论抽象在数学美中的功能与价值

一切数学对象、一种数学理论、一个数学体系的形成都是经过多级次、多层次、多种形式的抽象思维的产物,它们既揭示了各种事物数量本质和规律性,又在逻辑上的自恰性,系统的前后一贯性以及公式、定理、公理体系体现出形式上的简洁和内涵的深广。现代数学的更高的抽象程度,使数学达到了最大的简单性、统一性、纯粹性、深刻性、精巧性、严密性、清晰性、能动性。因此,数学美是一种学科美,而抽象美则是一种高度内含于数学学科的方法美。

On the function and value of abstraction in the beauty of mathematics

The formation of all the mathematical objects,a mathematical theory and a mathematical system is the product of a multi-level and various forms of abstract thinking.they revealed both the nature and regularity of various subjects,and also logical coherence of the system and formula,theorem,the formal justice system reflect the simple form and deep contents.The higher abstraction degree of Modern mathematics makes it reach the greatest simplicity,uniformity,purely sexual and profoundly sexual,artistic nature,rigour,clarity and dynamism.Therefore,the beauty of mathematics is a kind of beauty of course,and the beauty of abstraction is the beauty of methods highly contained in the course of mathematics.