恩格斯关于数学的界定及其史的考察

A Study on the History of Engels’ Mathematical View

恩格斯对于数学的论断“数学是研究现实世界的数量关系和空间形式的科学”是他数学观的核心,它对中国几代数学和数学教育工作者产生了深远影响。恩格斯基于笛卡尔、牛顿和莱布尼茨等数学家的近代数学成就,在批判地继承古希腊毕达哥拉斯、柏拉图、亚里士多德、德国的莱布尼茨和黑格尔等哲学家的数学哲学思想的基础上创造性地界定了何谓数学。该定义中的三要素——现实世界、数量关系和空间形式具有悠久的历史背景和数学哲学意义。中国和前苏联的数学家和数学哲学研究者们从现代数学发展的特点对该定义的历史局限性提出了批评,并给予了新的解释,赋予了新的内容。

Engels’ definition of mathematics,“mathematics is the science of studying the quantitative relations and spatial forms of the real world,” is the core of Engels’ mathematical view,which has exerted a profound influence on Chinese mathematics and mathematics educators for several generations.Based on the modern mathematical achievements of mathematicians such as Descartes,Newton and Leibniz,Engels critically inherited the mathematical philosophy of ancient Greek philosophers such as Pythagoras,Plato and Aristotle,and German philosopher such as Leibniz and Hegel,and creatively defined what is mathematics.The three elements in this definition,“real world” “quantitative relations ” and “spatial forms”,have a long historical background and a profound philosophic meaning of mathematics.Mathematicians and researchers on philosophy of mathematics in China and the former Soviet Union criticized the historical limitations of this definition from the characteristics of the development of modern mathematics,and gave new interpretations and added new contents.