1. 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

1. I believe that it is correct to say that the criteria for mathematicians to choose topics and to judge whether they have been successful are mainly aesthetic criteria, which is the case. von Neumann

2. 在数学里，分辨何是重要，何事不重要，知所选择是很重要的。广中平佑

2. In mathematics, it is very important to distinguish between what is important and what is not important, and to know what to choose. -- Guang Zhong Pingyou

3. 不管数学的任一分支是多么抽象，总有一天会应用在这实际世界上。罗巴切夫斯基

3. No matter how abstract any branch of mathematics may be, it will eventually be applied in this real world. Lobachevsky

4. 无限！再也没有其他问题如此深刻地打动过人类的心灵。希尔伯特

4. Infinity! No other question has ever touched the human heart so deeply. Hilbert

5. 历史使人贤明，诗造成气质高雅的人，数学使人高尚，自然哲学使人深沉，道德使人稳重，而伦理学和修辞学则使人善于争论。培根

5. History makes men wise, poetry creates people of refined taste, mathematics elevates the soul, natural philosophy deepens the mind, morality makes people steady, and ethics and rhetoric make people adept at debate. - Bacon

6. 一个没有几分诗人气的数学家永远成不了一个完全的数学家。维尔斯特拉斯

6. A mathematician without a bit of poetism can never become a complete mathematician. - Weierstrass

7. 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

7. Another reason for the high respect given to mathematics is that it is precisely mathematics that provides an unassailable guarantee of reliability to the precise natural sciences; without mathematics, they could not achieve such a level of reliability. - Einstein

8. 纯数学这门科学在其现代发展阶段，可以说是人类精神之最具独创性的创造。怀特海

8. Pure mathematics, as a science in its modern stage of development, can be said to be the most original creation of the human spirit. According to Whitehead...

9. 一个人若不会运用别人更好的方法来保持自己的热情，怎么能成为哲学家 。——梭洛。

9. How can one become a philosopher if they do not know how to apply someone else's better methods to maintain their passion? - Thoreau.

10. 现代高能物理到了量子物理以后，有很多根本无法做实验，在家用纸笔来算，这跟数学家想样的差不了多远，所以说数学在物理上有着不可思议的力量。邱成桐

10. Since the advent of quantum physics in modern high-energy physics, there are many things that cannot be experimentally tested. We rely on paper and pencils at home to calculate, which is not too different from what mathematicians would do. Therefore, mathematics has an incredible power in physics. -- Qiu Chengtong

11. 数学家就像情人给一个数学家最小的原理，他就会从中引出你必须承认的结果，并且从这个又引出另外一个。弗坦内里

11. A mathematician, like a lover giving the smallest principle to a mathematician, will deduce from it the results that you must acknowledge, and then derive another from that. Fattaleni

12. 数学之所以有高声誉，另一个理由就是数学使得自然科学实现定理化，给予自然科学某种程度的可靠性。爱因斯坦

12. Another reason for the high reputation of mathematics is that mathematics enables the natural sciences to achieve theorematization, providing a certain degree of reliability to the natural sciences. - Einstein

13. 数学是人类知识活动留下来最具威力的知识工具，是一些现象的根源。数学是不变的，是客观存在的，上帝必以数学法则建造宇宙……笛卡儿

13. Mathematics is the most powerful knowledge tool left behind by human intellectual activities, the source of some phenomena. Mathematics is immutable and objectively exists; God must have constructed the universe according to mathematical laws …… Descartes

14. 数学之所以比一切其它科学受到尊重，一个理由是因为他的命题是绝对可靠和无可争辩的，而其它的科学经常处于被新发现的事实**的危险。爱因斯坦

14. One reason why mathematics is more respected than all other sciences is that its propositions are absolutely reliable and uncontestable, whereas the other sciences often face the danger of being overturned by new discoveries. - Einstein

15. 一个没有几分诗人才能的数学家决不会成为一个完全的数学家……魏尔斯特拉斯

15. A mathematician who lacks a bit of poetic talent will never become a complete mathematician …… Weierstrass

16. 给我最大快乐的，不是已懂得知识，而是不断的学习；不是已有的东西，而是不断的获取；不是已达到的高度，而是继续不断的攀登。高斯

16. What brings me the greatest joy is not the knowledge I have acquired, but the continuous learning; not what I already possess, but the constant acquisition; not the height I have reached, but the ongoing climb. Gauss

17. 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

17. To feel the beauty of mathematics, to sense the harmony between numbers and forms, to perceive the elegance of geometry, this is a true sense of beauty that all genuine mathematicians are acutely aware of. Poincaré

