A COLLECTION OF GOOD WORDS
数学
Math
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.
对我影响最深的是，我意识到密码学和数学是非常高雅、纯粹的科学。我发现使用这些纯科学的目的不那么优雅。
Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
许多曾经有机会了解更多数学知识的人把数学和算术混为一谈，认为数学是一门枯燥无味的科学。然而，在现实中，这是一门需要大量想象力的科学。
Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.
并不是说几何学的命题只是近似正确的，而是它们在欧几里德空间中仍然是绝对正确的，而欧几里德空间长期以来一直被认为是我们经验的物理空间。
As a kid I quite fancied the romantic, Bohemian idea of being an artist. I expect I thought I could escape from the difficulties of maths and spelling. Maybe I thought I would avoid the judgement of the establishment.
当我还是个孩子的时候，我很喜欢做一个浪漫的，波希米亚式的艺术家。我想我可以摆脱数学和拼写的困难。也许我想我应该避免对体制的评判。
My favorite subject probably was math. I love math. Figures just intrigue me. I was really good at math. English probably was my worst subject. But I used to write a lot of poetry. I used to write poetry all the time.
我最喜欢的科目可能是数学。我爱数学。我对数字很感兴趣。我数学很好。英语可能是我最糟糕的科目。但是我曾经写过很多诗。我过去常常写诗。
It is impossible for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
任何一个大于第二个幂的数都不可能被写成两个类似幂的和。我对这一命题有一个真正奇妙的论证，这个论证的范围太窄，不能包含在内。
I visualized myself pulling on my mental thinking cap, jamming it down around my ears as I had taught myself to do. It was a tall, conical wizard's model, covered with chemical equations and formulae: a cornucopia of ideas.
我想象着自己戴上思维帽，像我教自己做的那样，把它塞到耳朵周围。这是一个高高的圆锥形巫师模型，上面布满了化学方程式和公式:各种各样的想法。
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
群论是数学的一个分支，一个人对某物做某件事，然后将结果与做同一件事对另一件事或另一件事对同一件事所得到的结果进行比较。
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
所有的数学科学都是建立在物理定律和数字定律之间的关系之上的，因此精确科学的目的是把自然界的问题简化为用数字运算来确定数量。
In my case, I used the elements of these simple forms - square, cube, line and color - to produce logical systems. Most of these systems were finite; that is, they were complete using all possible variations. This kept them simple.
在我的例子中，我使用了这些简单形式的元素——正方形、立方体、直线和颜色——来生成逻辑系统。这些系统大多是有限的;也就是说，他们完全使用了所有可能的变化。这使他们保持简单。
I believe sanity and realism can be restored to the teaching of Mathematical Statistics most easily and directly by entrusting such teaching largely to men and women who have had personal experience of research in the Natural Sciences.
我相信，如果把数理统计的教学主要委托给在自然科学领域有过研究经验的男性和女性，就可以最容易、最直接地恢复理智和现实主义。
The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
追求漂亮的公式和简洁的定理无疑会很快堕落为愚蠢的恶习，但追求严格的普遍性也会很快堕落为愚蠢的恶习，因为严格的普遍性是如此普遍，以至于它们无法适用于任何特定的情况。
KEEP EXPLORING
沿着这个主题，再读几句。
If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!
要使数学得到广泛的理解，我们需要强调它的优雅及其应用。有时候，大学似乎想强调这是多么困难!
I liked math - that was my favorite subject - and I was very interested in astronomy and in physical science.
我喜欢数学——那是我最喜欢的科目——我对天文学和物理科学非常感兴趣。
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。
Pure mathematicians just love to try unsolved problems - they love a challenge.
纯粹的数学家只是喜欢尝试未解决的问题——他们喜欢挑战。
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
如果我在沉睡了一千年后醒来，我的第一个问题将是:黎曼假说是否得到了证实?
The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.
量子理论的数学框架已经通过无数成功的测试，现在被普遍接受为对所有原子现象的一致和准确的描述。