直觉与潜意识（一） (6-2)

That not every one can invent is nowise mysterious. That not every one can retain a demonstration once learned may also pass. But that not every one can understand mathematical reasoning when explained appears very surprising when we think of it. And yet those who can follow this reasoning only with difficulty are in the majority; that is undeniable, and will surely not be gainsaid by the experience of secondary-school teachers.

不是每个人都能进行创造性的工作，这是很正常的。此外，也不是每个人都能记住学习过的例子。与之不同且令人惊讶的是，并不是每个人都能理解数学推导的过程，（从逻辑上看这是很奇怪的，见下文）。事实上，大多数人都很难跟上推导的节奏，这是不可否认的，当然，一个有经验的中学老师肯定也会同意这点。

And further: how is error possible in mathematics? A sane mind should not be guilty of a logical fallacy, and yet there are very fine minds who do not trip in brief reasoning such as occurs in the ordinary doings of life, and who are incapable of following or repeating without error the mathematical demonstrations which are longer, but which after all are only an accumulation of brief reasonings wholly analogous to those they make so easily. Need we add that mathematicians themselves are not infallible?...

让我们更进一步：在学习数学或研究数学时，为什么会出错？理智的头脑不应该犯逻辑谬误，有好头脑的人也不会被困在简短的推导中，因为对他们来说这就像处理日常事务一样简单，然而这些人却不能无误地跟上数学推导和演算的节奏，但这些数学演示毕竟只是简单推理的累积，完全类似于他们能够轻易得出的结论。难道说数学家们也做不到这点吗？

数学联邦政治世界观提示您：看后求收藏（同人小说网http://tongren.me），接着再看更方便。