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Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

  • -- G. H. Hardy 戈弗雷·哈罗德·哈代

从整体上看，纯数学明显比应用数学更有用。因为最重要的是技术，而数学技术主要是通过纯数学来教授的。

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Mathematical Techniques

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A technical solution may be defined as one that requires a change only in the techniques of the natural sciences, demanding little or nothing in the way of change in human values or ideas of morality.

技术解决方案可以定义为只需要改变自然科学的技术，很少或根本不需要改变人类价值观或道德观念。

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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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Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.

这是一个数学事实，负负得正，所以即使在不利的情况下也要积极思考。

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Injuries are part of the game, but sometimes we can avoid them by just practicing our techniques.

受伤是比赛的一部分，但有时我们可以通过练习我们的技术来避免受伤。

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