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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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The Canteen Boy, the reason you feel bad for him and you can laugh is because he, and I guess a lot of my characters, they don't notice they're getting made fun of. So they'll say something back that's not that great a quip, but in their mind they won the argument.

食堂的男孩，你为他感到难过的原因是你可以嘲笑他，我想我的很多角色，他们没有注意到他们被取笑了。所以他们会反驳说，这不是一个很好的讽刺，但在他们看来，他们赢得了辩论。

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We learn our belief systems as very little children, and then we move through life creating experiences to match our beliefs. Look back in your own life and notice how often you have gone through the same experience.

我们从很小的时候就开始学习我们的信仰体系，然后我们在生活中创造经验来匹配我们的信仰。回顾你自己的生活，注意你有多少次经历过同样的事情。

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Philosophical theories or ideas, as points of view, instruments of criticism, may help us to gather up what might otherwise pass unregarded by us.

哲学理论或思想，作为观点和批评的工具，可以帮助我们收集那些可能被我们忽视的东西。

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One can imagine that the ultimate mathematician is one who can see analogies between analogies.

可以想象，最终的数学家是一个能在类比之间看到类比的人。

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I like to move among painters, mathematicians, psychologists, people who can tell me something.

我喜欢在画家、数学家、心理学家中间走动，他们能告诉我一些事情。

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Theories that go counter to the facts of human nature are foredoomed.

违背人性事实的理论是注定要失败的。

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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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