18. 发现每一个新的群体在形式上都是数学的，因为我们不可能有其他的指导。达尔文

18. "We find that every new group is formally mathematical, because we cannot have any other guidance." - Darwin

19. 在数学的天地里，重要的不是我们知道什么，而是我们怎么知道什么。毕达哥拉斯

19. In the realm of mathematics, what is important is not what we know, but how we know it. - Pythagoras

20. 立志于物理学的人，不懂下列的事情是不行的：第一是数学，第二是数学，第三是数学。伦琴

20. For those who aspire to physics, it is imperative to understand the following: first is mathematics, second is mathematics, and third is mathematics. - Röntgen

21. 数缺形时少直观，形缺数时难入微又说要打好数学基础有两个必经过程：先学习、接受由薄到厚；再消化、提炼由厚到薄。华罗庚

21. When numbers are lacking, direct intuition is reduced; when shapes are missing, it is difficult to delve into the minute details. He also says that to lay a solid foundation in mathematics, there are two indispensable processes: first, to learn and accept from thin to thick; then, to digest and refine from thick to thin. Hua Loo-keng

22. 一个没有几分诗人才能的数学家决不会成为一个完全的数学家。魏尔斯特拉斯纯粹数学，就其本质而言，是逻辑思想的诗篇。爱因斯坦

22. A mathematician who lacks a bit of poetical talent will never become a complete mathematician. Weierstrass' pure mathematics, in its essence, is a poem of logical thought. - Einstein

23. 一门科学，只有当它成功地运用数学时，才能达到真正完善的地步。马克思

23. A science can only reach a truly perfect state when it successfully applies mathematics. — Marx

24. 多数的数学创造是直觉的结果，对事实多少有点儿直接的知觉或快速的理解，而与任何冗长的或形式的推理过程无关。卢卡斯

24. The majority of mathematical creations are the result of intuition, a somewhat direct perception of facts, or a rapid understanding, and have nothing to do with any lengthy or formal process of reasoning. Lucas

25. 在数学的领域中，提出问题的艺术比解答问题的艺术更为重要。――康托尔

25. In the field of mathematics, the art of posing questions is more important than the art of solving them. - Cantor

26. 我曾听到有人说我是数学的反对者，是数学的敌人，但没有人比我更尊重数学，因为它完成了我不曾得到其成就的业绩。哥德

26. I have heard people say that I am an opponent of mathematics, an enemy of mathematics, but no one respects mathematics more than I do, for it has achieved what I never could. Goethe

27. 以我一生最好的时光追寻那个目标，书已经写成了。现代人读或后代读都无关紧要，也许要等一百年才有一个读者。开普勒

27. I have spent the best years of my life chasing that goal, and the book has been written. Whether modern people read it or future generations do is of no importance; perhaps it will take a hundred years before there is a reader. Kepler

28. 观察可能导致发现,观察将揭示某种规则模式或定律。——波利亚

28. Observation may lead to discovery; observation will reveal some rule pattern or law. - Polya

29. 非数学归纳法在数学的研究中，起着不可缺少的作用。舒尔（I·Schur）

29. Non-mathematical induction plays an indispensable role in the research of mathematics. (I. Schur)

30. 这是一个可靠的规律，当数学或哲学著作的作者以模糊深奥的话写作时，他是在胡说八道。怀德海

30. This is a reliable rule: when an author of mathematical or philosophical works writes in vague and obscure language, he is talking nonsense. — Whitehead

31. 当数学家导出方程式和公式，如同看到雕像美丽的风景，听到优美的曲调等等一样而得到充分的快乐。柯普宁

31. Just as mathematicians derive equations and formulas, they obtain great joy, just like they enjoy the beautiful scenery of statues, listen to melodious tunes, and so on. — Kropotkin

32. 数学方法渗透并支配着一切自然科学的理论分支。它愈来愈成为衡量科学成就的主要标志了。冯纽曼?>

32. Mathematical methods permeate and dominate all branches of theoretical natural sciences. They are increasingly becoming the main indicator of scientific achievements. Von Neumann?

