数学发现与发明关系新说

A New Perspective on the Relationship between Mathematical Discovery and Invention

数学是发现还是发明是一个古老且争议不断的问题.数学是客观与主观、发现与发明的融合;数学的内涵是客观的、发现的,数学的表达方式是主观的、发明的,并且这种客观性与主观性、发现性与发明性是相对的,而不是绝对的.不同属性的数学内容的客观性与主观性、发现与发明的成分是不同的;数学在发现与发明的交织与融合中发展.数学发现是数学发明的基础与依据,发现是数学的第一性,发明性是数学的第二性.

Whether mathematics is a discovery or an invention is an old and controversial question.Mathematics is a fusion of objectivity and subjectivity,as well as a fusion of discovery and invention.The connotation of mathematics is objective and discoverable,and the expression of mathematics is subjective and inventive.And this objectivity and subjectivity,discovery and invention are relative rather than absolute.For mathematical content with different attributes,the proportion of objectivity and subjectivity as well as the proportion of discovery and invention are different.Mathematics develops in the interweaving and fusion of discovery and invention.Mathematical discovery is the foundation and basis of mathematical invention.Discovery is the primary nature of mathematics,and invention is the secondary nature of mathematics.