论数学可谬性的两个层次

The Two Levels of Mathematical Fallibility

首先回顾了宏观的数学可谬性,认为虽然它的提出具有重要的意义,但从数学实践的角度看仍存在不足之处。为此,提出了微观的数学可谬性,其主要表现为数学证明的可谬性。虽然数学证明的可谬性在数学发展的历史中一直存在,但在今天的数学发展中,由于一些新情况的出现,从而增加了数学证明可谬可能。最后给出了提出微观数学可谬性的意义。

This paper first reviews the mathematical macrofallibility, and argues that although it is of great significance, it still has shortcomings from the perspective of mathematical practice. It then puts forward the mathematical microfallibility, which is mainly manifested in the error of mathematical proof. Although the latter is common in the history of mathematics, in today＇s mathematical development, due to the emergence of some new situations in mathematical proof, fallibility increases in mathematical proof. And finally the paper stresses the value of the mathematical microfallibility.