审美意义,使数学与新工科、新医科、新农科、新文科交互共享,把数学文化的意义价值集约广大,积极推进中国特色人文社会科学的学科体系、学术体系、话语体系建设。

The characteristics of an era are in large part closely related to the mathematical activities in that period.This paper proposes the concept of humanistic mathematics and outlines a framework of humanistic mathematics that consists of the core,subcore and Galois field.The core revolves around mathematics,philosophy,and art;the subcore integrates humanities and social sciences;and the Galois field extends to system science,science and technology,ecology,and statistics.The paper highlights humanistic mathematics as a foundation,an instrument,a model,a critical thinking activity,a logical manifestation,and an aesthetic discipline.It intensifies the meaning and maximizes the significance of the mathematical culture in the synergy of New Engineering,New Medicine,New Agricultural Sciences,and New Liberal Arts in China.The paper contributes to the construction of the discipline system,academic system,and discourse system of humanities and social sciences with Chinese characteristics.