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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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In societies where modern conditions of production prevail, all of life presents itself as an immense accumulation of spectacles. Everything that was directly lived has moved away into a representation.

在现代生产条件普遍存在的社会中，所有的生活都表现为壮观景象的巨大积累。所有直接存在的东西都被移到了一种表现形式中。

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It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

说没有人会吹嘘自己对文学的无知几乎已经成了陈词滥调，但吹嘘自己对科学的无知、自豪地宣称自己在数学方面的无能是可以被社会接受的。

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One has to take a somewhat bold and dangerous line with this existence: especially as, whatever happens, we are bound to lose it.

一个人必须对这种存在采取某种大胆而危险的态度:特别是，无论发生什么，我们一定会失去它。

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Mathematics is the most beautiful and most powerful creation of the human spirit.

数学是人类精神最美丽、最强大的创造。

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