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I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

  • -- Georg Cantor 康托

我意识到，在这项事业中，我把自己置身于一种与广泛持有的有关数学无限大的观点和经常为数字的本质辩护的观点相反的立场。

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Mathematical concerning

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No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

无论一个数学定理看起来多么正确，一个人永远不应该满足于它没有什么不完美，直到它也给人一种美丽的印象。

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If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

如果真的如希尔伯特所言，数学是一场毫无意义的游戏，在纸上做着毫无意义的标记，那么我们唯一可以参考的数学经验就是在纸上做标记。

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In matters of truth and justice, there is no difference between large and small problems, for issues concerning the treatment of people are all the same.

在真理和正义的问题上，大问题和小问题没有区别，因为关于人民待遇的问题都是一样的。

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We are least open to precise knowledge concerning the things we are most vehement about.

对于那些我们最热衷的事情，我们最不愿意接受精确的知识。

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