math sentence by famous people

1、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Pure

2、 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But there is another reason for the hign 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，

3、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 fieldFor this reason a book on the new physics，if not purely descriptive of experimental work，must be essentially mathematica

4、l.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Natures 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，an

5、d 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Histories make men wise；poems nitty；the mathematics subtile；natural philosop

6、hy 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Mathematics is the most powerful technique for the understanding of pa

7、ttern，and for the analysis of the relation of patternsIf civilization continues to advance in the next two thousant 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Mathematics is a

8、 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

9、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 its 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 ye

10、ar，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 the universe，and to project the outcomes of el

11、ections，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The mathematical method is the essence of mathematics. He wh

12、o fully comprehends the method is a mathematicianMusic has much resemblance to algebra.Pure mathematics is real magicians wand.The real mathematician is an enthusiast person；without enthusiasm，no mathematics.One may be a mathematician of the first rank without being able to compute，it is possible to

13、 be a great computer without having the slightest idea of mathematics.What logarithms are to mathematics,that mathematics are to the other sciences.数学方法是数学的本质。数学家是能完全领悟数学方法的人。音乐与代数很类似。纯数学是真正的魔术师的魔杖。真正的数学家，其本质是一个热情洋溢的人，没有热情就没有数学。一个不擅于计算的人，有可能成为一个第一流的数学家，而一个没有丝毫数学观念的人，充其量只能成为一个大计算家。对数之于数学，恰如数学之于其它科学。

14、哈登伯格It is the man not the method that solves the problem.解决问题的是人,而不是方法。 马斯科Mathematics possesses an aesthetic value as clearly defined as that of music or poetry.数学如同音乐或诗一样显然地确实具有美学价值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 grea

15、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A mathematician， who is not also some thing of a poet，will never be a complete mathematician.没有一些诗人气质的数学家绝不是一位完全的数学家。魏尔斯特拉斯The essence of mathematics i

16、s 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Lagrange is the lofty pyramid

17、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 dont 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The instruction of children should aim gradually to combine knowing and doing . Among all sciences mathematics seems to be the o

18、nly one of a kind to satisfy this aim most completely.儿童教育的目的应该是逐渐地把知与行结合起来。在所有的学科中，数学似乎是能最完全地满足这一要求的惟一的一类学科。康德The only way to learn mathematics is to do mathematics.学习数学的惟一方法是做数学。哈尔莫斯If the educational potential of mathematics is to be realized，then the attention that has to be paid to its technica

19、l aspects must be balanced by attention paid to its structural ，historical，genetic and philosophical aspects.如果要把数学的教育潜能付诸实际，那么，既要注意到数学的技术方面，也必须注意到它的结构、历史、创生与哲学的方面，而且，各方面的注意须适当平衡。谢尼泽We must teach these people good，useful mathematics in a low-key，relaxed style，free from authoritarianism，so that they

20、come to feel not threatened by it，not daunted by its unfamiliar symbols，but comfortable with it and convinced that they are now better able to reach rational decisions and cope with our complicated world. Mathematics will then become not a barrier，but the key to unlock the door to a fuller life.我们必须

21、以低调的轻松的风格, 而不是满堂灌的独裁风格把好的、有用的数学教给这些人，这样，他们才不会感到在受数学的威胁，不会因不熟悉的符号而畏缩，他们才会喜欢上数学，并且相信他们能够很好地作出合理的判断，能够很好地对付复杂的现实问题。那么，数学将不再成为一种障碍，而将成为打开通向更充实生活的大门的钥匙。 希尔顿Some teachers demand that students solve mathematics problems only by the method taught in class，This process can thwart initiative，compound frustrat

22、ion，and promote avoidance.有的教师要求学生只用课堂上教的方法解数学题。这种做法会阻碍独创能力的发展，导致失败，并造成回避困难的心理。波雅妮When students are forced to develop their own approaches to unsolved problems，they benefit much more than from exposure to the mathematics alone.当一个学生被迫大展身手去对付未解决的问题时，比仅仅学习数学知识，其受益要多得多。 斯潘尼尔Do not imagine that mathemat

23、ics is hard and crabbed and repulsive to common sense， it is merely the etherealization of common sense.别把数学想象为硬梆梆的、死绞蛮缠的、令人讨厌的、有悖于常识的东西，它只不过是赋予常识以灵性的东西。 开尔文The attraction of mathematics is that its great fun.数学的魅力在于它是很有趣的学科。帕克特If you wish to learn swimming，you have to go into the water，and if you w

24、ish to become a problem solver，you have to solve problems.如果你想学会游泳，你必须下水；如果想成为解题能手，你必须解题。 波利亚It appears to me that if one wants to make progress in mathematics，one should study the masters and not the pupils.我似乎觉得，如果一个人想在数学方面有所进步，他必须向大师们学习，而不是向徒弟们学习。阿贝尔Conceptual thinking is the salt of mathematics.

