Abstract: 

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.

Key Words: 

Engels; View of mathematics; Actual world; Quantitative relations; Space forms