数学到底是发现还是发明——史宁中问题及其解答

Is Mathematics A Discovery Or An Invention──SHI Ning-zhong Problem and Its Solution

通过对数学发展过程的讨论 ,回答了著名学者史宁中先生提出的一个深刻而新颖的问题 :“数学到底是发现还是发明 ?”笔者通过对数学创新思维的分析和数学学科性质的讨论认为 ,数学兼有发现和发明两种特性 ,在整个数学发展的漫长过程中 ,发现和发明两种职能相辅相成 ,不能明确割裂开来。这是数学区别于真理的重要标志之一。把数学看做真理是对数学的一大误解 ,容易导致数学工作者缺乏假设能力而丧失创新能力。

Through the discussion to the developing process of mathematics, the article answers a profound and novel question, which is 'Is mathematics a discovery or an invention?', put forward by a famous scholar Mr. Shing Ning-zhong. Through the analysis to mathematical creative thought and the discussing to mathematical subject character, the article considers that mathematics has both discovering and inventing on characters. During the whole extensive process of mathematical development, the two functions 'discovering and inventing' complemented each other and can't be seperated clearly. This is one of important symbols that matheematics differs from truth. Regarding mathematics as truth is a misunderstanding to mathmatics, which can easily lead to lacking supposing ability and creative ability for mathematical scholars.