2. British philosopher Bacon (156 1- 1626) divided mathematics into "pure mathematics" and "mixed mathematics".
3.17th century, Descartes (1596-1650) thought: "All the sciences aimed at order and measurement are related to mathematics".
4./Kloc-In the 9th century, Engels discussed mathematics in this way: "The object of pure mathematics is the spatial form and quantitative relationship of the real world". According to Engels, mathematics can be defined as: "Mathematics is a science that studies the relationship between spatial forms and quantities in the real world."
5. In the late 19th century, Cantor (1845-1918), the founder of set theory, once said: "Mathematics is an absolutely free development discipline, which only obeys obvious thinking, that is, its concept must get rid of self-contradiction, and it must be defined clearly.
6. In 1950s, a group of influential mathematicians in the former Soviet Union tried to modify Engels' above definition to summarize the characteristics of the development of modern mathematics: "Modern mathematics is the possibility between various quantities, generally speaking, it is the mathematics of the relationship and interrelation between various variables".
7. Since 1980s, there has been a new attempt to modify the definition of mathematics to meet the requirements of the times. Mainly, a group of American scholars simply defined mathematics as the science of "mode": "The field of mathematics has always been called the science of mode, and its purpose is to reveal the structure and symmetry observed by people from the abstract world of nature and mathematics itself".