25、概念的思考是数学的特色。波士顿Facts are not much use，considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter. Theory is of the essence of facts. Without theory scientific knowledge would

26、be only worthy of the mad house.事实，只认为是事实，没有太大的用处。因其数量之多与显而易见的支离破碎，使人手足无措。但是，把他们融合成理论，并使之谐调，那么，情况就不同了。理论是事实的本质。没有理论，科学知识将只是一处疯人院。希维赛德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

27、, 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.

28、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

29、 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

30、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Those who assert that the mathematical sciences say nothing of the beautiful are in error. The chief forms of beauty are order, commensurability and precision.硬说数学科学无美可言的人是错误的。美的主要形式是秩序、匀称与明确。亚里斯多德The feeling of mathematical beauty , of the harmo

31、ny of numbers and forms, of geometric elegance. This is a true aesthetic feeling that all real mathematicians know.感觉到数学的美，感觉到数与形的协调，感觉到几何的优雅，这是所有真正的数学家都清楚的真实的美的感觉。 庞加莱The beauty of mathematics speaks for itself.数学之美是很自然明白地摆着的。哈尔莫斯I think it is correct to say that (the mathematicians) criteria of se

32、lection, and also those of success, are mainly aesthetical.我认为，说数学家选择课题的准则以及判断他是否成功的准则，主要的是美学准则，这是正确的。 冯.诺伊曼My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.我的工作总是力图把真与美结合起来，但是，当我不得不选择其中的一种时，我通常选择美。韦尔Aesthetic judgme

33、nts transcend both logic and applicability in the ranking of mathematical theorems: beauty and elegance have more to do with the value of a mathematical idea than does either strict truth or possible utility.在数学定理的评价中，审美标准既重于逻辑的标准，也重于实用的标准：在对数学思想的评价时，美与优雅比是否严密、正确，比是否有用都重要得多。斯蒂恩Pure mathematics can b

34、e practically useful and applied mathematics can be artistically elegant.纯粹数学可以是实际有用的，而应用数学也可以是优美高雅的。 哈尔莫斯Much research for new proofs of theorems already correctly established is undertaken simply because the existing proof have no aesthetic appeal.对早已正确认定的定理做进一步的研究，探索它的新证法，只不过是因为现有的证明欠缺美的魅力。 克莱因A

35、mathematician , like a painter or a poet, is a maker of patterns The mathematician s patterns, like the painters or poets ,must be beautifulBeauty is the first test:there is no permanent place in the world for ugly mathematics.数学家如画家或诗人一样，是款式的制造者数学家的款式，如同画家或诗人的款式，必须是美的世上没有丑陋数学的永久立身之地。 哈代 A peculiar

36、beauty reigns in the realm of mathematics, a beauty which resembles not so much the beauty of art as the beauty of nature and which affects the reflective mind , which has acquired an appreciation of it , very much like the later.一种奇特的美统治着数学王国，这种美不像艺术之美与自然之美那么相类似，但她深深地感染着人们的心灵，激起人们对她的欣赏，与艺术之美是十分相象的。

37、 库默May not Music be described as Mathematics of sence, Mathematics as Music of the reason? The soul of each the same! Thus the musician feels Mathematics, the mathematician thinks MusicMusic the dream, Mathematicsthe working lifeeach to receive its consummation from the other when the human intellig

38、ence, elevated to its perfect type, shall shine forth glorified in some future MozartDirichlet or BeethovenGaussa union already not indistinctly foreshadowed in the genius and lobours of a Helmholtz.难道不可以把音乐描绘成感觉的数学，而把数学描绘成理性的音乐吗？这样，音乐家感觉到数学，数学家想到音乐音乐是梦想，数学是工作的一生每一方都经由对方达到尽善尽美的境地，那时，人类的智慧达到完美的典型，将在某

39、个未来的莫扎特狄利克雷或贝多芬高斯的歌颂下而光彩夺目。这种联合已经在一个赫姆霍尔兹的天才和工作中清楚地预示出来了。西尔弗斯特I like to look at mathematics almost more as an art than as a science, for the activity of the mathematician, constantly creating as he is , guided though not controlled by the external world of the senses, bears a resemblance, not fancif

