Mathematics Education Centre, Loughborough University, UK.
Top Cogn Sci. 2013 Apr;5(2):270-82. doi: 10.1111/tops.12019.
In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians.
在本文中，我们报告了一项研究，其中有 109 位活跃于研究领域的数学家被要求判断一个据称是本科微积分中的有效证明。我们的研究有如下重要发现：(a) 数学家们对该论证是否为有效证明存在很大分歧；(b) 应用数学家比纯数学家更有可能判断该论证有效；(c) 认为该论证无效的参与者比认为其有效的参与者更自信；(d) 认为该论证有效的参与者通常不会改变他们的判断，即使面对其他数学家提出的为什么应该判断该证明无效的理由。这些发现表明，与文献中的一些说法相反，当代数学家之间并没有单一的有效性标准。