33. 数学是知识的工具，亦是其它知识工具的泉源。所有研究顺序和度量的科学均和数学有关。――笛卡尔

33. Mathematics is a tool of knowledge, and also the source of other tools of knowledge. All sciences that deal with order and measurement are related to mathematics. - Descartes

34. 数学科学不可动摇的基石，促进人类事业进步的丰富源泉……巴罗

34. The unshakable foundation of mathematical science, a rich source promoting the progress of human endeavors... Barrow

35. 虽然不允许我们看透自然界本质的秘密，从而认识现象的真实原因，但仍可能发生这样的情形：一定的虚构假设足以解释许多现象 。——欧拉。

35. Although it is not allowed for us to penetrate the secrets of the essence of nature, thus understanding the true causes of phenomena, it is still possible that certain fictional assumptions are sufficient to explain many phenomena. — Euler.

36. 新的数学方法和概念，常常比解决数学问题本身更重要。——华罗庚

36. New mathematical methods and concepts are often more important than the mathematical problems themselves. — Hua Loo-keng

37. 在学习中要敢于做减法，就是减去前人已经解决的部分，看看还有那些问题没有解决，需要我们去探索解决……华罗庚

37. In learning, one should dare to do subtraction, that is, to subtract the parts that have already been solved by predecessors, and see what other problems remain unsolved and need to be explored and solved... Hua Loo-keng

38. 要利用时间，思考一下一天之中做了些什么，是“正号”还是“负号”，倘若是“+”，则进步。倘若是“-”，就得吸取教训，采取措施 。——季米特洛夫。

38. Make use of time to reflect on what you have done throughout the day; is it a "positive" or "negative"? If it is "+", then you are making progress. If it is "-", you need to draw lessons and take measures.—Dimitrov.

39. 一个做学问的人，除了学习知识外，还要有tast，这个词不太好翻译，有的译成品味，喜爱。一个人要有大的成就，就要有相当清楚的tast。杨振宁

39. A scholar, besides acquiring knowledge, must also possess a certain 'tast,' which is not easy to translate. Some translations include 'appreciation' and 'liking.' For a person to achieve great success, they must have a rather clear 'tast.' - Yang Zhenning

40. 人生的磨难是很多的，所以我们不可对于每一件轻微的伤害都过于敏感。在生活磨难面前，精神上的坚强和无动于衷是我们抵抗罪恶和人生意外的最好武器。——洛克

40. Life is full of hardships, so we should not be overly sensitive to every minor injury. In the face of life's hardships, spiritual strength and indifference are our best weapons against evil and the unexpected twists and turns of life. — Locke

41. 数学中的一些美丽定理具有这样的特性：它们极易从事实中归纳出来，但证明却隐藏的极深。数学是科学之王。高斯

41. Some beautiful theorems in mathematics have the characteristic that they are极易归纳 from facts, but their proofs are hidden very deeply. Mathematics is the king of sciences. Gauss

42. 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。苏利文确。

42. In reality, there is nothing as enduring and wonderful as mathematics, which has stood the test of time for thousands of years. Sullivan agrees.

43. 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

43. Mathematics science presents the most brilliant example to show that, without the help of experiments, pure reasoning can successfully expand the cognitive realm of human beings. Kant

44. 数学中的一些美丽定理具有这样的特性：它们极易从事实中归纳出来，但证明却隐藏的极深。高斯

44. Some beautiful theorems in mathematics have the characteristic that they are极易归纳出来 from facts, but their proofs are hidden very deeply. Gauss

45. 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，能够真正欣赏数学的人数是很少的。贝尔斯

45. We can expect that with the development of education and entertainment, more people will appreciate music and painting. However, the number of people who truly appreciate mathematics is very small. - Bells

46. 数统治着宇宙 。——毕达哥拉斯。

46. Numbers rule the universe. —— Pythagoras.

47. 整数的简单构成，若干世纪以来一直是使数学获得新生的源泉。伯克霍夫

47. The simple structure of integers has been a source of renewal for mathematics for several centuries. Burkhof

48. 我把数学看成是一件有意思的工作，而不是想为自己建立什么纪念碑。可以肯定地说，我对别人的工作比自己的更喜欢。我对自己的工作总是不满意。拉格朗日

48. I regard mathematics as an interesting endeavor, rather than something to build a monument for myself. It can be safely said that I prefer others' work to my own. I am always dissatisfied with my own work. — Lagrange

49. 数学对观察自然做出重要的贡献，它解释了规律结构中简单的原始元素，而天体就是用这些原始元素建立起来的。开普勒

49. Mathematics has made an important contribution to the observation of nature, explaining the simple primitive elements in the structure of regularities, which celestial bodies are constructed from. Kepler

