A COLLECTION OF GOOD WORDS
数学
Mathematical
One cannot really argue with a mathematical theorem.
一个人不能真的用数学定理来辩论。
The laws of nature are but the mathematical thoughts of God.
自然法则不过是上帝的数学思想。
I hope no man takes what I said about the living and dieing of men for mathematical demonstration.
我希望没有人把我所说的人的生与死作为数学论证。
A pure mathematical series would be one in which each term is derived from the preceding term by a rule.
一个纯数学级数应该是一个每一项都由前一项根据规则推导出来的级数。
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
当埃斯库罗斯被遗忘时，阿基米德将被记住，因为语言会消亡，而数学思想不会。
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。
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
欧几里得告诉我，没有假设就没有证据。因此，在任何论证中，都要检验假设。
To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
在我看来，只强调美就像一个数学系统，只关注它自己的正数。
It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset.
现代物理学不可能用完全决定论来预测任何事情，因为它从一开始就涉及概率。
In a few decades of reconstruction, even the mathematical natural sciences, the ancient archetypes of theoretical perfection, have changed habit completely!
在几十年的重建中，甚至数学自然科学的原型理论的完善，都彻底改变了习惯!
Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts.
网络空间。在每个国家，每天都有数以亿计的合法操作者，通过教孩子数学概念，体验到一种双方同意的幻觉。
Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.
没有烦琐的工作，没有人能对纯数学研究是什么样子的，或能从纯数学研究中获得丰富的见解有任何具体的、全面的认识。
KEEP EXPLORING
沿着这个主题，再读几句。
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.
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。
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。
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。
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.
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。