名家谈数学(中英文对照)

1、名家谈数学中英文对照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.数学的本质是对外表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、

2、概念的类比、想象才能最强的人爱德华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，说明不用借助实验，纯粹的推理能成功地扩大人们的认知领域。康德But t

3、here 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，给精细的自然科学提供了无可置疑的可靠保证，没有数学，它们无法到达这样的可靠程度。爱因斯坦Mathematics is the tool specially suite

4、d for dealing with abstract concepts of any kind and there is no limit to its power in this fieldFor 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，特别合适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，一本阐述新物理学的书，假如不是单纯地描绘实验工作的，其本质上，必定是一本数

5、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 reg

6、ard it so数学是创造性的艺术，因为数学家创造了美妙的新概念；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宇宙的伟大建筑师如今开场以纯粹数学家的身份出现吉恩斯The grea

7、test 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 patternsIf civilization continues t

8、o advance in the next two thousand years ， the overwhelming novelty in human thought will be the dominance of mathematical understanding数学是理解形式与分析形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 s

9、light，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，诗歌使人聪明，数学使人精细，哲理使人深化，伦理学使人有修养，逻辑与修辞使人善辩。培根The adv

10、ancement and perfection of mathematics are intimately connected with the prosperity of the State数学的开展与完善和国家的繁荣兴盛息息相关。拿破仑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。它可以也必将作出显著的教育上的奉献。谢尼泽For me the attraction of turnin

11、g 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可以在思想的训练方面实际地作出奉献。苏利文Algebra is generous，she often gives more than is asked of her.代数学是大方大方的，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

12、downright practical to be prepared.不管你喜欢与否，数学为你翻开求职的大门，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

13、 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进步预测气象的才能,估计环境危险的影响的才能, 研究宇宙起源的才能，以

14、及筹划选举结果的才能。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

15、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.宋以后，京师所设小学馆和武学堂中的

16、老师称谓皆称之为“教谕。至元明清之县学一律循之不变。明朝入选翰林院的进士之师称“教习。到清末，学堂兴起，各科老师仍沿用“教习一称。其实“教谕在明清时还有学官一意，即主管县一级的教育生员。而相应府和州掌管教育生员者那么谓“教授和“学正。“教授“学正和“教谕的副手一律称“训导。于民间，特别是汉代以后，对于在“校或“学中传授经学者也称为“经师。在一些特定的讲学场合，比方书院、皇室，也称老师为“院长、西席、讲席等。Mathematical facts worthy of being studied are those which, by their analogy with other facts,

17、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

18、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。发现是区分，是选择。课本、报刊杂志中的成语、名言警句等俯首皆是,但学生写作文运用到文章中的甚少,即使运用也很难做到恰如其分。为什么?还是没有彻底“记死的缘故。要解决这个问题,方法很简单,每天花3-5分钟左右的时间记一条成语、一那么名言警句即可。可以写在后黑板的“积累专栏上每日一换,可以在每天课前的3分钟让学生轮流讲解,也可让学生个人搜集,每天往笔记本上抄写,老师定期检查等等。这样,一年就可记300多条成语、300多那么名言警句,日积月累,终究会成为一笔不小的财富。这些成语典故“贮藏在学生脑中,自然会出口成章,写作时便会随心所欲地“提取出来,使文章增色添辉。值得研究的数学事实是因它们与其它的事实相类似，可以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提醒与其它早道的事实有无可疑心的联络，而被错误地认为是互相无关的那些庞加莱与当今“老师一称最接近的“老师概念，最早也要