名家谈数学(中英文对照)

The essence of mathematics is the perception of logical relationships between seemingly disparate ideas；the most successful mathematicians are those whose range is widest and whose ability to see analogies and connect ideas is greatest.（数学的本质是对表面上看来完全不同的概念认识其内在的逻辑关系。最成功的数学家是知识面最宽、概念的类比、想象能力最强的人）—爱德华

Pure mathematics is， in its way，the poetry of logical ideas．(纯粹数学，就其本质而言，是逻辑思想的诗篇。）—爱因斯坦

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.（数学科学呈现出一个最辉煌的例子，表明不用借助实验，纯粹的推理能成功地扩大人们的认知领域。)—康德

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which，without mathematics，they could not attain.(数学受到高度尊崇的另一个原因在于：恰恰是数学，给精密的自然科学提供了无可置疑的可靠保证，没有数学，它们无法达到这样的可靠程度。）—爱因斯坦

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field．For this reason a book on the new physics，if not purely descriptive of experimental work，must be essentially mathematical.（数学是一项工具，特别适合于处理任何一类抽象概念，而且，它在这方面的作用是无止境的。因此，一本论述新物理学的书，如果不是单纯地描述实验工作的，其本质上，必定是一本数学书。）—狄拉克

Nature’s great book is written in mathematical symbol. (自然这一巨著是用数学符号写成的)—伽里略

Mathematics is a creative art because mathematicians create beautiful new concepts；it is a creative art because mathematicians live，act，and think live artists； and it is a creative art because mathematicians regard it so．(数学是创造性的艺术，因为数学家创造了美好的新概念；数学是创造性的艺术，因为数学家的生活、言行如同艺术家一样；数学是创造性的艺术，因为数学家就是这样认为的。）—哈尔莫斯

The essence of mathematics lies in its freedom．（数学的本质在于它的自由。）—康托尔

God ever arithmetizes.（上帝是一位数论学家。）—雅可比

The great Architect of the Universe now begins to appear as a pure mathematician（宇宙的伟大建筑师现在开始以纯粹数学家的身份出现）—吉恩斯

The greatest mathematicians, as Archimedes，Newton and Gauss，always united theory and application in equal measure.(如阿基米德、牛顿与高斯这样的最伟大的数学家，总是不偏不倚地把理论与应用结合起来。)—克莱因

Mathematics is the most powerful technique for the understanding of pattern，and for the analysis of the relation of patterns．．．If civilization continues to advance in the next two thousand years ， the overwhelming novelty in human thought will be the dominance of mathematical understanding．（数学是理解模式与分析模式关系的最有威力的工具．．．．．．只要在今后的两千年里，文明继续进步，人类思想中压倒一切的新事物，将是数学理智的统治。）—怀德海

Lagrange is the lofty pyramid of mathematical sciences.（拉格朗日是数学科学中高耸的金字塔。）—拿破仑

What we know is very slight，what we don’t know is immense. Man follows only phantoms.（我们所知道的是微乎其微的，我们所不知道的还是无穷无尽的。人们只是在追逐幻影。）—拉普拉斯

Histories make men wise；poems nitty；the mathematics subtle；natural philosophy deep；moral grave；logic and rhetoric able to contend．（历史使人明智，诗歌使人聪慧，数学使人精密，哲理使人深刻，伦理学使人有修养，逻辑与修辞使人善辩。）—培根

The advancement and perfection of mathematics are intimately connected with the prosperity of the State．（数学的发展与完善和国家的繁荣昌盛息息相关。）—拿破仑

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Mathematics is a crucial component of our culture. It can and should make a signal educational contribution.（数学是我们文化中极为重要的一个组成部分。它能够也必将作出显著的教育上的贡献。）—谢尼泽

For me the attraction of turning to mathematics is that in mathematics it is possible to actually make progress in a train of thought.（吸引我转向数学的原因在于数学能够在思想的训练方面实际地作出贡献。）—苏利文

Algebra is generous，she often gives more than is asked of her.（代数学是慷慨大方的，它给予人的往往比人们对她所要求的还要多。）—达朗贝尔

Like it or not, mathematics opens career doors, so it’s downright practical to be prepared.（不管你喜欢与否，数学为你打开求职的大门，因此，它是需要加以准备的真正实用的课程。）—波雅妮

Yet the part which mathematics plays in meteorology increases every year，and seems defined to increase（此外，数学在气象学方面所起的作用在逐年增大，而且，似乎还在不断地继续增大）—史密斯

More recent advances in the mathematical sciences have helped improve our ability to predict the weather ，to measure the effects of environmental hazards，to study the origin of the universe，and to project the outcomes of elections，Mathematical methods have become indispensable to the proper functioning of our technological society.(数学科学最近的进步帮助我们提高预测气象的能力,估计环境危险的影响的能力, 研究宇宙起源的能力，以及筹划选举结果的能力。数学方法对于我们这个技术社会真正发生效能已经变得不可缺少了。)—哈尔莫斯

Number rules the universe.(数统治着宇宙)—毕达哥拉斯

What, in fact, is mathematical discovery? It does not consist in making new combinations with mathematical entities that are already know. That can be done by anyone, and the combinations that could be so formed would be infinite in number, and the greater part of them would be absolutely devoid of interest. Discovery consists precisely in not constructing useless combinations, but in constructing those which are useful, which are an infinitely small minority. Discovery is discernment, selection.

Mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a mathematical law, in the same way that experimental facts lead us to the knowledge of a physical law. They are those which reveal unsuspected relations between other facts, long since known, but wrongly believed to be unrelated to each other.(实际上，什么是数学发现呢？它不在于把早已经知道的数学实体做新的组合。这是任何人都能做的，而能这样形成的组合也将有无限多种，其大多数肯定是没有任何意义的。发现恰恰在于不去构筑无用的组合，而在于构造有用的组合。这样的组合是极其稀少的。发现是辨别，是选择。

值得研究的数学事实是因它们与其它的事实相类似，能够引导我们去认识数学定律，正如实验事实引导我们去认识物理定律一样。值得研究的数学事实是能揭示与其它早已知道的事实有无可怀疑的联系，而被错误地认为是相互无关的那些)—庞加莱

Mathematics is the Queen of the Sciences，and Arithmetic the Queen of Mathematics．（数学是科学的女王，而数论是数学的女王。）—高斯