A COLLECTION OF GOOD WORDS
数学
Math
All science requires mathematics...the knowledge of mathematical things is almost innate in us...this is the easiest of sciences. A fact which is obvious in that no one’s brain rejects it. For laymen and people who are utterly illiterate know how to count and reckon.
所有的科学都需要数学……数学知识几乎是与生俱来的。这是最简单的科学。一个显而易见的事实是，没有人的大脑会排斥它。因为门外汉和完全不识字的人知道如何计算。
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
因此，对物理学的大部分和整个化学进行数学处理所必需的基本定律是完全知道的，而困难之处在于，应用这些定律会导致方程过于复杂而无法求解。
This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on.
这是一个棘手的领域，因为与简单的算术不同，要解决微积分问题——尤其是要执行积分——必须明智地选择应该使用哪种积分技术:分部积分、分部积分，等等。
In the present state of our knowledge, it would be useless to attempt to speculate on the remote cause of the electrical energy... its relation to chemical affinity is, however, sufficiently evident. May it not be identical with it, and an essential property of matter?
就我们目前所知，试图推测电能的遥远原因是没有用的。然而，它与化学亲合力的关系是十分明显的。难道它和物质的本质属性不一样吗?
In the first quarter of the nineteenth century the experimental proof for the interdependence of the composition and properties of chemical compounds resulted in the theory that they are mutually related, so that like composition governs like properties, and conversely.
十九世纪上半叶，化合物的组成和性质相互依赖的实验证明，产生了这样一种理论:它们是相互关联的，因此相似的组成决定相似的性质，反之亦然。
I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.
事实上，我认为它是数学技术的一大优势，它允许我们用代数方程来描述一个图案的一般特征，即使我们不知道决定其具体表现形式的数值。
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
每一个真正的进步都伴随着更锋利的工具和更简单的方法的发明，这在数学科学中是多么根深蒂固啊!与此同时，这些工具和方法有助于理解早期的理论，并把一些更复杂的发展抛诸脑后。
The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect. Who, then, would wish to prevent me from freely considering figures hanging on a balance imagined to be at an infinite distance beyond the confines of the world.
几何学家有一种特殊的特权，即通过抽象，运用智力来完成所有的结构。那么，谁会想要阻止我自由地思考那些悬在天平上的形象呢?
Architecture is an art which is basically geometrical. The cube is the basis of architecture because the right angle is necessary - the steps of a staircase consist of vertical and horizontal planes and the corners of rooms are nearly always right angles. We need right angles.
建筑是一门基本是几何的艺术。立方体是建筑的基础，因为直角是必要的——楼梯的台阶由垂直和水平平面组成，房间的角几乎总是直角。我们需要直角。
Most of the time I liked school and got good grades. In junior high, though, I hit a stumbling block with math - I used to come home and cry because of how frustrated I was! But after a few good teachers and a lot of perseverance, I ended up loving math and even choosing it as a major when I got to college.
大部分时间我喜欢学校，取得了好成绩。然而在初中的时候，我在数学上遇到了一个绊脚石——我常常回到家哭，因为我是多么的沮丧!但是经过几位好老师的努力和不懈的努力，我最终爱上了数学，甚至在我上大学时选择了数学作为我的专业。
Students never think it can be the teacher's fault and so I thought I was stupid. I was frustrated and would come home and cry because I couldn't do it. Then we got a new teacher who made math accessible. That made all the difference and I learned that it's how you present it that makes it scary or friendly.
学生们从来不认为这可能是老师的错，所以我认为我是愚蠢的。我很沮丧，回家后会哭，因为我做不到。然后我们有了一位新老师，他让数学变得触手可及。这让一切都不一样了，我明白了是你表达的方式让它变得可怕或友好。
[There is] a delusion that macro-economics is both viable and useful (a delusion encouraged by its extensive use of mathematics, which must always impress politicians lacking any mathematical education, and which is really the nearest thing to the practice of magic that occurs among professional economists).
(存在)一种错觉，认为宏观经济学既可行又有用(这种错觉是由其对数学的广泛应用所助长的，而这种广泛应用必然会给缺乏数学教育的政客留下深刻印象，而这实际上是职业经济学家中最接近魔术实践的东西)。
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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。
The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.
数学和物理对世界的抽象分析建立在空间和时间的概念上。
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!
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
数学把我们带入绝对必然性的领域，在这个领域里，不仅实际的词，而且每一个可能的词都必须符合。
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。