“离散数学”的范式革命及其意义

The paradigm revolution of discrete mathematics and its significance

20世纪中叶以来,随着计算机的诞生及其对科学与社会日渐显现的影响力,离散数学的思想和方法迅速发展,展现出了更为多样和充满活力的知识形态。离散数学的知识创新具有典型的数学范式革命性。作为对微积分范式的一种突破,离散数学超越了传统数学的知识界线,展现出在数学本体论、认识论与方法论上的新的哲学特征。与计算机与信息科学的发展相得益彰,离散数学范式具有离散化、算法化、计算性、复杂性以及与科学更为紧密的交互性等显著的当代科学革命特征,并显现出学科知识群与复杂性科学等独特的意蕴。

Since the middle of 20 thcentury,with the birth of computer and its increase effect on science and society,the thought and method of discrete mathematics have developed rapidly and new forms of knowledge with more multiple,tensions and vigor were emerged. The knowledge innovation of discrete mathematics has representative paradigm revolutionary character. As a breakthrough and transcending of the paradigm of calculus,the discrete mathematics has gone beyond the bound of traditional mathematics and showed new philosophical features in ontology,epistemology and methodology of mathematics. Complement with the development of computer and information science each other,the discrete mathematics demonstrated the contemporary scientific revolution features such as discretization,algorithmization,complexity and more tightly interaction with science,as well as the unique implication of group of disciplinary knowledge and complex science.