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For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

  • -- Richard Courant 库兰特

对于学者和门外汉来说，只有数学本身的积极经验，而不是哲学，才能回答这个问题:什么是数学?

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Mathematics Philosophy

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I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

我喜欢数学，因为它不是人类，它与这个星球或整个偶然的宇宙没有什么特别的关系——因为，就像斯宾诺莎笔下的上帝一样，它也不会反过来爱我们。

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To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it.

教人们如何在没有确定性的情况下生活，同时又不被犹豫所麻痹，这也许是我们这个时代哲学仍然能为那些研究哲学的人所做的主要事情。

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Grown-ups never understand anything for themselves, and it is tiresome for children to be always and forever explaining things to them.

成年人永远不会自己理解任何事情，而孩子们总是没完没了地向他们解释事情是令人厌烦的。

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The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

数学存在的时间越长，它就变得越抽象，因此也可能变得越实用。

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