直觉与潜意识（一） (6-1)

亨利·庞加莱（Henri Poincaré）是19世纪末，二十世纪初的领袖数学家，法国最伟大的数学家之一。他在数学、物理和哲学等方面有着众多创造性和基础性的贡献，也被称为“最后一位全才数学家”。与此同时，庞加莱还是少有的，对自己思考数学时大脑的工作状态有极大兴趣和深刻理解的数学家。下面这篇文章来自庞加莱的论文Mathematical Creation，向读者描述和展示了直觉与潜意识这两种数学创造中必不可少的元素。

The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outside world, in which it acts or seems to act only of itself and on itself, so that in studying the procedure of geometric thought we may hope to reach what is most essential in man's mind...

数学创造的源头是一个应该引起心理学家强烈兴趣的问题。 在数学创造活动中，人类的思维似乎对外界的依赖最少，且只对人类自身或只在人类自身上发挥作用，因此，在研究几何思想的过程中，我们希望寻得人类思维中必不可少的东西......

A first fact should surprise us, or rather would surprise us if we were not so used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds; if its evidence is based on principles common to all men, and that none could deny without being mad, how does it come about that so many persons are here refractory?

第一个事实会使我们感到惊讶——或者更确切地说——如果我们不太习惯它的话，我们便会感到惊讶：怎么会有人无法理解数学呢？如果数学仅仅调用逻辑的规则，比如一些所有正常人都会接受的规则；如果它的论据是基于一种对所有人来说都很普遍，而且正常人都不会去否认它的原则，那么怎么会有那么多人深陷其中呢？

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