40、ul I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no

41、one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are , do not make a painter or mathematician worthy of the name, no indeed are they the most important factors in the case. Other qualities of a far more subtle s

42、ort, chief among which in both cases is imagination, go to the making of a good artist of good mathematician.一般地说，我更想把数学视为是艺术，而不是科学。因为我们可以说，数学家的活动，当他受外部的理性世界所引导，而不是被控制时，不断地进行创造性的活动，与一个艺术家、一个画家的活动相类似，有着实在的，不是虚幻的相似点。数学家这一方面的严密演绎推理可以比喻为画家那一方面的绘画技巧。恰如没有一定技巧的人不能成为一位好画家一样，没有一定的精密推理能力的人不能成为一位好的数学家。但是，这些尽管是

43、他们的基本特质，还不足以使一个画家或数学家名副其实，画图技巧与推理能力，说实在的，终究不是最重要的因素。远为敏感的，为二者都是主要的一类特质是想象力，它才能造就一名杰出的艺术家或杰出的数学家。博歇We can hope that as education and leisure develop more people will enjoy music and painting. But the number of people who really enjoy mathematics is very small.我们能够期待，随着教育与娱乐的发展，将有更多的人欣赏音乐与绘画。但是，能够真正欣赏

44、数学的人数是很少的。贝尔斯Mathematics，like philosophy，is virtually inseparable from its history数学如同哲学一样，实际上无法与其历史割裂开来。爱德华Theres not much in existence thats really so good it will，like mathematics，last thousands of years在现实中，不存在像数学那样有如此多的东西，持续了几千年依然是确实的如此美好。 苏利文As long as algebra and geometry proceeded along sepa

45、rate paths，their advance was slow and their applications limitedBut when these sciences joined company，they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection只要代数和几何沿着各自的途径去发展，它们的进展将是缓慢的，他们的应用也是很有限的。但是，当这两门学科结成伴侣，它们都将从对方身上获得新鲜的活力，因此，以快速的步伐猛进，趋于完美。拉格朗日A

46、rithmetical symbols are written diagrams and geometrical figures are graphical formulas算术符号是书写出来的图形，而几何图形是绘画出来的公式。希尔伯特 Algebra is but written geometry and geometry is but figured algebra. 代数不过是书写的几何，而几何不过是图形的代数。索菲娅格梅茵(Sophie Germain，17761831年)If Euclid failed to kindle your youthful enthusiasm，then

47、you were not born to be a scientific thinker如果欧几里得几何未能激起你少年时代的热情，那么，你就不是一个天生的科学思想家。爱因斯坦There is no royal road to geometry没有为国王特设的通往几何学的道路。欧几里得Geometry is the art of correct reasoning on incorrect figures几何学是在不准确的图形上进行正确推理的艺术。波利亚 Geometry has two great treasures，one is the theorem of Pythagoras；the o

48、ther，the division of a line into extreme and mean ratioThe first we may compare to a measure of gold，the second we may name a precious jewel几何学有两大珍宝，其一是毕达哥拉斯定理，另一个是分一线段为中外比。前者我们可比之为黄金，后者，我们可称之为贵重的宝石。开普勒Knowhow is the most valuable part of mathematical knowledge，much more valuable than the mere posse

49、ssion of informationYet how should we teach knowhow? The students can learn it only by imitation and practice In mathematics，knowhow is the ability to solve problems，to construct demonstrations，and to examine critically solutions and demonstrations。And in mathematics，knowhow is much more important t

50、han the mere possession of information技巧是数学知识中最有价值的部分，比仅仅获得信息还要有价值得多。但是，我们应该怎样教技巧呢? 学生只有通过模仿与实践才能学到技巧。在数学中，技巧是解决问题的能力，是构想证明的能力，是敏锐地评判答案与证明的能力。因而，在数学中，技巧比仅仅掌握信息还重要得多。波利亚 Do not neglect analogies，they may lead to discoveryAnalogy is another fertile source of discovery别忽视类比，它能引导我们去发现。类比是发现的另一丰富的源泉。波利亚

51、Logic is the hygiene the mathematician practices to keep his ideas healthy and strong逻辑学是数学家藉以保持他的思想健康与强壮的卫生学。韦尔 Rigour has a crucial part to play in clarification。严密性对于数学的净化起着决定性的作用。波士顿(Tim Poston)Mathematical rigor is like clothing；in its style it ought to suit the occasion，and it diminished comfort and restricts freedom of movement if it is either too loose or too tight数学的严密性如同衣服。其式样应该适时，无论是太松或是太紧