50. 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

50. Pure mathematics can be actually useful, and applied mathematics can also be elegant and refined. - Halmos

51. 时间是个常数，但对勤奋者来说，是个‘变数’。用‘分’来计算时间的人比用‘小时’来计算时间的人时间多59倍……雷巴柯夫

51. Time is a constant, but to the diligent, it is a 'variable.' Those who calculate time in 'minutes' have 59 times more time than those who calculate time in 'hours'…… Rybakov

52. 我曾听到有人说我是数学的反对者，是数学的敌人，但没有人比我更尊重数学，因为它完成了我不曾得到其成就的业绩。――哥德

52. I have heard people say that I am an opponent of mathematics, an enemy of mathematics, but no one respects mathematics more than I do, for it has achieved what I have never been able to accomplish. -- Goethe

53. 非数学归纳法在数学的研究中，起着不可缺少的作用。

53. Non-mathematical induction plays an indispensable role in the research of mathematics.

54. 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

54. Mathematicians, like painters or poets, are creators of style... The style of a mathematician, like that of a painter or poet, must be beautiful... There is no permanent place for ugly mathematics in the world. Hardy

55. 一个国家只有数学蓬勃的发展，才能展现它国立的强大。数学的发展和至善和国家繁荣昌盛密切相关。拿破仑

55. Only with the vigorous development of mathematics can a country demonstrate its national strength. The development and perfection of mathematics are closely related to the prosperity and prosperity of the country. - Napoleon

56. 数学是人类的思考中最高的成就 。——米斯拉。

56. Mathematics is the highest achievement of human thought. – Mihajlo Idvorski Pupin.

57. 纯数学这门科学再其现代发展阶段，可以说是人类精神之最具独创性的创造。怀德海

57. Pure mathematics, in its modern development stage, can be said to be the most original creation of the human spirit. Whitehead

58. 几何无王者之道 。——欧几里得。

58. There is no king's road in geometry. - Euclid.

59. 事类相推，各有攸归，故枝条虽分而同本干知，发其一端而已。又所析理以辞，解体用图，庶亦约而能周，通而不黩，览之者思过半矣……刘徽

59. Similar things are interconnected, each having its own place. Therefore, although the branches are divided, they all share the same trunk, and we only need to explore one aspect of it. Furthermore, by analyzing principles through words and illustrating structures with diagrams, one can achieve a concise yet comprehensive understanding, and make it accessible without being tedious. Those who examine it will have thought through more than half of it... Liu Hui

60. 学习数学要多做习题，边做边思索。先知其然，然后知其所以然。苏步青

60. To learn mathematics, one should do more exercises and think while doing them. First, understand what it is, and then understand why it is so. -- Su Buqing

61. 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，能够真正欣赏数学的人数是很少的。——贝尔斯

61. We can expect that with the development of education and entertainment, more people will appreciate music and painting. However, the number of people who can truly appreciate mathematics is very small. —贝尔斯

62. 哲学家也要学数学，因为他必须跳出浩如烟海的万变现象而抓住真正的实质。……又因为这是使灵魂过渡到真理和永存的捷径。柏拉图

62. Philosophers also need to study mathematics, because they must rise above the myriad ever-changing phenomena to grasp the true essence... and because this is the shortcut for the soul to transition to truth and eternity. — Plato

63. 给我五个系数，我讲画出一头大象；给我六个系数，大象将会摇动尾巴。柯西

63. Give me five coefficients, and I can draw an elephant; give me six coefficients, and the elephant will wag its tail. Cauchy

64. 如果我继承可观的财产，我在数学上可能没有多少价值了。拉格朗日

64. If I inherit considerable wealth, I may have little value mathematically. Lagrange

65. 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

65. In reality, there is nothing as abundant as mathematics, which has been true and beautiful for thousands of years. Sullivan

66. 考虑了很少的那几样东西之后，整个的事情就归结为纯几何，这是物理和力学的一个目标……莱布尼茨

66. After considering only a few of the things, the whole matter boils down to pure geometry, which is a goal of physics and mechanics... Leibniz

67. 数无形时少直觉，形少数时难入微，数与形，本是相倚依，焉能分作两边飞。华罗庚

67. When there are few figures and no shape, intuition is lacking; when there are few shapes and little detail, it's hard to penetrate deeply. Numbers and shapes, after all, depend on each other, how can they be separated into two sides flying apart? — Hua Loo-keng

68. 在学习中要敢于做减法，就是减去前人已经解决的部分，看看还有那些问题没有解决，需要我们去探索解决。华罗庚

68. In learning, one should dare to perform subtraction, that is, to subtract the parts that have already been solved by predecessors, and see what other problems remain unsolved and require our exploration and resolution. — Hua Luogeng