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A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

  • -- Stefan Banach 斯特凡·巴纳赫

数学家是能在定理之间找到类比的人;一个更好的数学家能看到证明之间的类比，而最好的数学家能注意到理论之间的类比。

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Theories Mathematician Notice Analogy

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With this sense of the splendour of our experience and of its awful brevity, gathering all we are into one desperate effort to see and touch, we shall hardly have time to make theories about the things we see and touch.

有了这种体验的壮丽感和它可怕的简练感，把我们所有的一切都集中到一个绝望的努力去看和触摸，我们将几乎没有时间对我们所看到和触摸的事物做出理论。

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The world is full of hopeful analogies and handsome, dubious eggs, called possibilities.

这个世界充满了充满希望的类比和被称为“可能性”的漂亮而可疑的鸡蛋。

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Civilization exists by geological consent, subject to change without notice.

文明的存在是经地质同意的，如有变更，恕不另行通知。

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Have you noticed that it is easier to believe in the "no" than the "yes"?

你是否注意到，相信“不”比相信“是”更容易?

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Proof is an idol before whom the pure mathematician tortures himself.

证明是一个偶像，纯数学家在它面前折磨自己。

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When an analogy is really singing, it's what you want it to be.

当一个类比真的在唱歌时，它就是你想要的。

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Mathematics is written for mathematicians.

数学是为数学家写的。

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