A COLLECTION OF GOOD WORDS
数学
Math
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
数学作为人类思维的一种表达方式，反映了人类积极的意志、沉思的理性和对审美完美的渴望。其基本要素是逻辑与直觉、分析与建构、共性与个性。
But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.
但是不可能把一个立方体分成两个立方体，或者把四次方分成四次方，或者通常把正方形以外的任何幂分成类似的幂;关于这一点，我发现了一个显著的例证。这条边太窄，容不下它。
My main concern with the condition of mathematics in high school is that there's a lot of fear involved! Math is not, generally speaking, presented in a fun way. The concepts, as I see them, are fun, and that's the way I'd like to convey them myself.
我对高中数学状况的主要担忧是有很多恐惧!一般来说，数学不是以一种有趣的方式呈现的。在我看来，这些概念很有趣，这也是我想要表达它们的方式。
I tend to jot down moments, lines, interactions that don't really make any sense. I try and explain these scattered notes to my close friends, and they become more and more logical. I see screenwriting as a bit like a math equation which I have to solve.
我倾向于记下那些没有任何意义的瞬间、台词和互动。我试着向我的密友解释这些分散的笔记，他们变得越来越有逻辑。我认为剧本写作有点像一个数学方程，我必须解决它。
I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.
我选择了密码学。密码学始于数学。甚至从凯撒时代起，编码就基于数论和数学原理而发展起来。我决定使用这些原则，并设计了一个编码的作品。
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
如果科学推理局限于算术的逻辑过程，我们对物理世界的理解就不会走得太远。人们不妨尝试完全利用概率数学来把握扑克游戏。
I think philosophers can do things akin to theoretical scientists, in that, having read about empirical data, they too can think of what hypotheses and theories might account for that data. So there's a continuity between philosophy and science in that way.
我认为哲学家可以做一些类似于理论科学家的事情，在阅读了经验数据之后，他们也可以思考什么样的假设和理论可以解释这些数据。所以哲学和科学之间存在着连续性。
Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
现在的创造性数学家和过去一样，只受他们对对称性、简明性和普遍性的感觉以及对事物适应性的一种无法定义的感觉的指导，他们受到数学艺术的启发，而不是受到任何最终有用的前景的启发。
To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
把一个正方体分成另外两个正方体是不可能的，四次幂或者一般情况下，任何幂都不可能分成比二次幂更大的两次幂，我肯定已经找到了一个令人钦佩的证明，但它的边沿太窄，容不下它。
One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.
数学最令人惊奇的事情之一是，做数学的人通常对应用不感兴趣，因为数学本身就是一种美丽的艺术形式。它是结构和模式，这是我们喜欢的，这是我们开始的地方。
Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.
数学是一种神秘的力量的产物，没有人能理解它，而对美的无意识的认知肯定在其中扮演着重要的角色。从无穷无尽的设计中，一位数学家为了美观而选择了一种模式，并将其应用到实际中。
Soon afterwards I studied the inversion of sugar in the light of these considerations and immediately found that this classical reaction, too, was determined quantitatively by the same property of the acids, as was of course to be expected from the previous results.
不久之后，我根据这些考虑研究了糖的逆反应，并立即发现，这个经典的反应，也是由同样的性质的酸的数量决定的，这当然是可以从以前的结果预期。
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沿着这个主题，再读几句。
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。
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。
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
在我看来，数学科学是一个不可分割的整体，是一个有机体，它的活力取决于各部分之间的联系。
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!
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。